http://keithcu.com/wiki/api.php?action=feedcontributions&user=Eagle9&feedformat=atomSpaceElevatorWiki.com - User contributions [en]2018-08-18T18:28:58ZUser contributionsMediaWiki 1.31.0http://keithcu.com/wiki/index.php?title=OpenSpace_6&diff=3705OpenSpace 62014-08-19T15:00:25Z<p>Eagle9: </p>
<hr />
<div>== '''Removing the space debris by means of vertical artificial air stream''' ==<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
<br />
The '''space debris''' is the objects in orbit around Earth created by humans that no longer serve any useful purpose. They consist of everything from entire spent rocket stages and defunct satellites to explosion fragments, paint flakes, dust and slag from solid rocket motors, and other small particles that are much more dangerous since it is more difficult to oversee them than large objects.<br />
<br />
<br />
Since the beginning of the Space Age in 1957 a great amount of satellites have been sent into space and this increasing number is/will be (especially in future) a great problem. According to some assessments the space debris belt will very soon make problems even for putting the satellites on the orbit around the Earth. As known, more and more countries are getting involved in space exploration and therefore number of objects (both active and “dead” satellites) in space will increase rapidly. The worst thing is that the satellites are colliding to each other and thus creating more and more little objects (their fragments) around the Earth that are much more difficult to deal with than with big objects. This effect is known as “Kessler Syndrome” <sup>1</sup> <sup>2</sup>. One of such collide occurred in 2009, 10 of February when the inactive satellite '''Kosmos-2251''' collided with active one '''Iridium 33''' above the northern Siberia with the speed of 42 120 km/h. This collision destroyed both satellites and gave birth to one more space debris cloud consisting of numerous little objects (there are at least one thousand objects in this cloud with the size of more than 10 cm) <sup>3</sup>. If this tendency continues, if the ''critical density'' where the creation of new debris occurs faster than the various natural forces that remove these objects from orbit in space is reached and overcome, apparently after several ten years there will be some dust belt around the Earth.<br />
<br />
<br />
As well-known the satellites placed on the Low Earth orbit are falling down on our planet due to atmosphere’s insignificant resistance. If we able to increase this resistance then the satellites (space debris in our case) will fall on the Earth down much sooner. How this can be done? Surely, we cannot raise the whole atmosphere upwards, but its little part can be actually raised. This can be achieved if we build a gigantic vertical tube that will enable us to pump the atmospheric air upwards, and then the satellites will go through such stream, lose their kinetic energy and eventually fall down.<br />
<br />
<br />
The air stream should be quite broad after leaving the tube and actually this will definitely be so because we know from Physics that the air generally tries to occupy all the space left to it. So, generally the narrow stream cannot be created and by the way this would be unacceptable since the narrow stream would cut the satellites into two pieces and we do not absolutely need this. It is much better if the “blunt” resistance will slow down the satellite. <br />
<br />
<br />
The speed of the air stream leaving the tube should be enough in order it to reach the several km altitudes (the vast majority of the space debris is located exactly there) and then to return to the Earth. Of course, under such situation the speed of the air stream should be less then Escape Velocity-11.2 km/sec. We should also point out that the stream returning back to the Earth will also work and slow the satellites down (However, it should be noted that this is correct only for those satellites the orbits of which has got 0° inclinations relative to the Earth's equator). Also, it is remarkable that the returning stream will be much broader since just after leaving the tube it will be widened due to satellites’ collision which will scatter stream’s molecules and air’s natural expansion as it was mentioned in the previous paragraph. <br />
<br />
<br />
We should note that the air stream will not return to the same place where it was released from on the Earth but it will return to the place located a bit westwards. The reason of it is following: the air stream in the tube is moving vertically upwards but after it leaves the tube the Earth will keep rotating around its axis and after some amount of time the air stream will hit other place located westwards on the Earth. Eventually, the path of this stream will resemble curve line. <br />
<br />
<br />
What should be the height of this tube? Of course, the higher the tube is the better it is. As we think its height should be approximately 100 km, exactly this altitude is considered to be the boundary of space. If the tube is lower, then the air stream released from the tube will be scattered in the atmosphere prematurely. <br />
<br />
[[Image: 11opt.gif]]<br />
<br />
''The satellite orbits the Earth'' <br />
<br />
[[Image: 22opt.gif]]<br />
<br />
''The satellite is slowed down in upward moving air stream''<br />
<br />
<br />
Surely, it will cost too much to move the necessary amount of air in this tube vertically. To solve this problem at least partly we should use the winds blowing in the Earth’s atmosphere, particularly the '''Trade winds'''.<br />
<br />
<br />
The trade winds are the prevailing pattern of easterly surface winds found in the tropics, within the lower portion of the Earth's atmosphere, in the lower section of the troposphere near the Earth's equator. The trade winds blow predominantly from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisphere, strengthening during the winter and when the Arctic oscillation is in its warm phase. Historically, the trade winds have been used by captains of sailing ships to cross the world's oceans for centuries, and enabled European empire expansion into the Americas and trade routes to become established across the Atlantic and Pacific oceans<sup>4</sup>.<br />
[[Image: Map prevailing winds on earth saitistvis.png]]<br />
<br />
So, all we need to do is to let these winds to enter the tube where they will move upwards due to these winds’ constant pressure. Of course, the special calculations are needed in order we to know if this pressure is enough to force the air stream cover several hundred km altitude (100 km in tube and plus several hundred kilometers that should be covered by the air stream after leaving the tube in outer space) or not. In any case such approach will enable us to solve this problem at least partly. <br />
<br />
[[Image: Pasatebi Saitistvis.png]]<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Kessler_syndrome<br />
<br />
2. http://webpages.charter.net/dkessler/files/KesSym.html<br />
<br />
3. http://www.space.com/news/090211-satellite-collision.html<br />
<br />
4. http://en.wikipedia.org/wiki/Trade_wind</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_6&diff=3704OpenSpace 62014-08-19T14:59:10Z<p>Eagle9: </p>
<hr />
<div>== '''Removing the space debris by means of vertical artificial air stream''' ==<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
<br />
The '''space debris''' is the objects in orbit around Earth created by humans that no longer serve any useful purpose. They consist of everything from entire spent rocket stages and defunct satellites to explosion fragments, paint flakes, dust and slag from solid rocket motors, and other small particles that are much more dangerous since it is more difficult to oversee them than large objects.<br />
<br />
<br />
Since the beginning of the Space Age in 1957 a great amount of satellites have been sent into space and this increasing number is/will be (especially in future) a great problem. According to some assessments the space debris belt will very soon make problems even for putting the satellites on the orbit around the Earth. As known, more and more countries are getting involved in space exploration and therefore number of objects (both active and “dead” satellites) in space will increase rapidly. The worst thing is that the satellites are colliding to each other and thus creating more and more little objects (their fragments) around the Earth that are much more difficult to deal with than with big objects. This effect is known as “Kessler Syndrome” <sup>1</sup> <sup>2</sup>. One of such collide occurred in 2009, 10 of February when the inactive satellite '''Kosmos-2251''' collided with active one '''Iridium 33''' above the northern Siberia with the speed of 42 120 km/h. This collision destroyed both satellites and gave birth to one more space debris cloud consisting of numerous little objects (there are at least one thousand objects in this cloud with the size of more than 10 cm) <sup>3</sup>. If this tendency continues, if the ''critical density'' where the creation of new debris occurs faster than the various natural forces that remove these objects from orbit in space is reached and overcome, apparently after several ten years there will be some dust belt around the Earth.<br />
<br />
<br />
As well-known the satellites placed on the Low Earth orbit are falling down on our planet due to atmosphere’s insignificant resistance. If we able to increase this resistance then the satellites (space debris in our case) will fall on the Earth down much sooner. How this can be done? Surely, we cannot raise the whole atmosphere upwards, but its little part can be actually raised. This can be achieved if we build a gigantic vertical tube that will enable us to pump the atmospheric air upwards, and then the satellites will go through such stream, lose their kinetic energy and eventually fall down.<br />
<br />
<br />
The air stream should be quite broad after leaving the tube and actually this will definitely be so because we know from Physics that the air generally tries to occupy all the space left to it. So, generally the narrow stream cannot be created and by the way this would be unacceptable since the narrow stream would cut the satellites into two pieces and we do not absolutely need this. It is much better if the “blunt” resistance will slow down the satellite. <br />
<br />
<br />
The speed of the air stream leaving the tube should be enough in order it to reach the several km altitudes (the vast majority of the space debris is located exactly there) and then to return to the Earth. Of course, under such situation the speed of the air stream should be less then Escape Velocity-11.2 km/sec. We should also point out that the stream returning back to the Earth will also work and slow the satellites down (However, it should be noted that this is correct only for those satellites the orbits of which has got 0° inclinations). Also, it is remarkable that the returning stream will be much broader since just after leaving the tube it will be widened due to satellites’ collision which will scatter stream’s molecules and air’s natural expansion as it was mentioned in the previous paragraph. <br />
<br />
<br />
We should note that the air stream will not return to the same place where it was released from on the Earth but it will return to the place located a bit westwards. The reason of it is following: the air stream in the tube is moving vertically upwards but after it leaves the tube the Earth will keep rotating around its axis and after some amount of time the air stream will hit other place located westwards on the Earth. Eventually, the path of this stream will resemble curve line. <br />
<br />
<br />
What should be the height of this tube? Of course, the higher the tube is the better it is. As we think its height should be approximately 100 km, exactly this altitude is considered to be the boundary of space. If the tube is lower, then the air stream released from the tube will be scattered in the atmosphere prematurely. <br />
<br />
[[Image: 11opt.gif]]<br />
<br />
''The satellite orbits the Earth'' <br />
<br />
[[Image: 22opt.gif]]<br />
<br />
''The satellite is slowed down in upward moving air stream''<br />
<br />
<br />
Surely, it will cost too much to move the necessary amount of air in this tube vertically. To solve this problem at least partly we should use the winds blowing in the Earth’s atmosphere, particularly the '''Trade winds'''.<br />
<br />
<br />
The trade winds are the prevailing pattern of easterly surface winds found in the tropics, within the lower portion of the Earth's atmosphere, in the lower section of the troposphere near the Earth's equator. The trade winds blow predominantly from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisphere, strengthening during the winter and when the Arctic oscillation is in its warm phase. Historically, the trade winds have been used by captains of sailing ships to cross the world's oceans for centuries, and enabled European empire expansion into the Americas and trade routes to become established across the Atlantic and Pacific oceans<sup>4</sup>.<br />
[[Image: Map prevailing winds on earth saitistvis.png]]<br />
<br />
So, all we need to do is to let these winds to enter the tube where they will move upwards due to these winds’ constant pressure. Of course, the special calculations are needed in order we to know if this pressure is enough to force the air stream cover several hundred km altitude (100 km in tube and plus several hundred kilometers that should be covered by the air stream after leaving the tube in outer space) or not. In any case such approach will enable us to solve this problem at least partly. <br />
<br />
[[Image: Pasatebi Saitistvis.png]]<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Kessler_syndrome<br />
<br />
2. http://webpages.charter.net/dkessler/files/KesSym.html<br />
<br />
3. http://www.space.com/news/090211-satellite-collision.html<br />
<br />
4. http://en.wikipedia.org/wiki/Trade_wind</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_6&diff=3703OpenSpace 62014-08-19T14:57:51Z<p>Eagle9: </p>
<hr />
<div>== '''Removing the space debris by means of vertical artificial air stream''' ==<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
<br />
The '''space debris''' is the objects in orbit around Earth created by humans that no longer serve any useful purpose. They consist of everything from entire spent rocket stages and defunct satellites to explosion fragments, paint flakes, dust and slag from solid rocket motors, and other small particles that are much more dangerous since it is more difficult to oversee them than large objects.<br />
<br />
<br />
Since the beginning of the Space Age in 1957 a great amount of satellites have been sent into space and this increasing number is/will be (especially in future) a great problem. According to some assessments the space debris belt will very soon make problems even for putting the satellites on the orbit around the Earth. As known, more and more countries are getting involved in space exploration and therefore number of objects (both active and “dead” satellites) in space will increase rapidly. The worst thing is that the satellites are colliding to each other and thus creating more and more little objects (their fragments) around the Earth that are much more difficult to deal with than with big objects. This effect is known as “Kessler Syndrome” <sup>1</sup> <sup>2</sup>. One of such collide occurred in 2009, 10 of February when the inactive satellite '''Kosmos-2251''' collided with active one '''Iridium 33''' above the northern Siberia with the speed of 42 120 km/h. This collision destroyed both satellites and gave birth to one more space debris cloud consisting of numerous little objects (there are at least one thousand objects in this cloud with the size of more than 10 cm) <sup>3</sup>. If this tendency continues, if the ''critical density'' where the creation of new debris occurs faster than the various natural forces that remove these objects from orbit in space is reached and overcome, apparently after several ten years there will be some dust belt around the Earth.<br />
<br />
<br />
As well-known the satellites placed on the Low Earth orbit are falling down on our planet due to atmosphere’s insignificant resistance. If we able to increase this resistance then the satellites (space debris in our case) will fall on the Earth down much sooner. How this can be done? Surely, we cannot raise the whole atmosphere upwards, but its little part can be actually raised. This can be achieved if we build a gigantic vertical tube that will enable us to pump the atmospheric air upwards, and then the satellites will go through such stream, lose their kinetic energy and eventually fall down.<br />
<br />
<br />
The air stream should be quite broad after leaving the tube and actually this will definitely be so because we know from Physics that the air generally tries to occupy all the space left to it. So, generally the narrow stream cannot be created and by the way this would be unacceptable since the narrow stream would cut the satellites into two pieces and we do not absolutely need this. It is much better if the “blunt” resistance will slow down the satellite. <br />
<br />
<br />
The speed of the air stream leaving the tube should be enough in order it to reach the several km altitudes (the vast majority of the space debris is located exactly there) and then to return to the Earth. Of course, under such situation the speed of the air stream should be less then Escape Velocity-11.2 km/sec. We should also point out that the stream returning back to the Earth will also work and slow the satellites down (However, it should be noted that this is correct only for those satellites the orbits of which has got 0° inclinations). Also, it is remarkable that the returning stream will be much broader since just after leaving the tube it will be widened due to satellites’ collision which will scatter stream’s molecules and air’s natural expansion as it was mentioned in the previous paragraph. <br />
<br />
<br />
We should note that the air stream will not return to the same place where it was released from on the Earth but it will return to the place located a bit westwards. The reason of it is following: the air stream in the tube is moving vertically upwards but after it leaves the tube the Earth will keep rotating around its axis and after some amount of time the air stream will hit other place located westwards on the Earth. Eventually, the path of this stream will resemble curve line. <br />
<br />
<br />
What should be the height of this tube? Of course, the higher the tube is the better it is. As we think its height should be approximately 100 km, exactly this altitude is considered to be the boundary of space. If the tube is lower, then the air stream released from the tube will be scattered in the atmosphere prematurely. <br />
[[Image: 11opt.gif]]<br />
<br />
''The satellite orbits the Earth'' <br />
<br />
[[Image: 22opt.gif]]<br />
<br />
''The satellite is slowed down in upward moving air stream''<br />
<br />
<br />
Surely, it will cost too much to move the necessary amount of air in this tube vertically. To solve this problem at least partly we should use the winds blowing in the Earth’s atmosphere, particularly the '''Trade winds'''.<br />
<br />
<br />
The trade winds are the prevailing pattern of easterly surface winds found in the tropics, within the lower portion of the Earth's atmosphere, in the lower section of the troposphere near the Earth's equator. The trade winds blow predominantly from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisphere, strengthening during the winter and when the Arctic oscillation is in its warm phase. Historically, the trade winds have been used by captains of sailing ships to cross the world's oceans for centuries, and enabled European empire expansion into the Americas and trade routes to become established across the Atlantic and Pacific oceans<sup>4</sup>.<br />
[[Image: Map prevailing winds on earth saitistvis.png]]<br />
<br />
So, all we need to do is to let these winds to enter the tube where they will move upwards due to these winds’ constant pressure. Of course, the special calculations are needed in order we to know if this pressure is enough to force the air stream cover several hundred km altitude (100 km in tube and plus several hundred kilometers that should be covered by the air stream after leaving the tube in outer space) or not. In any case such approach will enable us to solve this problem at least partly. <br />
<br />
[[Image: Pasatebi Saitistvis.png]]<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Kessler_syndrome<br />
<br />
2. http://webpages.charter.net/dkessler/files/KesSym.html<br />
<br />
3. http://www.space.com/news/090211-satellite-collision.html<br />
<br />
4. http://en.wikipedia.org/wiki/Trade_wind</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_6&diff=3702OpenSpace 62014-08-18T17:36:38Z<p>Eagle9: </p>
<hr />
<div>== '''Removing the space debris by means of vertical artificial air stream''' ==<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
<br />
The '''space debris''' is the objects in orbit around Earth created by humans that no longer serve any useful purpose. They consist of everything from entire spent rocket stages and defunct satellites to explosion fragments, paint flakes, dust and slag from solid rocket motors, and other small particles that are much more dangerous since it is more difficult to oversee them than large objects.<br />
<br />
<br />
Since the beginning of the Space Age in 1957 a great amount of satellites have been sent into space and this increasing number is/will be (especially in future) a great problem. According to some assessments the space debris belt will very soon make problems even for putting the satellites on the orbit around the Earth. As known, more and more countries are getting involved in space exploration and therefore number of objects (both active and “dead” satellites) in space will increase rapidly. The worst thing is that the satellites are colliding to each other and thus creating more and more little objects (their fragments) around the Earth that are much more difficult to deal with than with big objects. This effect is known as “Kessler Syndrome” <sup>1</sup> <sup>2</sup>. One of such collide occurred in 2009, 10 of February when the inactive satellite '''Kosmos-2251''' collided with active one '''Iridium 33''' above the northern Siberia with the speed of 42 120 km/h. This collision destroyed both satellites and gave birth to one more space debris cloud consisting of numerous little objects (there are at least one thousand objects in this cloud with the size of more than 10 cm) <sup>3</sup>. If this tendency continues, if the ''critical density'' where the creation of new debris occurs faster than the various natural forces that remove these objects from orbit in space is reached and overcome, apparently after several ten years there will be some dust belt around the Earth.<br />
<br />
<br />
As well-known the satellites placed on the Low Earth orbit are falling down on our planet due to atmosphere’s insignificant resistance. If we able to increase this resistance then the satellites (space debris in our case) will fall on the Earth down much sooner. How this can be done? Surely, we cannot raise the whole atmosphere upwards, but its little part can be actually raised. This can be achieved if we build a gigantic vertical tube that will enable us to pump the atmospheric air upwards, and then the satellites will go through such stream, lose their kinetic energy and eventually fall down.<br />
<br />
<br />
The air stream should be quite broad after leaving the tube and actually this will definitely be so because we know from Physics that the air generally tries to occupy all the space left to it. So, generally the narrow stream cannot be created and by the way this would be unacceptable since the narrow stream would cut the satellites into two pieces and we do not absolutely need this. It is much better if the “blunt” resistance will slow down the satellite. <br />
<br />
<br />
The speed of the air stream leaving the tube should be enough in order it to reach the several km altitudes (the vast majority of the space debris is located exactly there) and then to return to the Earth. Of course, under such situation the speed of the air stream should be less then Escape Velocity-11.2 km/sec. We should also point out that the stream returning back to the Earth will also work and slow the satellites down. Also, it is remarkable that the returning stream will be much broader since just after leaving the tube it will be widened due to satellites’ collision which will scatter stream’s molecules and air’s natural expansion as it was mentioned in the previous paragraph. <br />
<br />
<br />
We should note that the air stream will not return to the same place where it was released from on the Earth but it will return to the place located a bit westwards. The reason of it is following: the air stream in the tube is moving vertically upwards but after it leaves the tube the Earth will keep rotating around its axis and after some amount of time the air stream will hit other place located westwards on the Earth. Eventually, the path of this stream will resemble curve line. <br />
<br />
<br />
What should be the height of this tube? Of course, the higher the tube is the better it is. As we think its height should be approximately 100 km, exactly this altitude is considered to be the boundary of space. If the tube is lower, then the air stream released from the tube will be scattered in the atmosphere prematurely. <br />
[[Image: 11opt.gif]]<br />
<br />
''The satellite orbits the Earth'' <br />
<br />
[[Image: 22opt.gif]]<br />
<br />
''The satellite is slowed down in upward moving air stream''<br />
<br />
<br />
Surely, it will cost too much to move the necessary amount of air in this tube vertically. To solve this problem at least partly we should use the winds blowing in the Earth’s atmosphere, particularly the '''Trade winds'''.<br />
<br />
<br />
The trade winds are the prevailing pattern of easterly surface winds found in the tropics, within the lower portion of the Earth's atmosphere, in the lower section of the troposphere near the Earth's equator. The trade winds blow predominantly from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisphere, strengthening during the winter and when the Arctic oscillation is in its warm phase. Historically, the trade winds have been used by captains of sailing ships to cross the world's oceans for centuries, and enabled European empire expansion into the Americas and trade routes to become established across the Atlantic and Pacific oceans<sup>4</sup>.<br />
[[Image: Map prevailing winds on earth saitistvis.png]]<br />
<br />
So, all we need to do is to let these winds to enter the tube where they will move upwards due to these winds’ constant pressure. Of course, the special calculations are needed in order we to know if this pressure is enough to force the air stream cover several hundred km altitude (100 km in tube and plus several hundred kilometers that should be covered by the air stream after leaving the tube in outer space) or not. In any case such approach will enable us to solve this problem at least partly. <br />
<br />
[[Image: Pasatebi Saitistvis.png]]<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Kessler_syndrome<br />
<br />
2. http://webpages.charter.net/dkessler/files/KesSym.html<br />
<br />
3. http://www.space.com/news/090211-satellite-collision.html<br />
<br />
4. http://en.wikipedia.org/wiki/Trade_wind</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace&diff=3701OpenSpace2014-08-18T17:25:09Z<p>Eagle9: </p>
<hr />
<div><div style="float:right; border:#CCCCCC solid 1px; background-color: #F7F7F7"><br />
<table cellspacing=0 cellpadding=0 width=550><br />
<br />
<tr><td colspan="3" align="center" style="background-color:#CCCCCC"><b>Title:</b> Open Work Space</td></tr><br />
<br />
<tr><br />
<td align="center" valign="middle" height=125 width=100 style='padding:10px'><br />
<div style="background-color:#CCCCFF; height:110px; width:90px"><br />
[Cover Img]<br />
</div><br />
</td><br />
<br />
<td align="left" valign="top"><br />
<div><br />
<b>About:</b><br /><br />
* Moderator: [[OpenSpace#edwards|Brad Edwards]]<br /><br />
</div><br />
</td><br />
<br />
<td align="left" valign="top"><br />
<div><br />
'''[[Article Tags|Tags]]''':<br /><br />
* This is open space for development<br />
</div><br />
</td><br />
</tr><br />
<br />
</table></div><br />
== Open Work Space ==<br />
<br />
Below are links to pages that are open for collaborative space elevator development work. Feel free to use. <br />
<br />
#To begin select a link that says "Open for Use". You will be directed to a template page that you can then edit. <br />
#Enter your basic information including name, e-mail and basic focus of development you want to pursue on this page.<br />
#Begin work.<br />
#Return to this page before you leave and modify the Title of the link to something appropriate to signify that the page in in use and fill in the other basic information.<br />
<br />
<center> '''Do not modify other people's pages without their permission.'''</center><br />
<br />
That is most of it. If you have questions please feel free to contact the [[user:edwards | Wiki administrators]]<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_1|Title:Economics:]] '''<br />
|width="450pt"|<br />
*Lead: Ed Gray<br />
*E-mail: ed_gray@sbcglobal.net<br />
*Focus: Discussion area for the Economics Team. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_2|Title:Companies involved in SE development:]] '''<br />
|width="450pt"|<br />
*Lead: Christopher J Petrella<br />
*E-mail: cpetrella@revengesoft.com<br />
*Focus: information about the companies that are developing technology for the Space Elevator. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_3|SPACE ELEVATOR VERSUS SPACE DEBRIS]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: The new method for eliminating the space debris at Low Earth Orbit (LEO) and Geostationary Orbit (GEO) is presented here. The paper shows how the Space Elevator can be used in struggling against the space debris that would be possible by means of deploying the huge metallic petals onboard the Space Elevator’s cabin moving along the cable. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_4|JUMP FROM SPACE]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: The paper JUMP FROM SPACE describes how it is possible to expand the facilities of one of the most excellent kind of sport-parachuting and descend from boundary to space-100 km altitude. This can be done by means of the Space Elevator. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_5| Space Catapult]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: A long rod with the assist of Space Elevator can be used for deep space missions. This method we called Space Catapult. <br />
|}<br />
<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_6|Removing the space debris by means of vertical artificial air stream]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: An upward moving air stream may actually enable us to remove the space debris placed on the Low Earth orbit. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_7|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_8|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_9|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_10|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_6&diff=3700OpenSpace 62014-08-18T17:24:37Z<p>Eagle9: </p>
<hr />
<div>== '''Removing the space debris by means of vertical artificial air stream''' ==<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
<br />
The '''space debris''' is the objects in orbit around Earth created by humans that no longer serve any useful purpose. They consist of everything from entire spent rocket stages and defunct satellites to explosion fragments, paint flakes, dust and slag from solid rocket motors, and other small particles that are much more dangerous since it is more difficult to oversee them than large objects.<br />
<br />
<br />
Since the beginning of the Space Age in 1957 a great amount of satellites have been sent into space and this increasing number is/will be (especially in future) a great problem. According to some assessments the space debris belt will very soon make problems even for putting the satellites on the orbit around the Earth. As known, more and more countries are getting involved in space exploration and therefore number of objects (both active and “dead” satellites) in space will increase rapidly. The worst thing is that the satellites are colliding to each other and thus creating more and more little objects (their fragments) around the Earth that are much more difficult to deal with than with big objects. This effect is known as “Kessler Syndrome” <sup>1</sup> <sup>2</sup>. One of such collide occurred in 2009, 10 of February when the inactive satellite '''Kosmos-2251''' collided with active one '''Iridium 33''' above the northern Siberia with the speed of 42 120 km/h. This collision destroyed both satellites and gave birth to one more space debris cloud consisting of numerous little objects (there are at least one thousand objects in this cloud with the size of more than 10 cm) <sup>3</sup>. If this tendency continues, if the ''critical density'' where the creation of new debris occurs faster than the various natural forces that remove these objects from orbit in space is reached and overcome, apparently after several ten years there will be some dust belt around the Earth.<br />
<br />
<br />
As well-known the satellites placed on the Low Earth orbit are falling down on our planet due to atmosphere’s insignificant resistance. If we able to increase this resistance then the satellites (space debris in our case) will fall on the Earth down much sooner. How this can be done? Surely, we cannot raise the whole atmosphere upwards, but its little part can be actually raised. This can be achieved if we build a gigantic vertical tube that will enable us to pump the atmospheric air upwards, and then the satellites will go through such stream, lose their kinetic energy and eventually fall down.<br />
<br />
<br />
The air stream should be quite broad after leaving the tube and actually this will definitely be so because we know from Physics that the air generally tries to occupy all the space left to it. So, generally the narrow stream cannot be created and by the way this would be unacceptable since the narrow stream would cut the satellites into two pieces and we do not absolutely need this. It is much better if the “blunt” resistance will slow down the satellite. <br />
<br />
<br />
The speed of the air stream leaving the tube should be enough in order it to reach the several km altitudes (the vast majority of the space debris is located exactly there) and then to return to the Earth. Of course, under such situation the speed of the air stream should be less then Escape Velocity-11.2 km/sec. We should also point out that the stream returning back to the Earth will also work and slow the satellites down. Also, it is remarkable that the returning stream will be much broader since just after leaving the tube it will be widened due to satellites’ collision which will scatter stream’s molecules and air’s natural expansion as it was mentioned in the previous paragraph. <br />
<br />
<br />
We should note that the air stream will not return to the same place where it was released from on the Earth but it will return to the place located a bit westwards. The reason of it is following: the air stream in the tube is moving vertically upwards but after it leaves the tube the Earth will keep rotating around its axis and after some amount of time the air stream will hit other place located westwards on the Earth. Eventually, the path of this stream will resemble curve line. <br />
<br />
<br />
What should be the height of this tube? Of course, the higher the tube is the better it is. As we think its height should be approximately 100 km, exactly this altitude is considered to be the boundary of space. If the tube is lower, then the air stream released from the tube will be scattered in the atmosphere prematurely. <br />
[[Image: 11opt.gif]]<br />
<br />
''The satellite orbits the Earth'' <br />
<br />
[[Image: 22opt.gif]]<br />
<br />
''The satellite is sowed down in upward moving air stream''<br />
<br />
<br />
Surely, it will cost too much to move the necessary amount of air in this tube vertically. To solve this problem at least partly we should use the winds blowing in the Earth’s atmosphere, particularly the '''Trade winds'''.<br />
<br />
<br />
The trade winds are the prevailing pattern of easterly surface winds found in the tropics, within the lower portion of the Earth's atmosphere, in the lower section of the troposphere near the Earth's equator. The trade winds blow predominantly from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisphere, strengthening during the winter and when the Arctic oscillation is in its warm phase. Historically, the trade winds have been used by captains of sailing ships to cross the world's oceans for centuries, and enabled European empire expansion into the Americas and trade routes to become established across the Atlantic and Pacific oceans<sup>4</sup>.<br />
[[Image: Map prevailing winds on earth saitistvis.png]]<br />
<br />
So, all we need to do is to let these winds to enter the tube where they will move upwards due to these winds’ constant pressure. Of course, the special calculations are needed in order we to know if this pressure is enough to force the air stream cover several hundred km altitude (100 km in tube and plus several hundred kilometers that should be covered by the air stream after leaving the tube in outer space) or not. In any case such approach will enable us to solve this problem at least partly. <br />
<br />
[[Image: Pasatebi Saitistvis.png]]<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Kessler_syndrome<br />
<br />
2. http://webpages.charter.net/dkessler/files/KesSym.html<br />
<br />
3. http://www.space.com/news/090211-satellite-collision.html<br />
<br />
4. http://en.wikipedia.org/wiki/Trade_wind</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_6&diff=3699OpenSpace 62014-08-18T17:22:20Z<p>Eagle9: </p>
<hr />
<div>== '''Removing the space debris by means of artificial air stream''' ==<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
<br />
The '''space debris''' is the objects in orbit around Earth created by humans that no longer serve any useful purpose. They consist of everything from entire spent rocket stages and defunct satellites to explosion fragments, paint flakes, dust and slag from solid rocket motors, and other small particles that are much more dangerous since it is more difficult to oversee them than large objects.<br />
<br />
<br />
Since the beginning of the Space Age in 1957 a great amount of satellites have been sent into space and this increasing number is/will be (especially in future) a great problem. According to some assessments the space debris belt will very soon make problems even for putting the satellites on the orbit around the Earth. As known, more and more countries are getting involved in space exploration and therefore number of objects (both active and “dead” satellites) in space will increase rapidly. The worst thing is that the satellites are colliding to each other and thus creating more and more little objects (their fragments) around the Earth that are much more difficult to deal with than with big objects. This effect is known as “Kessler Syndrome” <sup>1</sup> <sup>2</sup>. One of such collide occurred in 2009, 10 of February when the inactive satellite '''Kosmos-2251''' collided with active one '''Iridium 33''' above the northern Siberia with the speed of 42 120 km/h. This collision destroyed both satellites and gave birth to one more space debris cloud consisting of numerous little objects (there are at least one thousand objects in this cloud with the size of more than 10 cm) <sup>3</sup>. If this tendency continues, if the ''critical density'' where the creation of new debris occurs faster than the various natural forces that remove these objects from orbit in space is reached and overcome, apparently after several ten years there will be some dust belt around the Earth.<br />
<br />
<br />
As well-known the satellites placed on the Low Earth orbit are falling down on our planet due to atmosphere’s insignificant resistance. If we able to increase this resistance then the satellites (space debris in our case) will fall on the Earth down much sooner. How this can be done? Surely, we cannot raise the whole atmosphere upwards, but its little part can be actually raised. This can be achieved if we build a gigantic vertical tube that will enable us to pump the atmospheric air upwards, and then the satellites will go through such stream, lose their kinetic energy and eventually fall down.<br />
<br />
<br />
The air stream should be quite broad after leaving the tube and actually this will definitely be so because we know from Physics that the air generally tries to occupy all the space left to it. So, generally the narrow stream cannot be created and by the way this would be unacceptable since the narrow stream would cut the satellites into two pieces and we do not absolutely need this. It is much better if the “blunt” resistance will slow down the satellite. <br />
<br />
<br />
The speed of the air stream leaving the tube should be enough in order it to reach the several km altitudes (the vast majority of the space debris is located exactly there) and then to return to the Earth. Of course, under such situation the speed of the air stream should be less then Escape Velocity-11.2 km/sec. We should also point out that the stream returning back to the Earth will also work and slow the satellites down. Also, it is remarkable that the returning stream will be much broader since just after leaving the tube it will be widened due to satellites’ collision which will scatter stream’s molecules and air’s natural expansion as it was mentioned in the previous paragraph. <br />
<br />
<br />
We should note that the air stream will not return to the same place where it was released from on the Earth but it will return to the place located a bit westwards. The reason of it is following: the air stream in the tube is moving vertically upwards but after it leaves the tube the Earth will keep rotating around its axis and after some amount of time the air stream will hit other place located westwards on the Earth. Eventually, the path of this stream will resemble curve line. <br />
<br />
<br />
What should be the height of this tube? Of course, the higher the tube is the better it is. As we think its height should be approximately 100 km, exactly this altitude is considered to be the boundary of space. If the tube is lower, then the air stream released from the tube will be scattered in the atmosphere prematurely. <br />
[[Image: 11opt.gif]]<br />
<br />
''The satellite orbits the Earth'' <br />
<br />
[[Image: 22opt.gif]]<br />
<br />
''The satellite is sowed down in upward moving air stream''<br />
<br />
<br />
Surely, it will cost too much to move the necessary amount of air in this tube vertically. To solve this problem at least partly we should use the winds blowing in the Earth’s atmosphere, particularly the '''Trade winds'''.<br />
<br />
<br />
The trade winds are the prevailing pattern of easterly surface winds found in the tropics, within the lower portion of the Earth's atmosphere, in the lower section of the troposphere near the Earth's equator. The trade winds blow predominantly from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisphere, strengthening during the winter and when the Arctic oscillation is in its warm phase. Historically, the trade winds have been used by captains of sailing ships to cross the world's oceans for centuries, and enabled European empire expansion into the Americas and trade routes to become established across the Atlantic and Pacific oceans<sup>4</sup>.<br />
[[Image: Map prevailing winds on earth saitistvis.png]]<br />
<br />
So, all we need to do is to let these winds to enter the tube where they will move upwards due to these winds’ constant pressure. Of course, the special calculations are needed in order we to know if this pressure is enough to force the air stream cover several hundred km altitude (100 km in tube and plus several hundred kilometers that should be covered by the air stream after leaving the tube in outer space) or not. In any case such approach will enable us to solve this problem at least partly. <br />
<br />
[[Image: Pasatebi Saitistvis.png]]<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Kessler_syndrome<br />
<br />
2. http://webpages.charter.net/dkessler/files/KesSym.html<br />
<br />
3. http://www.space.com/news/090211-satellite-collision.html<br />
<br />
4. http://en.wikipedia.org/wiki/Trade_wind</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace&diff=3698OpenSpace2014-08-18T17:21:25Z<p>Eagle9: </p>
<hr />
<div><div style="float:right; border:#CCCCCC solid 1px; background-color: #F7F7F7"><br />
<table cellspacing=0 cellpadding=0 width=550><br />
<br />
<tr><td colspan="3" align="center" style="background-color:#CCCCCC"><b>Title:</b> Open Work Space</td></tr><br />
<br />
<tr><br />
<td align="center" valign="middle" height=125 width=100 style='padding:10px'><br />
<div style="background-color:#CCCCFF; height:110px; width:90px"><br />
[Cover Img]<br />
</div><br />
</td><br />
<br />
<td align="left" valign="top"><br />
<div><br />
<b>About:</b><br /><br />
* Moderator: [[OpenSpace#edwards|Brad Edwards]]<br /><br />
</div><br />
</td><br />
<br />
<td align="left" valign="top"><br />
<div><br />
'''[[Article Tags|Tags]]''':<br /><br />
* This is open space for development<br />
</div><br />
</td><br />
</tr><br />
<br />
</table></div><br />
== Open Work Space ==<br />
<br />
Below are links to pages that are open for collaborative space elevator development work. Feel free to use. <br />
<br />
#To begin select a link that says "Open for Use". You will be directed to a template page that you can then edit. <br />
#Enter your basic information including name, e-mail and basic focus of development you want to pursue on this page.<br />
#Begin work.<br />
#Return to this page before you leave and modify the Title of the link to something appropriate to signify that the page in in use and fill in the other basic information.<br />
<br />
<center> '''Do not modify other people's pages without their permission.'''</center><br />
<br />
That is most of it. If you have questions please feel free to contact the [[user:edwards | Wiki administrators]]<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_1|Title:Economics:]] '''<br />
|width="450pt"|<br />
*Lead: Ed Gray<br />
*E-mail: ed_gray@sbcglobal.net<br />
*Focus: Discussion area for the Economics Team. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_2|Title:Companies involved in SE development:]] '''<br />
|width="450pt"|<br />
*Lead: Christopher J Petrella<br />
*E-mail: cpetrella@revengesoft.com<br />
*Focus: information about the companies that are developing technology for the Space Elevator. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_3|SPACE ELEVATOR VERSUS SPACE DEBRIS]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: The new method for eliminating the space debris at Low Earth Orbit (LEO) and Geostationary Orbit (GEO) is presented here. The paper shows how the Space Elevator can be used in struggling against the space debris that would be possible by means of deploying the huge metallic petals onboard the Space Elevator’s cabin moving along the cable. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_4|JUMP FROM SPACE]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: The paper JUMP FROM SPACE describes how it is possible to expand the facilities of one of the most excellent kind of sport-parachuting and descend from boundary to space-100 km altitude. This can be done by means of the Space Elevator. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_5| Space Catapult]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: A long rod with the assist of Space Elevator can be used for deep space missions. This method we called Space Catapult. <br />
|}<br />
<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_6|Removing the space debris by means of artificial air stream]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: An upward moving air stream may actually enable us to remove the space debris placed on the Low Earth orbit. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_7|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_8|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_9|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_10|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_6&diff=3697OpenSpace 62014-08-18T17:19:16Z<p>Eagle9: </p>
<hr />
<div>== '''Removing the space debris by means of artificial air stream''' ==<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
<br />
The '''space debris''' is the objects in orbit around Earth created by humans that no longer serve any useful purpose. They consist of everything from entire spent rocket stages and defunct satellites to explosion fragments, paint flakes, dust and slag from solid rocket motors, and other small particles that are much more dangerous since it is more difficult to oversee them than large objects.<br />
<br />
<br />
Since the beginning of the Space Age in 1957 a great amount of satellites have been sent into space and this increasing number is/will be (especially in future) a great problem. According to some assessments the space debris belt will very soon make problems even for putting the satellites on the orbit around the Earth. As known, more and more countries are getting involved in space exploration and therefore number of objects (both active and “dead” satellites) in space will increase rapidly. The worst thing is that the satellites are colliding to each other and thus creating more and more little objects (their fragments) around the Earth that are much more difficult to deal with than with big objects. This effect is known as “Kessler Syndrome” <sup>1</sup> <sup>2</sup>. One of such collide occurred in 2009, 10 of February when the inactive satellite '''Kosmos-2251''' collided with active one '''Iridium 33''' above the northern Siberia with the speed of 42 120 km/h. This collision destroyed both satellites and gave birth to one more space debris cloud consisting of numerous little objects (there are at least one thousand objects in this cloud with the size of more than 10 cm) <sup>3</sup>. If this tendency continues, if the ''critical density'' where the creation of new debris occurs faster than the various natural forces that remove these objects from orbit in space is reached and overcome, apparently after several ten years there will be some dust belt around the Earth.<br />
<br />
<br />
As well-known the satellites placed on the Low Earth orbit are falling down on our planet due to atmosphere’s insignificant resistance. If we able to increase this resistance then the satellites (space debris in our case) will fall on the Earth down much sooner. How this can be done? Surely, we cannot raise the whole atmosphere upwards, but its little part can be actually raised. This can be achieved if we build a gigantic vertical tube that will enable us to pump the atmospheric air upwards, and then the satellites will go through such stream, lose their kinetic energy and eventually fall down.<br />
<br />
<br />
The air stream should be quite broad after leaving the tube and actually this will definitely be so because we know from Physics that the air generally tries to occupy all the space left to it. So, generally the narrow stream cannot be created and by the way this would be unacceptable since the narrow stream would cut the satellites into two pieces and we do not absolutely need this. It is much better if the “blunt” resistance will slow down the satellite. <br />
<br />
<br />
The speed of the air stream leaving the tube should be enough in order it to reach the several km altitudes (the vast majority of the space debris is located exactly there) and then to return to the Earth. Of course, under such situation the speed of the air stream should be less then Escape Velocity-11.2 km/sec. We should also point out that the stream returning back to the Earth will also work and slow the satellites down. Also, it is remarkable that the returning stream will be much broader since just after leaving the tube it will be widened due to satellites’ collision which will scatter stream’s molecules and air’s natural expansion as it was mentioned in the previous paragraph. <br />
<br />
<br />
We should note that the air stream will not return to the same place where it was released from on the Earth but it will return to the place located a bit westwards. The reason of it is following: the air stream in the tube is moving vertically upwards but after it leaves the tube the Earth will keep rotating around its axis and after some amount of time the air stream will hit other place located westwards on the Earth. Eventually, the path of this stream will resemble curve line. <br />
<br />
<br />
What should be the height of this tube? Of course, the higher the tube is the better it is. As we think its height should be approximately 100 km, exactly this altitude is considered to be the boundary of space. If the tube is lower, then the air stream released from the tube will be scattered in the atmosphere prematurely. <br />
[[Image: 11opt.gif]]<br />
<br />
''The satellite orbits the Earth'' <br />
<br />
[[Image: 22opt.gif]]<br />
<br />
''The satellite is sowed down in upward moving air stream''<br />
<br />
<br />
Surely, it will cost too much to move the necessary amount of air in this tube vertically. To solve this problem at least partly we should use the winds blowing in the Earth’s atmosphere, particularly the '''Trade winds'''.<br />
<br />
<br />
The trade winds are the prevailing pattern of easterly surface winds found in the tropics, within the lower portion of the Earth's atmosphere, in the lower section of the troposphere near the Earth's equator. The trade winds blow predominantly from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisphere, strengthening during the winter and when the Arctic oscillation is in its warm phase. Historically, the trade winds have been used by captains of sailing ships to cross the world's oceans for centuries, and enabled European empire expansion into the Americas and trade routes to become established across the Atlantic and Pacific oceans<sup>4</sup>.<br />
[[Image: Map prevailing winds on earth saitistvis.png]]<br />
<br />
So, all we need to do is to let these winds to enter the tube where they will move upwards due to these winds’ constant pressure. Of course, the special calculations are needed in order we to know if this pressure is enough to force the air stream cover several hundred km altitude (100 km in tube and plus several hundred kilometers that should be covered by the air stream after leaving the tube in outer space) or not. In any case such approach will enable us to solve this problem at least partly. <br />
<br />
[[Image: Pasatebi Saitistvis.png]]<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Kessler_syndrome<br />
<br />
2. http://webpages.charter.net/dkessler/files/KesSym.html<br />
<br />
3. http://www.space.com/news/090211-satellite-collision.html<br />
<br />
4. http://en.wikipedia.org/wiki/Trade_wind</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_6&diff=3696OpenSpace 62014-08-18T17:16:37Z<p>Eagle9: </p>
<hr />
<div>== '''Removing the space debris by means of artificial air stream''' ==<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
<br />
The '''space debris''' is the objects in orbit around Earth created by humans that no longer serve any useful purpose. They consist of everything from entire spent rocket stages and defunct satellites to explosion fragments, paint flakes, dust and slag from solid rocket motors, and other small particles that are much more dangerous since it is more difficult to oversee them than large objects.<br />
<br />
<br />
Since the beginning of the Space Age in 1957 a great amount of satellites have been sent into space and this increasing number is/will be (especially in future) a great problem. According to some assessments the space debris belt will very soon make problems even for putting the satellites on the orbit around the Earth. As known, more and more countries are getting involved in space exploration and therefore number of objects (both active and “dead” satellites) in space will increase rapidly. The worst thing is that the satellites are colliding to each other and thus creating more and more little objects (their fragments) around the Earth that are much more difficult to deal with than with big objects. This effect is known as “Kessler Syndrome” <sup>1</sup> <sup>2</sup>. One of such collide occurred in 2009, 10 of February when the inactive satellite '''Kosmos-2251''' collided with active one '''Iridium 33''' above the northern Siberia with the speed of 42 120 km/h. This collision destroyed both satellites and gave birth to one more space debris cloud consisting of numerous little objects (there are at least one thousand objects in this cloud with the size of more than 10 cm) <sup>3</sup>. If this tendency continues, if the ''critical density'' where the creation of new debris occurs faster than the various natural forces that remove these objects from orbit in space is reached and overcome, apparently after several ten years there will be some dust belt around the Earth.<br />
<br />
<br />
As well-known the satellites placed on the Low Earth orbit are falling down on our planet due to atmosphere’s insignificant resistance. If we able to increase this resistance then the satellites (space debris in our case) will fall on the Earth down much sooner. How this can be done? Surely, we cannot raise the whole atmosphere upwards, but its little part can be actually raised. This can be achieved if we build a gigantic vertical tube that will enable us to pump the atmospheric air upwards, and then the satellites will go through such stream, lose their kinetic energy and eventually fall down.<br />
<br />
<br />
The air stream should be quite broad after leaving the tube and actually this will definitely be so because we know from Physics that the air generally tries to occupy all the space left to it. So, generally the narrow stream cannot be created and by the way this would be unacceptable since the narrow stream would cut the satellites into two pieces and we do not absolutely need this. It is much better if the “blunt” resistance will slow down the satellite. <br />
<br />
<br />
The speed of the air stream leaving the tube should be enough in order it to reach the several km altitudes (the vast majority of the space debris is located exactly there) and then to return to the Earth. Of course, under such situation the speed of the air stream should be less then Escape Velocity-11.2 km/sec. We should also point out that the stream returning back to the Earth will also work and slow the satellites down. Also, it is remarkable that the returning stream will be much broader since just after leaving the tube it will be widened due to satellites’ collision which will scatter stream’s molecules and air’s natural expansion as it was mentioned in the previous paragraph. <br />
<br />
<br />
We should note that the air stream will not return to the same place where it was released from on the Earth but it will return to the place located a bit westwards. The reason of it is following: the air stream in the tube is moving vertically upwards but after it leaves the tube the Earth will keep rotating around its axis and after some amount of time the air stream will hit other place located westwards on the Earth. Eventually, the path of this stream will resemble curve line. <br />
<br />
<br />
What should be the height of this tube? Of course, the higher the tube is the better it is. As we think its height should be approximately 100 km, exactly this altitude is considered to be the boundary of space. If the tube is lower, then the air stream released from the tube will be scattered in the atmosphere prematurely. <br />
[[Image: 11opt.gif]]<br />
<br />
''The satellite orbits the Earth'' <br />
<br />
[[Image: 22opt.gif]]<br />
<br />
''The satellite is sowed down in upward moving air stream''<br />
<br />
<br />
Surely, it will cost too much to move the necessary amount of air in this tube vertically. To solve this problem at least partly we should use the winds blowing in the Earth’s atmosphere, particularly the '''Trade winds'''.<br />
<br />
<br />
The trade winds are the prevailing pattern of easterly surface winds found in the tropics, within the lower portion of the Earth's atmosphere, in the lower section of the troposphere near the Earth's equator. The trade winds blow predominantly from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisphere, strengthening during the winter and when the Arctic oscillation is in its warm phase. Historically, the trade winds have been used by captains of sailing ships to cross the world's oceans for centuries, and enabled European empire expansion into the Americas and trade routes to become established across the Atlantic and Pacific oceans.<br />
[[Image: Map prevailing winds on earth saitistvis.png]]<br />
<br />
So, all we need to do is to let these winds to enter the tube where they will move upwards due to these winds’ constant pressure. Of course, the special calculations are needed in order we to know if this pressure is enough to force the air stream cover several hundred km altitude (100 km in tube and plus several hundred kilometers that should be covered by the air stream after leaving the tube in outer space) or not. In any case such approach will enable us to solve this problem at least partly. <br />
<br />
[[Image: Pasatebi Saitistvis.png]]<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Kessler_syndrome<br />
<br />
2. http://webpages.charter.net/dkessler/files/KesSym.html<br />
<br />
3. http://www.space.com/news/090211-satellite-collision.html</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_6&diff=3695OpenSpace 62014-08-18T17:15:50Z<p>Eagle9: </p>
<hr />
<div>== '''Removing the space debris by means of artificial air stream''' ==<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
<br />
The '''space debris''' is the objects in orbit around Earth created by humans that no longer serve any useful purpose. They consist of everything from entire spent rocket stages and defunct satellites to explosion fragments, paint flakes, dust and slag from solid rocket motors, and other small particles that are much more dangerous since it is more difficult to oversee them than large objects.<br />
<br />
<br />
Since the beginning of the Space Age in 1957 a great amount of satellites have been sent into space and this increasing number is/will be (especially in future) a great problem. According to some assessments the space debris belt will very soon make problems even for putting the satellites on the orbit around the Earth. As known, more and more countries are getting involved in space exploration and therefore number of objects (both active and “dead” satellites) in space will increase rapidly. The worst thing is that the satellites are colliding to each other and thus creating more and more little objects (their fragments) around the Earth that are much more difficult to deal with than with big objects. This effect is known as “Kessler Syndrome” <sup>1</sup> <sup>2</sup>. One of such collide occurred in 2009, 10 of February when the inactive satellite '''Kosmos-2251''' collided with active one '''Iridium 33''' above the northern Siberia with the speed of 42 120 km/h. This collision destroyed both satellites and gave birth to one more space debris cloud consisting of numerous little objects (there are at least one thousand objects in this cloud with the size of more than 10 cm) <sup>3</sup>. If this tendency continues, if the ''critical density'' where the creation of new debris occurs faster than the various natural forces that remove these objects from orbit in space is reached and overcome, apparently after several ten years there will be some dust belt around the Earth.<br />
<br />
<br />
As well-known the satellites placed on the Low Earth orbit are falling down on our planet due to atmosphere’s insignificant resistance. If we able to increase this resistance then the satellites (space debris in our case) will fall on the Earth down much sooner. How this can be done? Surely, we cannot raise the whole atmosphere upwards, but its little part can be actually raised. This can be achieved if we build a gigantic vertical tube that will enable us to pump the atmospheric air upwards, and then the satellites will go through such stream, lose their kinetic energy and eventually fall down.<br />
<br />
The air stream should be quite broad after leaving the tube and actually this will definitely be so because we know from Physics that the air generally tries to occupy all the space left to it. So, generally the narrow stream cannot be created and by the way this would be unacceptable since the narrow stream would cut the satellites into two pieces and we do not absolutely need this. It is much better if the “blunt” resistance will slow down the satellite. <br />
<br />
<br />
The speed of the air stream leaving the tube should be enough in order it to reach the several km altitudes (the vast majority of the space debris is located exactly there) and then to return to the Earth. Of course, under such situation the speed of the air stream should be less then Escape Velocity-11.2 km/sec. We should also point out that the stream returning back to the Earth will also work and slow the satellites down. Also, it is remarkable that the returning stream will be much broader since just after leaving the tube it will be widened due to satellites’ collision which will scatter stream’s molecules and air’s natural expansion as it was mentioned in the previous paragraph. <br />
<br />
<br />
We should note that the air stream will not return to the same place where it was released from on the Earth but it will return to the place located a bit westwards. The reason of it is following: the air stream in the tube is moving vertically upwards but after it leaves the tube the Earth will keep rotating around its axis and after some amount of time the air stream will hit other place located westwards on the Earth. Eventually, the path of this stream will resemble curve line. <br />
<br />
<br />
What should be the height of this tube? Of course, the higher the tube is the better it is. As we think its height should be approximately 100 km, exactly this altitude is considered to be the boundary of space. If the tube is lower, then the air stream released from the tube will be scattered in the atmosphere prematurely. <br />
[[Image: 11opt.gif]]<br />
<br />
''The satellite orbits the Earth'' <br />
<br />
[[Image: 22opt.gif]]<br />
<br />
''The satellite is sowed down in upward moving air stream''<br />
<br />
Surely, it will cost too much to move the necessary amount of air in this tube vertically. To solve this problem at least partly we should use the winds blowing in the Earth’s atmosphere, particularly the '''Trade winds'''.<br />
<br />
The trade winds are the prevailing pattern of easterly surface winds found in the tropics, within the lower portion of the Earth's atmosphere, in the lower section of the troposphere near the Earth's equator. The trade winds blow predominantly from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisphere, strengthening during the winter and when the Arctic oscillation is in its warm phase. Historically, the trade winds have been used by captains of sailing ships to cross the world's oceans for centuries, and enabled European empire expansion into the Americas and trade routes to become established across the Atlantic and Pacific oceans.<br />
[[Image: Map prevailing winds on earth saitistvis.png]]<br />
<br />
So, all we need to do is to let these winds to enter the tube where they will move upwards due to these winds’ constant pressure. Of course, the special calculations are needed in order we to know if this pressure is enough to force the air stream cover several hundred km altitude (100 km in tube and plus several hundred kilometers that should be covered by the air stream after leaving the tube in outer space) or not. In any case such approach will enable us to solve this problem at least partly. <br />
<br />
[[Image: Pasatebi Saitistvis.png]]<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Kessler_syndrome<br />
<br />
2. http://webpages.charter.net/dkessler/files/KesSym.html<br />
<br />
3. http://www.space.com/news/090211-satellite-collision.html</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_6&diff=3694OpenSpace 62014-08-18T17:14:59Z<p>Eagle9: </p>
<hr />
<div>== '''Removing the space debris by means of artificial air stream''' ==<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
The '''space debris''' is the objects in orbit around Earth created by humans that no longer serve any useful purpose. They consist of everything from entire spent rocket stages and defunct satellites to explosion fragments, paint flakes, dust and slag from solid rocket motors, and other small particles that are much more dangerous since it is more difficult to oversee them than large objects.<br />
<br />
Since the beginning of the Space Age in 1957 a great amount of satellites have been sent into space and this increasing number is/will be (especially in future) a great problem. According to some assessments the space debris belt will very soon make problems even for putting the satellites on the orbit around the Earth. As known, more and more countries are getting involved in space exploration and therefore number of objects (both active and “dead” satellites) in space will increase rapidly. The worst thing is that the satellites are colliding to each other and thus creating more and more little objects (their fragments) around the Earth that are much more difficult to deal with than with big objects. This effect is known as “Kessler Syndrome” <sup>1</sup> <sup>2</sup>. One of such collide occurred in 2009, 10 of February when the inactive satellite '''Kosmos-2251''' collided with active one '''Iridium 33''' above the northern Siberia with the speed of 42 120 km/h. This collision destroyed both satellites and gave birth to one more space debris cloud consisting of numerous little objects (there are at least one thousand objects in this cloud with the size of more than 10 cm) <sup>3</sup>. If this tendency continues, if the ''critical density'' where the creation of new debris occurs faster than the various natural forces that remove these objects from orbit in space is reached and overcome, apparently after several ten years there will be some dust belt around the Earth.<br />
<br />
<br />
As well-known the satellites placed on the Low Earth orbit are falling down on our planet due to atmosphere’s insignificant resistance. If we able to increase this resistance then the satellites (space debris in our case) will fall on the Earth down much sooner. How this can be done? Surely, we cannot raise the whole atmosphere upwards, but its little part can be actually raised. This can be achieved if we build a gigantic vertical tube that will enable us to pump the atmospheric air upwards, and then the satellites will go through such stream, lose their kinetic energy and eventually fall down.<br />
<br />
The air stream should be quite broad after leaving the tube and actually this will definitely be so because we know from Physics that the air generally tries to occupy all the space left to it. So, generally the narrow stream cannot be created and by the way this would be unacceptable since the narrow stream would cut the satellites into two pieces and we do not absolutely need this. It is much better if the “blunt” resistance will slow down the satellite. <br />
<br />
<br />
The speed of the air stream leaving the tube should be enough in order it to reach the several km altitudes (the vast majority of the space debris is located exactly there) and then to return to the Earth. Of course, under such situation the speed of the air stream should be less then Escape Velocity-11.2 km/sec. We should also point out that the stream returning back to the Earth will also work and slow the satellites down. Also, it is remarkable that the returning stream will be much broader since just after leaving the tube it will be widened due to satellites’ collision which will scatter stream’s molecules and air’s natural expansion as it was mentioned in the previous paragraph. <br />
<br />
<br />
We should note that the air stream will not return to the same place where it was released from on the Earth but it will return to the place located a bit westwards. The reason of it is following: the air stream in the tube is moving vertically upwards but after it leaves the tube the Earth will keep rotating around its axis and after some amount of time the air stream will hit other place located westwards on the Earth. Eventually, the path of this stream will resemble curve line. <br />
<br />
<br />
What should be the height of this tube? Of course, the higher the tube is the better it is. As we think its height should be approximately 100 km, exactly this altitude is considered to be the boundary of space. If the tube is lower, then the air stream released from the tube will be scattered in the atmosphere prematurely. <br />
[[Image: 11opt.gif]]<br />
<br />
''The satellite orbits the Earth'' <br />
<br />
[[Image: 22opt.gif]]<br />
<br />
''The satellite is sowed down in upward moving air stream''<br />
<br />
Surely, it will cost too much to move the necessary amount of air in this tube vertically. To solve this problem at least partly we should use the winds blowing in the Earth’s atmosphere, particularly the '''Trade winds'''.<br />
<br />
The trade winds are the prevailing pattern of easterly surface winds found in the tropics, within the lower portion of the Earth's atmosphere, in the lower section of the troposphere near the Earth's equator. The trade winds blow predominantly from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisphere, strengthening during the winter and when the Arctic oscillation is in its warm phase. Historically, the trade winds have been used by captains of sailing ships to cross the world's oceans for centuries, and enabled European empire expansion into the Americas and trade routes to become established across the Atlantic and Pacific oceans.<br />
[[Image: Map prevailing winds on earth saitistvis.png]]<br />
<br />
So, all we need to do is to let these winds to enter the tube where they will move upwards due to these winds’ constant pressure. Of course, the special calculations are needed in order we to know if this pressure is enough to force the air stream cover several hundred km altitude (100 km in tube and plus several hundred kilometers that should be covered by the air stream after leaving the tube in outer space) or not. In any case such approach will enable us to solve this problem at least partly. <br />
<br />
[[Image: Pasatebi Saitistvis.png]]<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Kessler_syndrome<br />
<br />
2. http://webpages.charter.net/dkessler/files/KesSym.html<br />
<br />
3. http://www.space.com/news/090211-satellite-collision.html</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_6&diff=3693OpenSpace 62014-08-18T17:14:02Z<p>Eagle9: </p>
<hr />
<div>== '''Removing the space debris by means of artificial air stream''' ==<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
The '''space debris''' is the objects in orbit around Earth created by humans that no longer serve any useful purpose. They consist of everything from entire spent rocket stages and defunct satellites to explosion fragments, paint flakes, dust and slag from solid rocket motors, and other small particles that are much more dangerous since it is more difficult to oversee them than large objects.<br />
<br />
Since the beginning of the Space Age in 1957 a great amount of satellites have been sent into space and this increasing number is/will be (especially in future) a great problem. According to some assessments the space debris belt will very soon make problems even for putting the satellites on the orbit around the Earth. As known, more and more countries are getting involved in space exploration and therefore number of objects (both active and “dead” satellites) in space will increase rapidly. The worst thing is that the satellites are colliding to each other and thus creating more and more little objects (their fragments) around the Earth that are much more difficult to deal with than with big objects. This effect is known as “Kessler Syndrome” <sup>1</sup> <sup>2</sup>. One of such collide occurred in 2009, 10 of February when the inactive satellite '''Kosmos-2251''' collided with active one '''Iridium 33''' above the northern Siberia with the speed of 42 120 km/h. This collision destroyed both satellites and gave birth to one more space debris cloud consisting of numerous little objects (there are at least one thousand objects in this cloud with the size of more than 10 cm) <sup>3</sup>. If this tendency continues, if the ''critical density'' where the creation of new debris occurs faster than the various natural forces that remove these objects from orbit in space is reached and overcome, apparently after several ten years there will be some dust belt around the Earth.<br />
<br />
As well-known the satellites placed on the Low Earth orbit are falling down on our planet due to atmosphere’s insignificant resistance. If we able to increase this resistance then the satellites (space debris in our case) will fall on the Earth down much sooner. How this can be done? Surely, we cannot raise the whole atmosphere upwards, but its little part can be actually raised. This can be achieved if we build a gigantic vertical tube that will enable us to pump the atmospheric air upwards, and then the satellites will go through such stream, lose their kinetic energy and eventually fall down.<br />
The air stream should be quite broad after leaving the tube and actually this will definitely be so because we know from Physics that the air generally tries to occupy all the space left to it. So, generally the narrow stream cannot be created and by the way this would be unacceptable since the narrow stream would cut the satellites into two pieces and we do not absolutely need this. It is much better if the “blunt” resistance will slow down the satellite. <br />
<br />
The speed of the air stream leaving the tube should be enough in order it to reach the several km altitudes (the vast majority of the space debris is located exactly there) and then to return to the Earth. Of course, under such situation the speed of the air stream should be less then Escape Velocity-11.2 km/sec. We should also point out that the stream returning back to the Earth will also work and slow the satellites down. Also, it is remarkable that the returning stream will be much broader since just after leaving the tube it will be widened due to satellites’ collision which will scatter stream’s molecules and air’s natural expansion as it was mentioned in the previous paragraph. <br />
<br />
We should note that the air stream will not return to the same place where it was released from on the Earth but it will return to the place located a bit westwards. The reason of it is following: the air stream in the tube is moving vertically upwards but after it leaves the tube the Earth will keep rotating around its axis and after some amount of time the air stream will hit other place located westwards on the Earth. Eventually, the path of this stream will resemble curve line. <br />
<br />
What should be the height of this tube? Of course, the higher the tube is the better it is. As we think its height should be approximately 100 km, exactly this altitude is considered to be the boundary of space. If the tube is lower, then the air stream released from the tube will be scattered in the atmosphere prematurely. <br />
[[Image: 11opt.gif]]<br />
<br />
''The satellite orbits the Earth'' <br />
<br />
[[Image: 22opt.gif]]<br />
<br />
''The satellite is sowed down in upward moving air stream''<br />
<br />
Surely, it will cost too much to move the necessary amount of air in this tube vertically. To solve this problem at least partly we should use the winds blowing in the Earth’s atmosphere, particularly the '''Trade winds'''.<br />
<br />
The trade winds are the prevailing pattern of easterly surface winds found in the tropics, within the lower portion of the Earth's atmosphere, in the lower section of the troposphere near the Earth's equator. The trade winds blow predominantly from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisphere, strengthening during the winter and when the Arctic oscillation is in its warm phase. Historically, the trade winds have been used by captains of sailing ships to cross the world's oceans for centuries, and enabled European empire expansion into the Americas and trade routes to become established across the Atlantic and Pacific oceans.<br />
[[Image: Map prevailing winds on earth saitistvis.png]]<br />
So, all we need to do is to let these winds to enter the tube where they will move upwards due to these winds’ constant pressure. Of course, the special calculations are needed in order we to know if this pressure is enough to force the air stream cover several hundred km altitude (100 km in tube and plus several hundred kilometers that should be covered by the air stream after leaving the tube in outer space) or not. In any case such approach will enable us to solve this problem at least partly. <br />
<br />
[[Image: Pasatebi Saitistvis.png]]<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Kessler_syndrome<br />
<br />
2. http://webpages.charter.net/dkessler/files/KesSym.html<br />
<br />
3. http://www.space.com/news/090211-satellite-collision.html</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace&diff=3692OpenSpace2014-08-18T17:12:56Z<p>Eagle9: </p>
<hr />
<div><div style="float:right; border:#CCCCCC solid 1px; background-color: #F7F7F7"><br />
<table cellspacing=0 cellpadding=0 width=550><br />
<br />
<tr><td colspan="3" align="center" style="background-color:#CCCCCC"><b>Title:</b> Open Work Space</td></tr><br />
<br />
<tr><br />
<td align="center" valign="middle" height=125 width=100 style='padding:10px'><br />
<div style="background-color:#CCCCFF; height:110px; width:90px"><br />
[Cover Img]<br />
</div><br />
</td><br />
<br />
<td align="left" valign="top"><br />
<div><br />
<b>About:</b><br /><br />
* Moderator: [[OpenSpace#edwards|Brad Edwards]]<br /><br />
</div><br />
</td><br />
<br />
<td align="left" valign="top"><br />
<div><br />
'''[[Article Tags|Tags]]''':<br /><br />
* This is open space for development<br />
</div><br />
</td><br />
</tr><br />
<br />
</table></div><br />
== Open Work Space ==<br />
<br />
Below are links to pages that are open for collaborative space elevator development work. Feel free to use. <br />
<br />
#To begin select a link that says "Open for Use". You will be directed to a template page that you can then edit. <br />
#Enter your basic information including name, e-mail and basic focus of development you want to pursue on this page.<br />
#Begin work.<br />
#Return to this page before you leave and modify the Title of the link to something appropriate to signify that the page in in use and fill in the other basic information.<br />
<br />
<center> '''Do not modify other people's pages without their permission.'''</center><br />
<br />
That is most of it. If you have questions please feel free to contact the [[user:edwards | Wiki administrators]]<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_1|Title:Economics:]] '''<br />
|width="450pt"|<br />
*Lead: Ed Gray<br />
*E-mail: ed_gray@sbcglobal.net<br />
*Focus: Discussion area for the Economics Team. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_2|Title:Companies involved in SE development:]] '''<br />
|width="450pt"|<br />
*Lead: Christopher J Petrella<br />
*E-mail: cpetrella@revengesoft.com<br />
*Focus: information about the companies that are developing technology for the Space Elevator. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_3|SPACE ELEVATOR VERSUS SPACE DEBRIS]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: The new method for eliminating the space debris at Low Earth Orbit (LEO) and Geostationary Orbit (GEO) is presented here. The paper shows how the Space Elevator can be used in struggling against the space debris that would be possible by means of deploying the huge metallic petals onboard the Space Elevator’s cabin moving along the cable. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_4|JUMP FROM SPACE]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: The paper JUMP FROM SPACE describes how it is possible to expand the facilities of one of the most excellent kind of sport-parachuting and descend from boundary to space-100 km altitude. This can be done by means of the Space Elevator. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_5| Space Catapult]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: A long rod with the assist of Space Elevator can be used for deep space missions. This method we called Space Catapult <br />
|}<br />
<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_6|Removing the space debris by means of artificial air stream]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: An upward moving air stream may actually enable us to remove the space debris placed on the Low Earth orbit. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_7|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_8|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_9|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_10|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace&diff=3691OpenSpace2014-08-18T17:12:02Z<p>Eagle9: </p>
<hr />
<div><div style="float:right; border:#CCCCCC solid 1px; background-color: #F7F7F7"><br />
<table cellspacing=0 cellpadding=0 width=550><br />
<br />
<tr><td colspan="3" align="center" style="background-color:#CCCCCC"><b>Title:</b> Open Work Space</td></tr><br />
<br />
<tr><br />
<td align="center" valign="middle" height=125 width=100 style='padding:10px'><br />
<div style="background-color:#CCCCFF; height:110px; width:90px"><br />
[Cover Img]<br />
</div><br />
</td><br />
<br />
<td align="left" valign="top"><br />
<div><br />
<b>About:</b><br /><br />
* Moderator: [[OpenSpace#edwards|Brad Edwards]]<br /><br />
</div><br />
</td><br />
<br />
<td align="left" valign="top"><br />
<div><br />
'''[[Article Tags|Tags]]''':<br /><br />
* This is open space for development<br />
</div><br />
</td><br />
</tr><br />
<br />
</table></div><br />
== Open Work Space ==<br />
<br />
Below are links to pages that are open for collaborative space elevator development work. Feel free to use. <br />
<br />
#To begin select a link that says "Open for Use". You will be directed to a template page that you can then edit. <br />
#Enter your basic information including name, e-mail and basic focus of development you want to pursue on this page.<br />
#Begin work.<br />
#Return to this page before you leave and modify the Title of the link to something appropriate to signify that the page in in use and fill in the other basic information.<br />
<br />
<center> '''Do not modify other people's pages without their permission.'''</center><br />
<br />
That is most of it. If you have questions please feel free to contact the [[user:edwards | Wiki administrators]]<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_1|Title:Economics:]] '''<br />
|width="450pt"|<br />
*Lead: Ed Gray<br />
*E-mail: ed_gray@sbcglobal.net<br />
*Focus: Discussion area for the Economics Team. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_2|Title:Companies involved in SE development:]] '''<br />
|width="450pt"|<br />
*Lead: Christopher J Petrella<br />
*E-mail: cpetrella@revengesoft.com<br />
*Focus: information about the companies that are developing technology for the Space Elevator. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_3|SPACE ELEVATOR VERSUS SPACE DEBRIS]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: The new method for eliminating the space debris at Low Earth Orbit (LEO) and Geostationary Orbit (GEO) is presented here. The paper shows how the Space Elevator can be used in struggling against the space debris that would be possible by means of deploying the huge metallic petals onboard the Space Elevator’s cabin moving along the cable. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_4|JUMP FROM SPACE]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: The paper JUMP FROM SPACE describes how it is possible to expand the facilities of one of the most excellent kind of sport-parachuting and descend from boundary to space-100 km altitude. This can be done by means of the Space Elevator. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_5| Space Catapult]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: A long rod with the assist of Space Elevator can be used for deep space missions. This method we called Space Catapult <br />
|}<br />
<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_6|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: An upward moving air stream may actually enable us to remove the space debris placed on the Low Earth orbit. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_7|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_8|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_9|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_10|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace&diff=3690OpenSpace2014-08-18T17:09:41Z<p>Eagle9: </p>
<hr />
<div><div style="float:right; border:#CCCCCC solid 1px; background-color: #F7F7F7"><br />
<table cellspacing=0 cellpadding=0 width=550><br />
<br />
<tr><td colspan="3" align="center" style="background-color:#CCCCCC"><b>Title:</b> Open Work Space</td></tr><br />
<br />
<tr><br />
<td align="center" valign="middle" height=125 width=100 style='padding:10px'><br />
<div style="background-color:#CCCCFF; height:110px; width:90px"><br />
[Cover Img]<br />
</div><br />
</td><br />
<br />
<td align="left" valign="top"><br />
<div><br />
<b>About:</b><br /><br />
* Moderator: [[OpenSpace#edwards|Brad Edwards]]<br /><br />
</div><br />
</td><br />
<br />
<td align="left" valign="top"><br />
<div><br />
'''[[Article Tags|Tags]]''':<br /><br />
* This is open space for development<br />
</div><br />
</td><br />
</tr><br />
<br />
</table></div><br />
== Open Work Space ==<br />
<br />
Below are links to pages that are open for collaborative space elevator development work. Feel free to use. <br />
<br />
#To begin select a link that says "Open for Use". You will be directed to a template page that you can then edit. <br />
#Enter your basic information including name, e-mail and basic focus of development you want to pursue on this page.<br />
#Begin work.<br />
#Return to this page before you leave and modify the Title of the link to something appropriate to signify that the page in in use and fill in the other basic information.<br />
<br />
<center> '''Do not modify other people's pages without their permission.'''</center><br />
<br />
That is most of it. If you have questions please feel free to contact the [[user:edwards | Wiki administrators]]<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_1|Title:Economics:]] '''<br />
|width="450pt"|<br />
*Lead: Ed Gray<br />
*E-mail: ed_gray@sbcglobal.net<br />
*Focus: Discussion area for the Economics Team. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_2|Title:Companies involved in SE development:]] '''<br />
|width="450pt"|<br />
*Lead: Christopher J Petrella<br />
*E-mail: cpetrella@revengesoft.com<br />
*Focus: information about the companies that are developing technology for the Space Elevator. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_3|SPACE ELEVATOR VERSUS SPACE DEBRIS]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: The new method for eliminating the space debris at Low Earth Orbit (LEO) and Geostationary Orbit (GEO) is presented here. The paper shows how the Space Elevator can be used in struggling against the space debris that would be possible by means of deploying the huge metallic petals onboard the Space Elevator’s cabin moving along the cable. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_4|JUMP FROM SPACE]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: The paper JUMP FROM SPACE describes how it is possible to expand the facilities of one of the most excellent kind of sport-parachuting and descend from boundary to space-100 km altitude. This can be done by means of the Space Elevator. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_5| Space Catapult]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: A long rod with the assist of Space Elevator can be used for deep space missions. This method we called Space Catapult <br />
|}<br />
<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_6|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Giorgi Lobzhanidze<br />
*E-mail: giorgi9@gmail.com<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_7|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_8|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_9|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}<br />
<br />
<br /><br />
{| border="1" style="background:transparent;"<br />
|-<br />
|width="450pt"|'''[[OpenSpace_10|Title:Open for Use:]] '''<br />
|width="450pt"|<br />
*Lead: Place Name Here<br />
*E-mail: Place E-mail Here<br />
*Focus: Write a brief line or two on what the page is to work on. This is so other might step up to help. <br />
|}</div>Eagle9http://keithcu.com/wiki/index.php?title=File:Map_prevailing_winds_on_earth_saitistvis.png&diff=3689File:Map prevailing winds on earth saitistvis.png2014-08-17T12:28:05Z<p>Eagle9: Eagle9 uploaded a new version of &quot;File:Map prevailing winds on earth saitistvis.png&quot;</p>
<hr />
<div></div>Eagle9http://keithcu.com/wiki/index.php?title=File:Map_prevailing_winds_on_earth_saitistvis.png&diff=3688File:Map prevailing winds on earth saitistvis.png2014-08-17T12:26:36Z<p>Eagle9: Eagle9 uploaded a new version of &quot;File:Map prevailing winds on earth saitistvis.png&quot;</p>
<hr />
<div></div>Eagle9http://keithcu.com/wiki/index.php?title=File:Map_prevailing_winds_on_earth_saitistvis.png&diff=3687File:Map prevailing winds on earth saitistvis.png2014-08-17T12:23:54Z<p>Eagle9: Eagle9 uploaded a new version of &quot;File:Map prevailing winds on earth saitistvis.png&quot;</p>
<hr />
<div></div>Eagle9http://keithcu.com/wiki/index.php?title=File:Map_prevailing_winds_on_earth_saitistvis.png&diff=3686File:Map prevailing winds on earth saitistvis.png2014-08-17T12:23:14Z<p>Eagle9: Eagle9 uploaded a new version of &quot;File:Map prevailing winds on earth saitistvis.png&quot;</p>
<hr />
<div></div>Eagle9http://keithcu.com/wiki/index.php?title=File:Pasatebi_Saitistvis.png&diff=3685File:Pasatebi Saitistvis.png2014-08-17T12:19:59Z<p>Eagle9: </p>
<hr />
<div></div>Eagle9http://keithcu.com/wiki/index.php?title=File:Map_prevailing_winds_on_earth_saitistvis.png&diff=3684File:Map prevailing winds on earth saitistvis.png2014-08-17T12:17:12Z<p>Eagle9: </p>
<hr />
<div></div>Eagle9http://keithcu.com/wiki/index.php?title=File:22opt.gif&diff=3683File:22opt.gif2014-08-17T11:58:35Z<p>Eagle9: </p>
<hr />
<div></div>Eagle9http://keithcu.com/wiki/index.php?title=File:11opt.gif&diff=3682File:11opt.gif2014-08-17T11:54:29Z<p>Eagle9: </p>
<hr />
<div></div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_3&diff=3681OpenSpace 32014-08-15T17:15:52Z<p>Eagle9: </p>
<hr />
<div>== '''SPACE ELEVATOR VERSUS SPACE DEBRIS''' ==<br />
<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
<br />
=INTRODUCTION=<br />
<br />
The '''space debris''' is the objects in orbit around Earth created by humans that no longer serve any useful purpose. They consist of everything from entire spent rocket stages and defunct satellites to explosion fragments, paint flakes, dust and slag from solid rocket motors, and other small particles that are much more dangerous since it is more difficult to oversee them than large objects.<br />
<br />
Since the beginning of the Space Age in 1957 a great amount of satellites have been sent into space and this increasing number is/will be (especially in future) a great problem. According to some assessments the space debris belt will very soon make problems even for putting the satellites on the orbit around the Earth. As known, more and more countries are getting involved in space exploration and therefore number of objects (both active and “dead” satellites) in space will increase rapidly. The worst thing is that the satellites are colliding to each other and thus creating more and more little objects (their fragments) around the Earth that are much more difficult to deal with than with big objects. This effect is known as “Kessler Syndrome” <sup>1</sup> <sup>2</sup>. One of such collide occurred in 2009, 10 of February when the inactive satellite '''Kosmos-2251''' collided with active one '''Iridium 33''' above the northern Siberia with the speed of 42 120 km/h. This collision destroyed both satellites and gave birth to one more space debris cloud consisting of numerous little objects (there are at least one thousand objects in this cloud with the size of more than 10 cm) <sup>3</sup>. If this tendency continues, if the ''critical density'' where the creation of new debris occurs faster than the various natural forces that remove these objects from orbit in space is reached and overcome, apparently after several ten years there will be some dust belt around the Earth.<br />
<br />
To deal with the problem of space debris various ideas have been suggested such as: to "sweep" space debris back into Earth's atmosphere, including automated tugs, laser brooms to vaporize or nudge particles into rapidly-decaying orbits, or huge aerogel blobs to absorb impacting junk and eventually fall out of orbit with them trapped inside. We think that there actually could be one more way to deal with this problem and for this purpose we need to use the '''Space Elevator'''.<br />
<br />
<br />
<br />
=REMOVING THE SPACE DEBRIS AT LOW EARTH ORBIT=<br />
<br />
How the space debris objects could be generally eliminated? We could either decrease their speed or change their orbit(s) towards the Earth so that they to enter the atmosphere with the downward trajectory and then be burnt up. The first way: decreasing their current speed beyond lower than ''Orbital Velocity'' (or with another words-diminishing their ''kinetic energy'') and thus forcing them to enter the atmosphere and their final burning could be very promising. In practice it could be reached by means of creating and building some physical obstacle on their way.<br />
<br />
As well-known, the Space Elevator will be tall vertical structure built on equator and will have height of approximately several ten thousand kilometers or even more and its cable will cross the region called the Low Earth Orbit (LEO) where the density of space debris objects is especially very high (see picture below). Therefore, the danger caused by the space debris will be especially dangerous for Space Elevator. Hence, we think that it would be very logical and useful to use to Space Elevator in struggling against its primary obstacle-space debris.<br />
<br />
[[Image:Spacedebrissmall.jpg]]<br />
<br />
''Spatial density of space debris by altitude according to ESA MASTER-2001''<br />
<br />
<br />
Now, what kind of physical obstacle could impede space debris objects? We imagine it like some metallic petals fastened on the cabin moving along the Space Elevator’s cable. The petals will play role of the obstacle that will prevent the space debris objects and get rid of them. Their number should be two-distributed rightwards and leftwards from the cabin and they should be placed so that as more space debris objects to collide with them as possible. Of course, since the satellites (and hence space debris objects) orbit around the Earth with various inclination it would be very difficult to place the petals so that all the space debris objects to collide with them. However, we know that most of satellites orbit from West to Eastwards, therefore the petals should be placed approximately along the geographic meridians. In such case many satellites’ orbit will make the ''right angle'' (or close to ''right angle'') to petals. We can see below on the picture how we imagine this construction:<br />
<br />
[[Image: A.JPG]]<br />
<br />
Here the question might arise: the number of space debris object is quite high (space debris’s the total mass is estimated at 5,500 tones <sup>4</sup>, as for their number, the large objects over 10 centimeters is estimated at 19 000, between 1 and 10 centimeters approximately 500,000, and estimates that debris items smaller than 1 centimeter probably exceeds tens of millions <sup>5</sup>), besides it is increasing each year, they are spread at huge volume in space and how effectively such construction will deal with this problem? Our answer would be this: each satellite when orbiting around the Earth cross the equator twice during one revolution. Whatever inclination the satellite has, 0° or 90°, it has circular or elongated orbit-each satellite ''is crossing'' the equator. This crossing place may occur above any point on the Earth’s surface and sooner or later each satellite will definitely cross the place where the Space Elevator is built and will collide with these petals. The larger the petals are, the sooner this will happen.<br />
<br />
We think that these petals should be manufactured so that the space debris objects must not reflect (jump away) from the petals. First of all the huge kinetic energy of the satellite may shift the cable and consequently the whole Space Elevator from its current position and this is undesirable. Besides, apparently no material would be able to withstand such collision. Therefore, we think that the space debris objects should pierce the petal; such collision will decrease space debris object’s speed and kinetic energy (the part of its energy will be spent for heating the metallic petals) and it (more precisely its fragments) will enter the atmosphere relatively soon. The exact time of entrance will depend on how much space debris’s object’s speed will be decreased, on their orbital characteristics (circular/elongated orbit; apparently the satellite with elongated orbit will enter the atmosphere later than the one with circular orbit) and altitude. Here these petals would operate somehow like the foam balloons (as we have already mentioned they are one of the proposed methods for eliminating the space debris), however unlike the balloons, the petals can move upwards/downwards along the Space Elevator’s cable and meet the space debris objects when necessary very quickly and this will be their great advantage-ability of eliminating the significant amount of space debris during relatively short period of time.<br />
<br />
What will be the difference between the velocities of the satellites and Space Elevator’s cable? In other words, at which speed the space debris objects will collide with these metallic petals? Well, it depends on the altitude mainly and on satellite’s orbital characteristics-eccentricity. It is well-known that the value of the ''Orbital Velocity'' decreases with increasing the altitude while Space Elevator’s cable’s velocity (''tangential velocity'') increases with increasing altitude. But at ''Low Earth Orbit'' the difference between these velocities will be quite high, several kilometers per second or so. In the chart presented below we can see this difference:<br />
<br />
[[Image: Cxrili.gif]]<br />
<br />
We see that difference between ''Orbital Velocity'' and Space Elevator’s cable’s ''tangential'' speed at LEO (at the altitude of 300-1000 km) is quite high and the vast majority of the space debris objects are placed exactly there.<br />
<br />
Obviously, this structure cannot work operate in order to eliminate the space debris at geostationary orbit and nearby since the difference between the velocities of the satellite and Space Elevator’s cable will be close to zero and therefore no collision will occur. However, we will discuss this issue in details a bit later in this paper.<br />
<br />
Here we explain the mechanism of cleaning the LEO with these petals more thoroughly. When the space debris object pierces the petal it loses its speed and hence its orbit changes in the following manner: the circular orbit turns into the elliptical one with the apogee placed at the same altitude but with the perigee placed downwards. When the space debris object reaches the perigee it is exposed to more atmospheric drag and consequently it loses its altitude and eventually burn up in the atmosphere.<br />
<br />
Here the questions arise: will the Space Elevator withstand the mass/weight of this whole construction (surely it will weigh not one metric tone)? Space elevator will have to serve many different kinds of payloads probably everyday (however it will remain unclear until the Space Elevator is really built when we will know its cabin’s ascending speed in practice) and this construction (cabin plus petals) will definitely make additional problem for its performance. Where is solution? Our answer would be this: the amount of space debris is increasing each year rapidly. Very soon it will be simply necessary to take some measurements against this problem whatever money and effort it needs. Therefore, it will be useful at least temporarily to use the Space Elevator in struggle against its primary obstacle-space debris and after ending this job the Space Elevator will work without problems. Besides, since the satellites generally orbit the Earth quite quickly, we think that such construction will be able to deal with the space debris problem very quickly, probably within several weeks of course with the condition that it works properly. After ending its job, in other words when these petals will be almost completely destroyed (pierced in many places), the cabin will get rid of them and they will simply fall on the Earth. Or, actually the cabin can go down and thus bring these destroyed and useless petals back to the Earth. As for the petals’ total weight, of course they should not be more than Space Elevator’s lifting capacity; this capacity is not well-known yet but probably it will not exceed one hundred metric tons, therefore petals’ weight should be about several ten metric tons or so.<br />
<br />
How the pierced petals will be fallen down to the Earth? At the LEO the Space Elevator’s cable’s tangential velocity is more than Earth’s rotational speed, therefore any object released from the Space Elevator will fall down and a bit forward, that is eastwards also in order to outstrip the Space Elevator’s cable. Note, that this is favorable circumstance because this guaranties that the petals when falling down will never collide with the cable.<br />
<br />
However, the ''Low Earth Orbit'' is filled not only with space debris, there are and will be the active satellites also and these petals could destroy them too and this is strictly undesirable. We think that the solution to this problem could be following: there is several space debris tracking systems working by a number of ground-based radar facilities and telescopes as well as by a space-based telescope, such as the United States Strategic Command's (USSTRATCOM) <sup>6</sup> with its ''United States Space Surveillance Network'' <sup>7</sup> collecting data about all kinds of near-space objects-their orbits, altitude, inclination and so on. Some other nations have also developed their own analogous systems for the same purpose, like European MASTER-2001 (Meteoroid and Space Debris Terrestrial Environment Reference (MASTER) model). These efforts lead creating the detailed catalogues holding any necessary information about thousands of artificial objects in space. More precisely, two separate catalog databases are maintained under the USSTRATCOM: a primary catalog by the Air Force Space Command (AFSPC), and an alternate catalog by the Naval Space Command (NSC). The number of cataloged objects is nearly 20,000 <sup>8</sup> <sup>9</sup> <sup>10</sup>. As for Europeans, the MASTER-2001 population consists of 17 800 objects larger than 10 cm <sup>11</sup>. So, if there is information/warning from the Earth that an active satellite is approaching to these petals, the cabin will simply move upwards or downwards (actually descending is easier of course since in this case no energy will be required unlike ascending); the size of the artificial satellites generally are not high, several meters only or even less, so apparently such measurements will be absolutely enough to avoid such undesirable collision. The Space Elevator’s cabin may actually have its own radar to discover incoming and previously undetected space debris object to meet them immediately with the petals until this object(s) hit the Space Elevator’s cable.<br />
<br />
The size, more precisely the square of the petals should be quite vast to cover large area in space for eliminate as many debris as possible. At the same time, taking into consideration the fact that all satellites sooner or later will cross the equator above some certain place above the Earth, we conclude the huge size of the petals is not final goal, and therefore some ''golden mean'' should be found for the petals’ size. <br />
<br />
Some space debris objects orbit around the Earth with great inclined orbit (polar for example) and they may hit the petal not with the ''right angle'' but with less one and we think that this would undesirable because in case of such collision the space debris object will not pierce the petal (there will be probability that the object will jump aside from them) but will slightly change their orbiting direction. To avoid this, the cabin can rotate (see the image below) the petals around itself so that the space debris objects will collide with them at right angle.<br />
<br />
[[Image: New Image.JPG]]<br />
<br />
One more thing, probably the most important: can we be sure that the speed of the space debris’ fragments after collision will be less than their initial one? It is crucial question since if fragments still have the same speed, they will stay in the same orbit and this construction on the Space Elevator with petals will be absolutely useless and even harmful because in this case the space debris objects’ amount will be increased. Therefore, it is extremely important that these petals to decrease space debris objects’ speed and also the fragments of the petals that will separate from them after collision to have speed less than ''Orbital Velocity'' on the current altitude. If this is achieved this whole undertaking will be justified. Apparently, this will be guaranteed because it is obvious that the satellite moving at huge speed when hitting ''almost stationery'' object (petals in this case) will convey its kinetic energy to stationery one and will lose the speed. The part of the energy will be spent for piercing and heating the petals. As for petals’ fragments, their speed will be increased compare to petals initial speed because of collision but still will be less than ''Orbital Velocity'' and therefore they will enter the atmosphere even sooner than fragments from the space debris’ objects.<br />
<br />
=Material for the petals=<br />
<br />
Now, what kind of material should be used for manufacturing these petals? Metal? Plastic? It is prematurely to speak about this aspect today since this is purely technical, engineering question. The primary requirement is that the material used for manufacturing the petals should not be very stiff, otherwise after satellite’s collision with petals the satellite will not be able to pierce the petal. At the same time the petals should not be very fragile, otherwise after collision it will be broken completely into little pieces. Finally we should choose such material that will enable us to manufacture the petal that will not be broken into little pieces after collision with the space debris object but will make the hole in the petal and some part of the material around the hole will be detached from the petal and then eventually fall on the Earth. One more requirement set against such petals is that they must be quite large (we think that for effective performance their area should be about several thousand square meters or more) and quite thin, otherwise they will be extremely heavy and no Space Elevator will be able to carry them.<br />
<br />
These petals could be used for all kinds of space debris objects with the same success and this is their great advantage over other methods where there are some difficulties of removing little pieces from space, for example by means of lasers it would be quite difficult to aim at the little, almost invisible pieces in space and remove them; the petals will be exposed to collision from ''all size'' of space debris objects.<br />
<br />
Next question: how and where these huge petals should be deployed in space? We think that from the beginning these petals must be folded and in space, more precisely at the altitude of 100 km or a bit more they will be deployed like the solar panels on the satellites are deployed. We suppose that this altitude (about 100 km above the sea level) will be convenient for deployment due to two reasons: 1) If the petals are deployed lower, for example at the altitude of 50-60 km above the sea level, it could make problems for ascending the cabin with already deployed petals since they are huge and air friction (during ascent) or winds existing at high altitudes will make problems-so deployment of the petals should be occurred in space and not in atmosphere. 2) The deployment should occur lower than LEO otherwise the space debris objects could harm not-yet-deployed petals and this is undesirable since the space debris objects should collide with ''deployed'' petals only.<br />
<br />
Actually there could be other solution to this problem: if it is turned out that it is much easier to manufacture huge petals than deploying them into space, in this case the Space Elevator should carry ''unfolded/(already)deployed'' petals into space.<br />
<br />
As for the fragments’ falling place, it could not be defined in advance. Of course, the Space Elevator itself will be placed at some certain place on the Earth but first of all there will be difference between speeds of the petals’ fragments and space debris objects’ ones due to their initial different speeds (we can see it on the chart represented above-on the Low Earth Orbit this difference is quite high) and this difference varies, therefore their falling place would be at the various places on the Earth. Besides, many things depends at what altitude the collision will occur. The higher occurs it the less chance the space debris object will have to be exposed to atmospheric drag at its perigee; so we think that it would be more difficult to calculate their exact falling place.<br />
<br />
And one more issue about the construction of the petals themselves. Actually only the future practice can show us their necessary size and hence-their mass. If it is turned out that quite large petals are needed they to work properly, then one more technical question will arise: should the petals be like one monolithic sheet or should they consist of many little sheets interconnected to each other? From the technical point of view both approaches could be realized, however from the following considerations we think that one monolithic sheet still would be better to be designed and manufactured:<br />
<br />
As well-known, the space debris mostly consists of numerous very little pieces created from satellite collision. It would be very difficult, almost impossible to follow ''all of them''; to know exactly their location; to precisely predict their collision time to petals. If the petals are made from many little sheets interconnected to each other, then their collision to space debris dust clouds (we have already mentioned about one such cloud created in 2009) may lead to destruction of the ''metallic rods'' connecting the sheets and hence disintegrating the whole construction. If such collision destroys the rods, the petal may simply break into several above-mentioned sheets ''without'' doing its primary job, while the one monolithic sheet will have more chance to withstand and hence maintaining its integrity and to continue its job. Here we can see both probable kinds of petals:<br />
<br />
[[Image: 2 kinds of petals.JPG]]<br />
<br />
<br />
=Some ideas about metallic rods connecting the Space Elevator’s cabin with petals=<br />
<br />
First of all: what kind of cross-section should they have? We think that the best solution would be the oval one with the sharp edges directed towards satellites’ moving direction because if some satellite hits the rods (instead of hitting the petals) then the sharp-edged rod would have more chance to cut the satellite while the circular-section rod would be relatively easily destroyed at such collision and this would lead to complete destroying the whole structure.<br />
<br />
Also, there is no necessity the rod to cover/connect the petals from all four sides but it (the rod) should connect the cabin to petal(s) only. Besides, it would be useful if this rod is a bit elastic since at collision with space debris object the rigid rod may cause Space Elevator’s cable’s shift (due to satellite’s huge kinetic energy) and this would be undesirable; if the rod is elastic, then the collision will cause petals’ vibration only relative to the cabin.<br />
<br />
=Additional petal=<br />
<br />
For protecting this whole structure, more precisely for protecting the cabin itself from undesirable collision the additional protective petals could be deployed in front of the cabin. As we imagine, there actually could be pair of petals with their common “nose” highly directed forward. This pair should operate in a bit different way-the space debris objects will not pierce them but hit them at low angle, change their flying direction and hit the main petals. We think that such measurement, installing these additional petals is absolutely necessary because the cabin and the cable ''must not'' be damaged by the collision in no circumstances, otherwise it may lead to destroying the Space Elevator that is absolutely intolerable. In the picture below we can see these protective petals:<br />
<br />
[[Image: 45.JPG]]<br />
<br />
In case of emergency if one of the petals is lost will the second one be able to continue operating? Well, mainly it depends on the remained petal’s mass and Space Elevator’s lifting capacity. If it turned out that the Space Elevator is able to withstand the load (that is second petal) hanging ''at one side only'', then the performance should be continued until the second petal is completely pierced and released down. Otherwise the remained petal should be ''immediately'' released to avoid cabin’s tilt.<br />
<br />
What time it will take this structure to continue operating after ending its job again? Mainly it depends on cabin’s ascending velocity and on the time needed to replace pierced petals with new ones. As for ascent velocity it is not well-known yet, however according to current speed of the climbers at the space elevator games (about 2 m/s) it would take about 80 days to reach the geostationary orbit; but the Low Earth Orbit that is especially filled with space debris and needs to be cleaned first of all is approximately hundred times closer to the Earth’s surface, therefore one day would be absolutely enough for the cabin to get this orbit and begin operating, even the less time will be needed to descend to the Earth. Some amount of time will be taken to replace old petals with new ones (this time is approximately directly proportional to petals’ area). So, as we propose this whole structure could actually work in a ''continuous mode'' (this is very important) until the Low Earth Orbit is cleaned enough.<br />
<br />
This work actually has got some unfinished issues, such as: the petals may not withstand the heat generated by the collision-so the melting temperature and heat capacity of the materials used for manufacturing the petals should be quite high. In space the petals could also deform and change their shape due to high temperature caused by collision. The probable solution to this problem could be using such material for petals that will enable to emit the heat in the form of infrared radiation as quickly as possible. Currently we shall leave solving these problems to future since actually it is technical, engineering problem and does not directly concern to our proposal.<br />
<br />
This method described in this paper has got the following advantage: we do not need to allocate a huge amount of money to realize it. The whole point is that the Space Elevator will be built for '''other''' purpose-to decrease payload’s sending cost to space and the necessary money will be allocated for it. And as soon as the Space Elevator is built it should be used first of all in struggling against its primary obstacle-the space debris and when it will be done the Space Elevator may begin working to deliver the payload into space. So, struggling against space debris is Space Elevator’s additional but necessary function. If it was not so, nobody would build such an expensive structure as Space Elevator ''only for'' struggling against space debris, and manufacturing the petals and fastening them to the Space Elevator’s cabin does not demand a lot of money.<br />
<br />
<br />
=REMOVING THE GEOSYNCHRONOUS SPACE DEBRIS=<br />
<br />
As we have already said, the space debris objects at/near the geostationary orbit cannot be removed by means of the technology described earlier in this paper and we explained why. Therefore, for this purpose a bit different approach should be used and we conventionally call it ''space broom''. We imagine it in the following manner:<br />
<br />
The Space Elevator’s cabin reaching the geostationary orbit stops at this altitude and then deploys the petal with ''very long rod'' consisting of two parts and connecting the petal to cabin. The cabin with the electric motor will move/rotate the rod with petal so that it to touch the satellite against its own orbiting direction, thus slows it down and turn its orbit into ellipse. This ellipse will have the same apogee that it had before but with much lower perigee where the satellite will nearly touch atmosphere’s rarefied layers and consequently due to atmospheric drag its orbit would decay. Because of geostationary orbit’s altitude-35 786 kilometers quite high delta-v would be needed for de-orbiting, about 1,500 m/s. The petal should touch the satellite softly (in order not to break it into little pieces since it would lead multiplication of the space debris) it and then very quickly increases the push to reach the above-mentioned delta-v. After this, ''space broom'' (thus we call this long rod with the petal) will deal with next satellite to remove it.<br />
<br />
Under such approach we do not need the huge petal (its area should be commensurable to satellite’s size), besides the petals can be made of any material that would withstand such insignificant touch to satellite. Petal’s inner side (that actually touches the satellite) should be covered with some soft and porous material that would guarantee soft touch to satellite. But from the other hand, the rod connecting the Space Elevator’s cabin to the petal should be quite long due to following reason:<br />
<br />
As well-known, the geostationary satellites are “fixed” relative to Earth’s surface, the same concerns the Space Elevator. This means that these satellites are fixed relative to Space Elevator and its cabin and are placed (actually “will be” would be more suitable phrase) at some certain distance from it and as a rule these distances are equal to hundreds and thousands of kilometers (to have clear idea about these distances, it would be enough to recall that the circumference of the imaginary circle at the geostationary altitude around the Earth is equal to 264 924 kilometers). Therefore, to get them very long rod would be needed since it is no likely that ''exactly'' space debris objects to be found in the close vicinities of the Space Elevator since operating and “dead” satellites are distributed at the geostationary orbit ''approximately equally''. The longer this rod is the more useless satellites it can remove from the orbit and lower down to the Earth.<br />
<br />
But of course not all of the geostationary satellites are the space debris; some of them are still operating satellites that ''must not'' be touched by ''space broom'', but in fact it may touch them when deploying in space and thus accidentally change their orbits (this is absolutely intolerable, the geostationary satellites should have the circular orbit at the certain altitude-35 786 km). This is the reason why we should use the ''space broom'' with the rod consisting of ''two'' parts. The first electric motor installed on the Space Elevator’s cabin will move/rotate the whole ''space broom'' around the Space Elevator’s cabin while the second electric motor installed between these two parts will move/rotate the second part so that the petal (fastened to the second part’s end) to be in front of satellite, then touches this satellite and lower it down to the Earth as described above. So, both electric motors will operate to aim at the necessary satellite that should be removed from the orbit; the second motor will also serve to pushing the satellite. This situation is depicted on the image below:<br />
<br />
[[Image: 77.JPG]]<br />
<br />
In order to maintain stable push during the process of de-orbiting we think that the petal should make the right angle to satellite’s trajectory, otherwise the satellite can slide out from the petals. Therefore we think that the third electro motor should be installed between the rod’s second part and the petal that will control petals’ attitude towards the satellite which we intend to remove from its current orbit.<br />
<br />
Of course, rotating this ''two-part'' rod needs a lot of energy; therefore the rod should be made of very light material and can be actually very thin. In fact, the only requirement set against the material is that is must not be elastic, but it must be ''rigid'', otherwise when moving the long rod it may actually vibrate and it will probably make problem for precise targeting the needed space debris object.<br />
<br />
Generally, there it is possible ''space broom''’s a bit different way of operating. As mentioned above for de-orbiting the geostationary satellite quite high delta-v would be needed-1,500 m/s while for escaping from the Earth a bit less delta-v is required. Indeed, the satellite’s speed at the geostationary orbit is equal to 3 km/sec and the value of the ''Escape Velocity'' at this altitude is equal to 4.32 km/sec; this means that for removing the geostationary satellite we can either de-orbit it and for this purpose 1.5 km/sec in needed, or we can accelerate the satellite and in this case the necessary delta-v is equal 1.32 km/sec (this is the difference between the values of the ''Escape Velocity'' and ''Orbital Velocity'' at the geostationary orbit). As we see it is a bit easier for the ''space broom'' to force the satellite leave the Earth rather than to lower it down. The detailed way of operating of the ''space broom'' would be absolutely the same-the petal will push the satellite softly, and then ''very quickly'' increases the push to reach the needed velocity. In fact, the only difference will be the circumstance that when we intend to remove the satellite placed ''eastwards'' of the Space Elevator we should ''accelerate'' it while during removing the satellite placed ''westwards'' of the Space Elevator we should ''decelerate'' and lower it down. The reason of it is that the Earth (and the Space Elevator also) rotates from westwards to eastwards, therefore when accelerating the satellite it is possible to send it out from the Earth’s orbit without fearing that it may actually hit the Space Elevator or its long cable and this would be possible if the accelerating satellite is placed eastwards of the Space Elevator, that is ''in front'' of this structure; as for the satellites that we intend to decelerate their orbits (already turned into ellipse) they can collide with the Space Elevator and its cable in any case (without depending at which side of the Space Elevator they were placed from the beginning) and to avoid such undesirable collision we can use the very structure of the pair of petals described in the first part of this paper. However, we think that if the ''space broom'' when decelerating the satellites also changes/tilt their flying trajectory with the several degrees then satellite’s path will not cross/hit the Space Elevator and its cable. To achieve this, the ''space broom'' should push the satellite backwards and also a bit laterally.<br />
<br />
Also, we think that it would be useful the petal to have some video camera and/or radar to identify exactly the very space debris object that should be removed from the geostationary orbit. Of course, the ground-based stations with their database can indicate precisely enough where to the petal should be directed for pushing the satellite; however we think that to make sure that the ''space broom'' is removing the needed space debris object and not the operating satellite the video camera and/or radar would be good assistant.<br />
<br />
Now, how the ''space broom'' could be carried from the Earth and then deployed in space? We should not forget that ''space broom''’s proposed length should be hundreds or thousands of kilometers, otherwise its performance would be ineffective and hence its building would not be justified; besides its rod should consist of two parts. To our mind the Space Elevator’s cabin when ascending should carry rod’s first part’s initial end (the one that is actually fastened to the cabin with the first electric motor) while the other end with second part will be placed on the base station near the Space Elevator. When the cabin ''reaches and overcomes'' the altitude equal rod’s first part’s length then it would carry the second part along the Space Elevator’s cable, just like we raise the chain with its rings from the floor in our hands. After reaching the geostationary altitude that is being in the state of weightlessness, the electric motor(s) will position the rod in the needed location and the ''space broom'' will begin operating as described above.<br />
<br />
=Source of energy for space broom=<br />
<br />
Two electric motors for moving the ''space broom'' and precise aiming at the space debris object(s) need source of energy. This problem generally is linked to the problem of getting the energy for the Space Elevator as such. Therefore, we think that when this very problem is solved in a general sense, the part of this energy could be actually distributed for operating the ''space broom'' (the Space Elevator’s cabin does need energy when hanging fixed on the cable at the geostationary altitude unlike lower altitudes where the cabin should use the brakes to maintain some certain altitude). As for alternative source of energy, we could use huge solar panels or nuclear reactor placed at Space Elevator’s cabin; as concerns transmitting the energy to second electric motor and video camera/radar, it could be accomplished through the rod (in this case the rod will act as ordinary electric cable) itself or by means of microwave/laser beam.<br />
<br />
One important issue about the ''space broom''. Generally nobody tries to de-orbit the geostationary satellites since it requires huge amount of fuel\energy and this is justified because it would be too expensive to afford sending the satellite into space with additional fuel for de-orbiting. But the ''space broom'' is a different matter since for its operating we need spending not the fuel but the energy that we can get from the solar panels in a continuous mode.<br />
<br />
How much time it will take the ''space broom'' to clean the geostationary orbit from space debris objects? We think that just after the ''space broom'' finds and directs downwards the aimed object it should continue this job-finding and removing other geostationary space debris objects; in other words we propose that the ''space broom'' should begin its performance with removing the ''outermost'' (relative to Space Elevator’s current position) space debris object that it can physically reach with its rod’s full stretch (in this case the rod will be ''almost'' fully opened). As soon as the first object is removed the ''space broom'' should remove the second one and so forth until removing all space debris objects lying on one certain side of the Space Elevator, for example to the east. After finishing this job the ''space broom'' should do the same work on the other side of the Space Elevator; after doing this its performance will be done and we can descend the ''space broom'' down to the Earth. So, how much time will be spent on this? This time approximately depends on detailed information about exact location of the geostationary space debris objects; the more detailed we know this, the less time will be spent for searching and aiming at the object that we intend to remove; this time also depends on how quickly the electric motors can work, the mass of the rod and on the energy distributed for the ''space broom''. We propose that this is the matter of several days or so, however only the practice can show us the space broom’s real rate of performance.<br />
<br />
When describing above the ''space broom''’s operating mechanism we mentioned that the petal after touching softly the satellite should increase the push ''very quickly''. Why it is so important? For de-orbiting the satellite we should decrease its speed by 1.5 km/sec and when doing this the petals carrying the satellite will cover some certain distance in space. It would be very useful if this distance is as short as possible because if this distance is too high the satellite can actually hit to other ones placed at the same orbit. In other words, satellite’s speed should be accelerated/decelerated as quickly as possible. This circumstance by the way somehow restricts the amount of the geostationary satellites that can be removed by the ''space broom'' because if the satellite is too far from the Space Elevator then the ''space broom'' will be able to reach it as such, but it will not be capable to decelerate the satellite properly.<br />
<br />
As we mentioned above the geostationary satellites are ''approximately equally'' distributed at their orbit and that the circumference/length of this orbit is quite high-264 924 kilometers. To clean this orbit completely from the useless junk very long rod would be needed for the ''space broom'' and it is not likely to be designed and manufactured from the technical point of view. This means that the ''space broom'' is capable for cleaning its near vicinities only, as for cleaning the whole geostationary orbit this construction should be delivered down after finishing its job and then carried in space by other Space Elevators (of course if they are built) built at other places on the Earth.<br />
<br />
And one more note about ''space broom''’s possible working range. As we have already seen the number of the space debris objects that can be removed with this construction mainly depends on rod’s length, but nothing impedes us to use it for removing not only the geostationary space debris but also the ones orbiting the Earth at near altitudes-higher and lower. The mechanism of operating would absolutely the same with the exception of one detail-when eliminating the object ''moving relative'' to ''space broom'' this very circumstance (that is difference between the speeds of non-geostationary satellite and ''space broom'' fixed relative to the Earth) should be taken into consideration when aiming at the moving object, the same concerns the ''geosynchronous'' satellites that are not fixed relative to the Earth and Space Elevator unlike geostationary ones.<br />
<br />
In practice using the methods described in the paper presented here with other ones will enable the humankind to clean the low and high Earth orbits from the space debris and to make the both manned and unmanned spaceflights safe.<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Kessler_syndrome<br />
<br />
2. http://webpages.charter.net/dkessler/files/KesSym.html<br />
<br />
3. http://www.space.com/news/090211-satellite-collision.html<br />
<br />
4. http://www.guardian.co.uk/science/2008/feb/24/spaceexplorationspacejunk<br />
<br />
5. http://orbitaldebris.jsc.nasa.gov/faqs.html#3<br />
<br />
6. http://en.wikipedia.org/wiki/United_States_Strategic_Command <br />
<br />
7. http://www.au.af.mil/au/awc/awcgate/usspc-fs/space.htm<br />
<br />
8. Neal, H. L.; S.L. Coffey, S.H. Knowles (1997). "Maintaining the Space Object Catalog with Special Perturbations". Astrodynamics (Sun Valley, ID: AAS/AIAA) v.97 (Part II): 1349–1360.<br />
<br />
9. Vallado, David (2001). Fundamentals of Astrodynamics and Applications. Torrance: Microcosm Press. p. 958. ISBN 1881883124.<br />
<br />
10. Hoots, Felix R.; Ronald L. Roehrich (December 1980). "SPACETRACK REPORT NO. 3 - Models for Propagation of NORAD Element Sets". ADC/DO6 (Peterson AFB: Project Spacetrack Reports, Office of Astrodynamics, Aerospace Defense Center).<br />
<br />
11. http://www.esa.int/esapub/bulletin/bulletin133/bul133f_klinkrad.pdf page 5<br />
<br />
<br />
<br />
'''Appendix''': <br />
<br />
Animations illustrating the cleaning process:<br />
<br />
At ''Low Earth Orbit'': <br />
<br />
[[Image: Cleaning the Low Earth Orbit.gif]]<br />
<br />
At ''Geostationary'' orbit <br />
<br />
[[Image: Cleaning the Geostationary Orbit.gif]]</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_5&diff=3674OpenSpace 52013-09-21T13:09:23Z<p>Eagle9: /* The technical aspects regarding the Space Catapult */</p>
<hr />
<div>== '''Space Catapult''' ==<br />
<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
=INTRODUCTION=<br />
<br />
<br />
The new method for sending the spacecrafts in deep space is presented here. The paper describes the long rod rotated by electro motor placed at the Space Elevator’s counterweight and at Lagrangian points. This simple structure will enable the rod to gain high velocity and carry the payload with it. After reaching the desired speed the rod will release the payload that will fly in space along the imaginary circle’s tangent. This structure we called Space Catapult and it should work with the assist of Space Elevator. This latter should be used for carrying the payload from the Earth to Space Catapult’s rod.<br />
<br />
For exploring the outer space the humankind generally uses the rocket engines, mostly chemical-propelled ones. They enable us the explore near-Earth celestial bodies and other planets in the solar system. They even enabled us to send several deep space missions beyond the solar system such as '''Pioneer-10''', '''Pioneer-11''', '''Voyager-1''', '''Voyager-2''', however by means of this technology the flight lasts undesirably long and it seems to be impossible to reach remote celestial bodies in space such as stars, so new technologies are necessary for this purpose. However new technologies do not necessary imply new kind of rocket engines, such as ''Ion Drives'' because they are capable for gaining several ten times higher speeds only, but for remote celestial bodies even they are not suitable. Besides, they need a huge amount of energy to be stored onboard the spacecraft and this will make additional problems. So, high speed should be achieved with absolutely different approach. How this can be done?<br />
<br />
High speed can be easily achieved by means of fast-rotating rod around the electric motor. The motor’s rotational speed can be very high; the rod also can be quite long, hence the rod’s end’s linear speed can be extremely high, absolutely unachievable for any other technologies nowadays. The payload should be fastened at the rod’s end where the linear speed generally reaches maximal value. After reaching the necessary speed the rod will release the payload that will fly along the tangent from the current position. Thus the electric energy can be turned into payload’s speed and its velocity could be as high as we wish (except the ''speed of light'' of course). In principle the '''Space Catapult''' (thus we call this structure) would be the simplest, the most convenient and direct way for converting the energy/electricity into speed and conveying it to payload. <br />
<br />
As we see the Space Catapult is quite uncomplicated structure, however if we wish to gain high speeds we should deploy it in space, not on the Earth. Indeed, our planet is surrounded with dense atmosphere that impedes any quick motion, so if we rotate the rod quickly the atmospheric drag and generated heat would burn it very soon, therefore the Space Catapult should be built and deployed in space only, and as we suppose-at the Space Elevator’s counterweight. In other words, the Space Elevator’s counterweight will operate as Space Catapult. See image below:<br />
[[File:Space-catapult.jpg]]<br />
Generally, what is the Space Elevator ['''1''']['''2''']? According to modern concepts it will be the tall vertical structure built on equator and will have height of several ten thousand kilometers with its thin cable fastened to the base station on the Earth and with counterweight placed higher geostationary orbit. Because of balance between centrifugal force and gravity this structure will be stretched and the cabin will move along its cable carrying the goods into high orbit. After delivering the payload, the cabin will descend and carry the next one.<br />
In Space Elevator’s concepts several solutions have been proposed to act as a counterweight: <br />
<br />
1. Heavy, captured asteroid <br />
<br />
2. Space dock, space station or spaceport positioned past geostationary orbit <br />
<br />
3. Extension of the cable itself far beyond geostationary orbit. <br />
<br />
The third idea has gained more support in recent years due to the relative simplicity of the task and the fact that a payload that went to the end of the counterweight-cable would acquire considerable velocity relative to the Earth, allowing it to be launched into interplanetary space. However this idea cannot be completely shared by us due to following reason: <br />
<br />
It is well-known that the values of both '''Orbital''' and '''Escape Velocities''' decreases with increasing the altitude while the '''tangential velocity''' of Space Elevator’s cable increases. We can see the differences between them from the chart presented below:<br />
[[Image: Cxrili.gif]]<br />
<br />
As we see from this chart the ''tangential velocity'' of the Space Elevator even at its end (144 000 or 200 000 km altitude) is not very high to decrease the necessary time for covering the distance from the Earth to remote celestial bodies significantly. To achieve this, even the longer Space Elevator would be needed (its ''tangential velocity'' is directly proportional to its length) and this circumstance would complicate the technical task for building such Space Elevator. Because of this, there is no necessity to extend the cable itself far beyond geostationary orbit as proposed in the third variant. In any case, we have already seen that by means of Space Catapult it is possible to gain such huge velocities that are absolutely unachievable with other technologies, for example with Space Elevator. Therefore, using the counterweight and placing the Space Catapult there definitely has got some technical sense. <br />
<br />
However, we think that the question where the Space Catapult should be placed needs further discussion. Theoretically, the Space Catapult with its payload and nuclear reactor/solar panel needed for rotating the rod may be mounted not only at the counterweight, but on the Space Elevator’s cabin also that can carry all these goods to space in a usual way, as it should do it according to Space Elevator’s modern concepts. This option is quite possible, however for realizing this we need to know the mass of the payload, nuclear reactor/solar panels’ mass plus Space Catapult’s mass from one hand and Space Elevator’s lifting capacity (this ''must'' be more) from other hand, but these data are not available nowadays, therefore we think that the Space Catapult should be still mounted at the Space Elevator’s counterweight where it will be possible to send the payloads into deep space in ''continuous mode'' at high velocities.<br />
<br />
As we saw the Space Catapult is capable to gain very high velocities; however there is being developed other technologies and they in future will enable the spacecraft to fly at high speeds in space. These are Ion Drive systems, more precisely the most perspective one-''Variable Specific Impulse Magnetoplasma Rocket'' (VASIMR) which still under development can be used in future for deep space missions. Can these engines and Space Catapult be the rivals in space? Since none of them have been built and used in space yet we cannot give a persuasive answer to this question; however still it is possible to underline Space Catapult’s one significant advantage: if the future spacecraft uses the VASIMR (or any other kind of Ion Drive) engine it will definitely need to be equipped with nuclear reactor, otherwise the spacecraft will not be able to gain high speeds, also it will need to carry fuel tanks for this purpose. As for the Space Catapult, it can give much higher speed to spacecraft, besides it will have ''stationery'' power plant (see ''Energy source placed on the Space Elevator’s counterweight'') at the Space Elevator’s counterweight, so the payload will ''not'' have to carry the nuclear reactor onboard and this circumstance will lighten the work for deep space spacecraft. Besides, we should not forget that unlike the spacecrafts equipped with ion drive engines the Space Catapult will need no fuel for gaining high velocities. <br />
<br />
Briefly, Space Catapult’s advantages over any kind of propulsion systems are: <br />
<br />
1. Ability to gain any speed that is absolutely unachievable by means of other kinds of engines. <br />
<br />
2. No need by spacecraft to carry energy source that would make it too heavy and impracticable.<br />
<br />
=The Space Catapult needs long rod=<br />
<br />
When building the Space Catapult at Space Elevator’s counterweight we should install quite long rod there, the shorter the rod is, the easier would be installing it, however we should note that rod cannot be extremely short, let’s say 1 km length or so due to following reason:<br />
<br />
When we are going to send some payload into space, we need not only high velocity, but one certain direction also. The little inaccuracy in direction, inclination in several arcminutes is actually acceptable since the spacecraft would easily balance it with its engines; however great inclination from the initial direction would send the spacecraft into the completely different direction and in such case the whole mission will fail.<br />
<br />
If two Space Catapult’s rods have the length of let’s say 1 kilometer and 10 kilometers, then for giving to payload some certain linear speed (for instance 100 km/sec) these rods should rotate at different angular velocity. It is easy to ascertain that the shorter rod should rotate 10 times faster to gain the same linear speed than the rod with more length. But the faster the rod rotates, the more difficult will be to “catch” the needed moment for releasing the payload from the rod for sending it towards some certain direction. If the rod is too short, then it has to rotate very quickly for gaining some certain linear speed and therefore it will be extremely difficult catching the needed moment for releasing the payload. Hence, too short rod can make problem for sending the payload to some certain direction in space especially at high velocities. So, based on payload’s needed velocity we should find rod’s desired, minimal length that will enable us to send the payload in space to necessary direction without fear that it may yaw from the course. <br />
<br />
However, rod’s length will be crucial for payload’s abilities for withstanding the acceleration also. As an example, we can try to calculate its value which the payload will have to withstand during rod’s rotation. The acceleration of the body rotating at the circle with some constant velocity is calculated by the following formula:<br />
<br />
[[File: Acceleration - Copy.jpg]] <br />
<br />
Where a is acceleration in ''m/sec''<sup>2</sup>, ''v'' is payload’s linear velocity on the circle in ''m/sec'' and ''r'' is radius of the circle in ''meters'', in our case it is equal to rod’s length. Let’s assume that the rod is 100 km length and the electromotor rotates it so that payload’s speed is equal to 50 km/sec, in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design and manufacture the spacecraft’s subsystems (avionic and etc.) capable to withstand such acceleration. This circumstance somehow restricts the speeds that we can achieve, in any case their values actually depends on spacecrafts’ abilities for withstanding g-loads. But what can we do if much higher speeds are needed? The answer directly derives from that formula: the radius should be more; by the way note that this is additional reason why the longer rod is more useful. If we are able to make the extra long rod, then this will enable us to gain much higher velocities. <br />
<br />
What material should be used for manufacturing the rod? It is obvious that if very high speeds are needed the rod should be long and even in this case the acceleration at its end will be quite high, therefore ''sufficiently strong and light materials'' are needed for this purpose and making them is as similar challenge as in case of Space Elevator where the same requirements arises for the cable’s material. The lightness is needed because in case of heavy rod a lot of energy will be needed to rotate it; the strength is needed because in case of lack this property the rod will be destroyed due to great acceleration.<br />
<br />
=The mechanism for holding and releasing the payload=<br />
<br />
How the payload can be held by Space Catapult’s rod during rotation and how it can be released from the rod? We think that using ''electromagnet plus mechanical holding devices'' would be a good solution. More precisely, after the payload is attached to the rod it must be held by means of both methods until the rod accelerates and reaches necessary velocity (it may take even several days), but with approaching the desired speed the mechanical device should release the payload however the electromagnet(s) should still hold it. The explanation of such approach is following: generally the mechanical devices are much slower/sluggish in performance than electronic ones. We have already said that when releasing the payload the extreme accuracy is needed and mechanical devices cannot guarantee ''the exact time of releasing'' the payload unlike electronic ones. That is, it’s unlikely that mechanical devices can release the payload at some certain moment when needed while in case of electromagnet it would be enough to cease electric current there, it would lead to immediate vanishing of the magnetic field and sending the payload along the tangent from the point where the payload would be at the current moment. <br />
<br />
<br />
We think that the ''fastest control system'' would enable to release the payload to certain direction. This system (extremely fast-operating computer plus measuring equipments) should know the current position of the rod’s end, the current speed, the needed direction and be capable for computing the necessary moment for giving the order for diminishing the voltage for electromagnets and hence releasing the payload to desired direction and velocity.<br />
<br />
=Rod’s plane of rotation towards the Earth=<br />
<br />
The Space Catapult’s rod when rotating makes the circular plane/flatness in space and this plane may be horizontal/parallel to Earth surface, that is making the right angle to Space Elevator’s cable or it may be placed along the cable; see the both possible situations here:<br />
<br />
[[File: Planes-of-rotation - Copy.jpg]] <br />
<br />
Both approaches have got their advantages/disadvantages and here we will discuss this question, first of all from the point of view of safety.<br />
<br />
For gaining extremely high velocities quite long rod would be needed, maybe with the length of several thousand kilometers or even more. If such rod is placed ''along'' the Space Elevator’s cable then the rod during rotation will cross many orbits from the ''Medium Earth Orbit'' to ''High'' ones. When rotating, the rod may actually hit any satellite and/or space debris object and such collision can lead to rod’s complete destruction; therefore we should choose such plane which would be much more free from any artificial objects; hence if the rod rotates ''horizontally/parallel'' to Earth’s surface at high enough altitude where the satellites’ population is relatively low then this measurement would justify itself because under such circumstance the rod will not cross satellites’ orbits (rod’s plane of rotation will simply coincide to ''one'' orbit’s path). However, we should also note that this altitude actually depends on the Space Elevator’s proposed length. Indeed, the Space Catapult’s rod should be mounted at the Space Elevator’s counterweight; this counterweight from its side should be placed at the end of the Space Elevator at such altitude where the satellites’ population is as low as possible. This means that Space Elevator’s proposed height should be agreed with mounting Space Catapult on its counterweight. According to various databases the number of man-made objects at high orbits, more precisely beyond geostationary orbit is much less than on the lower orbits ['''3''']['''4''']['''5''']['''6'''], therefore the Space Catapult with its rod should be located at the altitude of 50 000-60 000 km above the sea level. At such altitude the space is almost free and nothing will impede rod’s rapid rotation. Besides, the satellites at high orbits are orbiting around the Earth slower than on the lower orbits (as known any satellite orbits around its primary body slower in apogee than in perigee), therefore if some tracking system is mounted at Space Elevator’s counterweight then it will enable the Space Catapult to avoid undesired collision with satellites during Space Catapult’s performance. In other words, the Space Catapult should operate only when the there are no satellites near its vicinities.<br />
<br />
Now we will try to discuss this question from other side.<br />
<br />
How the payload can be transferred from the Space Elevator’s cabin to the Space Catapult’s rod? One way is following: cabin reaches the counterweight where the payload will be released, then payload will be mechanically conveyed to rod, continues its way ''on the rod'' (like the train rides on the rails) and after reaching rod’s end it stops, the rod begins rotating and after gaining necessary linear speed it releases the payload to needed direction. This method is generally realizable; however it seems to be too complicated and unpromising compare to the second one: the Space Catapult’s rod is stopped in space so that it to be directed downwards to the Earth and be parallel to Space Elevator’s cable. The Space Elevator’s cabin moving along the cable with payload stops at the cable ''near'' the end of the Space Catapult’s rod and releases the payload that will fly to the rod, attaches itself to the rod’s end (here the electromagnets would be useful), the rod begins rotating and after gaining needed linear speed will release the payload to necessary direction.<br />
<br />
This second way seems to be more promising because the first one is much more complicated as we have already said: first of all there would be needed some mechanical devices for transferring the payload from the Space Elevator’s cabin to counterweight, the counterweight should have the hole for the payload to move through it from below (we should not forget that the Space Catapult should be mounted ''at'' the counterweight, not ''beneath'' it), besides the rod should be made so that it to have some conveying surface (rails for instance) the payload to move on it. As we see it would be much more convenient if it is possible to convey the payload from the cabin to the rod directly and this would be feasible under the second method which is depicted below:<br />
<br />
[[File: Convey.jpg]] <br />
<br />
One more aspect regarding Space Catapult’s position. This structure, its rod, its electro motor and etc should be mounted at Space Elevator’s counterweight so that the rod to be placed westwards from the cable. The reason of it is following: when the Space Elevator’s cabin stops and releases the payload (which should fly to Space Catapult’s rod) the current speed of which will/should be more than the value of the ''Orbital/Escape Velocity'' at the current altitude. After releasing the payload will fly westwards and upwards because its orbit will be ellipse, under ellipse the payload will fly higher to apogee and at the speed less than Space Elevator’s current speed at the given altitude, in other words the released payload will “lag behind” the Space Elevator’s cable; therefore payloads’ ''stopping points'' at the cable and Space Catapult’s rod’s length should be calculated and chosen so that the payload to fly directly towards rod’s end. This process would be feasible in both cases-if the rod’s plane of rotation is parallel to Earth’s surface and if it is placed along the cable-but still this would be easier for the payload to achieve the rod’s end if the rod is placed along the cable because at least the distance that the payload should cover in space will be less.<br />
<br />
The length of the Space Catapult’s rod placed at the Space Elevator’s counterweight might vary since for various spaceflight purposes different initial speed will be needed and relatively low speed could be achieved by means of shorter rod. Because of this reason it might be necessary to change Space Catapult’s rod’s length, therefore it would be useful if the rod consists of two parts where the first part would be perpetually attached to electro motor and the second one will be attached to the first part if necessary. For this operation Space Catapult’s rod should be placed along the cable since the relative nearness would make this operation quite easy and it could be accomplished by the crew directly from the Space Elevator’s cabin stopped at the needed altitude. <br />
<br />
For deciding the question how the Space Catapult’s rod should be placed towards the Space Elevator’s cable we should take into consideration one substantial circumstance-to which direction do we plan to send the payload in space by means of Space Catapult? This circumstance will influence deciding this problem due to following reason:<br />
<br />
In case ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and if rod’s plane of rotation is parallel to Earth equator, then this plane will be orthogonal to Earth’s rotation axis. This axis from its side is tilted to ''ecliptic plane'' by 66° 34'. This means that Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 23°26'. Here follows very important consequence: under above-mentioned conditions the rod when rotating will be capable for covering only the part of the ''celestial sphere'' from 0° to 23°26' (counted from ''ecliptic plane'' northwards and southwards to ''Ecliptic poles''). This is about one fourth of the ''celestial sphere'' (23°/90°), this will not make problems if we intend to use the Space Catapult for exploring the solar system’s planets because their orbits’ tilts towards ''ecliptic plane'' do not exceed 7° (for planet Mercury, for other planets this tilt is even less); however we will not be able to send the payload for example to the nearest star ''Alpha Centaurs'' because this star is located at -42 degree according to ''ecliptic coordinate system'' in the celestial sphere.<br />
<br />
The situation will drastically change ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and ''if'' rod’s plane of rotation is orthogonal to Earth’s equator and therefore parallel to Earth’s axis of rotation. We have already discussed this option when we mentioned that the rod should be placed westwards from the cable and explained why it would be useful-for delivering the payload from Space Elevator’s cabin to Space Catapult’s rod. Under such conditions the Space Catapult will be capable to aim to any point on the ''celestial sphere''. Indeed, the Earth with the Space Elevator rotates around its axis and Space Elevator’s counterweight draws an imaginary circle in space. This circle is tilted to ''ecliptic plane'' at 23°26' and crosses this plane in two point called ''ascending'' and ''descending nodes''. The other points that are 90° away from these nodes we call point(s) of ''maximum elevation/depression'' (relative to ''ecliptic plane''). When the Space Elevator is at a''scending/descending node'' its rod and hence the payload can be directed to any point from 0º to 66º on the celestial sphere northwards and southwards from ecliptic plane. This makes about 75 % of celestial sphere. See the image depicting this situation:<br />
<br />
[[File: Node.jpg]]<br />
<br />
But when the space Elevator reaches the points of ''maximum elevation/depression'' then its rod during rapid rotation may be directed to any point from southern ''Ecliptic pole'' to ''Northern pole'' at the celestial sphere because at these points rod’s ''plane of rotation'' is orthogonal to ''ecliptic plane'' and thus the rotating rod can aim to ecliptic poles as well as other points. See this situation below:<br />
<br />
[[File: Elevation.jpg]] <br />
<br />
The situation will be similar if the Space Catapult’s rod is orthogonally placed towards cable. Under such approach Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 66° 34' and the Space Catapult will be capable to cover ''three fourths'' (66°/90°) of the ''celestial'' ''sphere'' when the Space Elevator is at the points of ''maximum elevation/depression'' and the whole celestial sphere when the Space Elevator is at ascending/descending nodes. For aiming the needed point on the celestial sphere the Earth should occupy the appropriate attitude towards the stars during the revolution around its axis, the same thing should be done under previous case described in the paragraph above. <br />
<br />
In conclusion, thinking about rod’s plane of rotation towards the Earth, we should note one important difference between above-mentioned approaches: if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, then in case of emergency during Space Catapult’s performance (for example if the Space Catapult’s rod is cut by sudden meteorite bombardment) the rod’s part with the payload may simply crash to the Earth at huge velocity if the rod at this moment is directed to the Earth. This cannot happen if Space Catapult’s rod’s plane of rotation is orthogonal to Space Elevator’s cable because payload’s rotational path will not be directed towards the Earth and hence its flying trajectory will never cross the Earth.<br />
<br />
=Braking the Space Catapult’s rod=<br />
<br />
After releasing the payload at necessary speed and direction, the Space Catapult’s rod will have a huge angular velocity that needs to be decreased to zero in order the Space Catapult’s rod to get another payload in motionless position and then to send it to space. <br />
What methods can we use to reduce Space Catapult’s rod’s rotation to zero? There are several possible ways: <br />
<br />
1. The electromotor designed for accelerating the rod may actually play a role of brakes, more precisely after releasing the payload to space the electromotor should operate/rotate in the opposite direction, hence rod’s rotational speed will be diminished to zero after that electromotor will stop operating. Under such method a bit less energy will be spent for decelerating the rod than in case of accelerating because when decelerating the rod is free from payload. <br />
<br />
2. An ordinary mechanical brakes, however due to electro motor’s and rod’s sizes a huge brake(s) would be needed to be installed on the Space Elevator’s counterweight and this circumstance would make additional problems from the engineering point of view. Nevertheless, we should admit that under such method we would not need as much energy as during accelerating; on the contrary, in this process the heat will be emitted as it generally happens during braking. <br />
<br />
3. For decelerating the rod we can use the well-known phenomenon in physics-''electromagnetic induction'': when the c''onductor/ closed circuit'' moves into the magnetic field the electric current is generated there. In case of Space Catapult we can use this phenomenon in the following manner: the conductor should be wrapped around the whole length of the rod like a helix and there should be possibility that this conductor to be turned into the ''closed circuit'' by means of mechanically connecting its ends (see the image below). After releasing the payload at necessary speed and direction this circuit should be closed, then according to ''electromagnetic induction'' the electric current will be generated in the conductor and the energy of this electric current will come from rod’s kinetic energy. Therefore, inducted electric current in the enclosed circuit will force this circuit and rod to lose kinetic energy and speed. The part of the generated electric current will be spent in prevailing conductor’s electric resistance:<br />
<br />
[[File: Helix.jpg]] <br />
<br />
The advantage of this method is that for decelerating the rod no energy will be required, as for drawback-much time will be required for this purpose because at the altitude of several ten thousand kilometers the Earth’s magnetic field is quite weak and the effect described in the paragraph above will need much time to operate and give necessary result. <br />
<br />
4. The above-described third method could be realized in a bit different way: if the conductor wrapped around the rod is a closed circuit and if we conduct the electricity there then the electric current will generate its own magnetic field that will counteract with Earth’s one. More precisely, according to ''Lenz's law'' induced current’s magnetic field will be in such a direction as to oppose the motion or change causing it, in other words induced current’s magnetic field will counteract outer magnetic field’s any change and this will cause decelerating rod’s rotation and finally its stopping. <br />
<br />
5. The obvious disadvantage of the third and fourth method described above is weakness of the Earth’s magnetic field because of which decelerating the rod may be delayed in time. For solving this problem we can create artificial magnetic field by means of electromagnets. Particularly, one electromagnet should be placed at the Space Elevator’s counterweight, very close to Space Catapult’s rod. The second electromagnet should be placed directly on the Space Catapult’s rod close to first electromagnet (actually, instead of this second electromagnet there could be used the conductor wrapped around the rod as we described above in previous methods). The reason of this nearness is that magnetic field generally weakens directly proportional to distance’s third power and much time will be needed for decelerating Space Catapult’s rod if two electromagnets are far from each other.<br />
<br />
This method probably will consume the most amount of energy but at the same time it will be the most effective because it does not depend on outer factors such as Earth’s magnetic field which is quite weak at the altitude of several ten thousand kilometers above the sea level. <br />
<br />
Eventually, which methods for decelerating the Space Catapult’s rod would be the best? As we see each one of them have got their advantages and disadvantages. We can state that we should choose one of them according to spaceflight’s profile and goal. Particularly, if we decide to send the spacecraft into the deep space mission where especially high speed is necessary then in this case ''longer/more massive'' rod would be needed rotating at very high speed. Under such circumstance much energy will be needed for accelerating/decelerating the rod. We should also take into consideration the fact how frequently the Space Catapult will operate, in other words how mane payloads it will have to send into space per some certain amount of time, week/month and etc. If time interval between two following missions is relatively high then we should choose the method that will consume less energy and more time for decelerating the rod. On the contrary, if the Space Catapult has to send payloads very often then we should choose the method that will consume more energy and enable the rod to decelerate faster. In other words, we should find ''golden mean'' between consuming time and energy. We should also take into account how much energy supply will be produced at the Space Elevator’s counterweight (see ''Energy source placed on the Space Elevator’s counterweight'') and what part of this energy can we spend for accelerating/decelerating the rod.<br />
<br />
The rod’s rotations can be decelerated much faster than accelerated; the reason of it is that when accelerating the rod has got some sophisticated device as payload and generally unmanned spacecrafts are capable to high g-loads, but still for them some restrictions exist. After the payload is released at needed direction and speed, the rod can decelerate much faster because the rod itself is quite simple device without any complex and sophisticated details. <br />
<br />
We can actually use several methods, such as the third one and then the first/fifth ones. This would be justified because of following reason: as we have already said when decelerating with the third/forth method the problem of weakness of the Earth’s magnetic field would occur, therefore much time would be necessary for described method(s) to perform and give us result. However, we should note that in the beginning when the rod rotates very quickly this method would still operate strong enough. This derives from Faraday's law of induction stating that “the electromotive force generated is proportional ''to the rate of change of the magnetic flux''”. Therefore, in the beginning when the rod is rotating very quickly we can use the third/forth method(s) and when the rod significantly brakes we can apply to the first/fifth ones-they do not depend on Earth magnetic field. In other words, such approach would greatly help us in finding the golden mean between spending energy and time necessary for decelerating the rod. <br />
<br />
And finally: after releasing the payload the Space Catapult’s rod can actually give us energy. More precisely, the electro motor itself can serve as electric generator also since we know that the same machine can operate as electric motor if it is fed with electricity and as generator for electricity if its rotor is rotated by other machines. Therefore after releasing the payload when the electro motor’s rotor is rotating very quickly it can give us energy, in result of which the rod will lose its kinetic energy and speed, as for generated energy it can be sent downwards to the Earth for our terrestrial needs (see the next section in this paper) or stored onboard the Space Elevator’s counterweight. This approach has got one substantial advantage: it does not imply additional mass (wrapped wire) that will cause problems because rotating heavier rod would consume more energy.<br />
<br />
=Energy source placed on the Space Elevator’s counterweight=<br />
<br />
As well-known, the Space Elevator’s cabin needs energy when moving along the cable and it can get it from the Earth by means of various ways, such as: laser beam, microwaves, through the cable itself and etc. On the other hand, Space Catapult also needs much energy for rotating the rod and for this purpose some energy source should be placed on the Space Elevator’s counterweight, presumably solar panels array. Doing this would demand additional funding and engineering work and this undertaking should be justified, so how can we prove that placing energy source on the counterweight would be necessary and useful? We should not forget that the energy generally could be simply transmitted from the Earth without carrying any material for energy source on counterweight; so we can justify this undertaking if we declare/prove that: <br />
<br />
1. Energy source should be designed for ''both'' Space Elevator’s cabin and Space Catapult’s rod. We can imagine it as array of numerous solar panels producing enough energy for both above-mentioned constructions. For this purpose solar panels would be better solution than nuclear reactor because they do not need nuclear fuel to be carried from the Earth to counterweight, also they are capable for producing energy in a continuous mode. By the way this circumstance will enable us to send the payload to space by Space Catapult whenever we want without depending existence nuclear fuel at the counterweight. <br />
<br />
2. Transmitting energy from the counterweight (“from above”) is better and advantageous than doing the same thing from Earth (“from below”). Indeed, when we try to transmit energy (laser or microwave beam) from the Earth to ascending cabin, the part of energy is inevitably lost and dispersed in the Earth’s atmosphere and (this is point of the question) this continues during the whole process of ascent. On the contrary, when transmitting the energy from counterweight to cabin the energy will be lost only on the little part of this voyage, more specifically until the cabin leaves the atmosphere (100 km in height) and when cabin leaves it the energy will be transmitted in vacuum without loss. <br />
<br />
3. For receiving the energy from the Earth the huge solar panels (in case of laser beam) or antennas (in case of microwaves) will be needed to be mounted on the counterweight and this is additional mass and additional engineering work.<br />
<br />
We think that these arguments given above are enough for shoving that placing energy source on the Space Elevator’s counterweight have advantages over transmitting energy from the Earth and as conclusion we can state that energy source on counterweight would serve both space transportation systems-Space Elevator and Space catapult. <br />
<br />
As addition, we could use the energy produced on the counterweight for terrestrial needs also. Indeed, there have been developed numerous projects for receiving energy from space since 60-ies implying producing it by means of solar panels and then transmitting to the Earth. Combining all these three goals we can conclude that placing solar power plant on the Space Elevator’s counterweight would be triply useful and advantageous. In other words, when the Space Catapult and Space Elevator do not function, the energy produced on the counterweight should be directly transmitted to the Earth for our terrestrial needs and thus the idea of Space Elevator, Space Catapult and space power plant will be combined in one project.<br />
<br />
=Assembling the Space Catapult=<br />
<br />
Assembling in space such a huge structure as Space Catapult will not be an easy task from the technical point of view and definitely needs special engineering approach. Besides, we think that Space Catapult’s rod should be mounted at the Space Elevator’s counterweight separately from every other parts of the Space Catapult (e.g. electro motor and etc.); this circumstance is caused by rod’s gigantic sizes. More precisely, electric motor and plus any other equipments necessary for Space Catapult’s performance should be delivered to space by means of Space Elevator in a usual way; as for Space Catapult’s rod, it is a different matter and it should be delivered and mounted separately in the end. <br />
<br />
Eventually, Space Catapult’s rod will be quite long, perhaps much more than 100 kilometers. It is obvious that delivering such a long rod as ''one single unit'' would be quite difficult task; also it is possible that due to its total mass the Space Elevator’s cabin will not be able to deliver such rod at all, but we have already mentioned that the Space Catapult may have the rod with various length; more precisely the rod may consist of two/more parts. In such case these parts should be delivered towards the counterweight separately and then assembled. <br />
<br />
But the Space Elevator’s cabin can actually deliver the Space Catapult’s rod as ''one single unit'' in space. We think that this would depend only on rod’s mass. The Space Elevator’s lifting capacity is not well-known yet; however apparently it will not exceed one hundred metric tons and if Space Catapult’s rod is made of extra light material then cabin will be able to deliver it in space and in such case the following question will arise: how the cabin will deliver such a huge object in space without any damage?<br />
<br />
This can be done by means of two cabins. Generally, Space Elevator’s conception implies only one cabin moving along the cable, but for some special purpose (like delivering Space Catapult’s rod in space) we can use the second cabin also that will descend downwards after finishing its job and will not participate in Space Elevator’s further performance. As for the process of delivering the rod, we can imagine it in a following manner: at first the rod will be placed horizontally on the Earth (thus it must be manufactured and then transported to the Space Elevator’s base station), then the Space Elevator’s first cabin will carry rod’s one end along the cable while the rod’s second end will be moved on the Earth so that the rod to take more and more vertical position. When the rod is in vertical position the second cabin will capture rod’s second end and will carry it in space. We think that without the second cabin it would be quite difficult for one cabin only to carry long/heavy rod because the rod may actually shake and crash to the Space Elevator’s cable and this is absolutely undesirable. <br />
<br />
So, as we see in principle it looks to be quite easy, however the assembling may complicate due to rod’s length. In this case it would be better to carry not the rod as ''one single unit'' but its parts and then to assemble them in space in the following manner: ''two'' cabins will carry the first part as described above, when this part is delivered to space and temporarily hung at the cable the next two cabins will carry the second part that will be attached to the first one from below; the other parts will be delivered to space and assembled into the rod in the same way. <br />
<br />
The obvious disadvantage of the above-described method is that each part needs two cabins on the Space Elevator’s cable, besides the humans will be needed for assembling the rod from these parts in the atmosphere’s upper layers; therefore we think that the first way-delivering the rod into space as one single unit still would be easier and more realistic; besides we should take into consideration the fact that if the rod is assembled the additional devices will be needed ''on the rod itself'' for joining these parts and this circumstance would lead to increasing the rod’s total mass and this is undesirable. See the image showing assembling process:<br />
<br />
[[File: Assembling.jpg]] <br />
<br />
Whatever design/structure the rod has-assembled from several parts or as one single unit, it must be delivered to its destination-Space Elevator’s counterweight and must be fastened to electro motor’s own axis. But the problem is that the rod will be quite long and also the fact that Space Catapult’s electro motor will be placed at counterweight’s upper side (or at the ''lateral'' side if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), so it will be necessary the rod coming from below to be moved to counterweight’s upper/lateral side, besides the rod should be docked with electro motor’s axis as accurately as possible. How is it possible to realize such complex engineering operation? Here we can indicate one possible theoretical way: <br />
<br />
The rod will be parallel to Space Elevator’s cable when carried by cabin, but later the cabin’s mechanisms should rotate it so that the rod to be orthogonal to Space Elevator’s cable (this will not be necessary if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), exactly in this position the rod should be delivered to counterweight, besides the rod when moving along the cable should be shifted a bit upwards (relative to the Earth) than the cabin itself. Under such conditions we will easily achieve docking the rod to electro motor’s own axis which from its side should have some trapping device (magnetic for example) to “catch” the rod and thus guarantee docking the rod to electro motor and finishing assembling the Space Catapult as a whole. But if the rod’s plane of rotation is parallel to cable then assembling process will be much easier because the ascending rod may directly dock to electro motor’s own axis. See the image showing this process:<br />
<br />
[[File: Deliver - Copy.jpg]] <br />
<br />
We think that it would be useful if one Space Elevator is built specially for Space Catapult with its base station located on the land, not the ocean. This would be justified because transporting Space Catapult’s rod from its place of manufacture to Space Elevator’s base station should occur on the land by means of several transports simultaneously (due to rod’s great length), this will enable us to deliver the rod to its destination without any damage while this kind of operation is hardly possible on the water.<br />
<br />
=The technical aspects regarding the Space Catapult=<br />
<br />
As an example, we can try to calculate/ascertain all possible kinds of aspects regarding the rod with some certain mass and sizes, for example we can assume the Space Catapult has got 100 km length rod. <br />
<br />
The circumference of the circle that this rod’s end will draw in space will be equal to 2πr=628 km. As we have already mentioned payload’s abilities for withstanding the g-load is restricted, so if the electromotor rotates the rod so that payload’s speed is equal to 50 km/sec (this means that it will take 12.56 seconds for the rod to make one complete revolution), in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design the spacecraft that will withstand such acceleration, but what about the rod itself? Which material can be used for designing this rod, what will be its mass and how much energy and time will be needed for the rod to reach this velocity? <br />
<br />
For manufacturing the rod we should choose the material with very low density and highest value of strength. Currently, the ''Carbon nanotubes'' are the best candidates for this purpose. What will the mass of the rod made of this material? This depends on width also and it should be as less as possible (otherwise the rod will be too heavy and too wide for transporting from manufacture place to Space Elevator’s base station and for delivering it to space by means of Space Elevator) but from the other hand the ''applied load'' will not let us to design very narrow rod.<br />
<br />
Let’s assume that we intend to launch the payload with the mass of 10 000 kg (during calculation we will use ''SI system'' only). To clarify what kind of material will be able to withstand the acceleration we should calculate and then compare two values: the ''applied load'' and ''tensile strength''. For calculating the first one we should multiply g-load (which we already know-2 550 g) to its mass-10 000 kg, we will get 25 500 000. As for calculating tensile strength, we should take its values (for Carbon nanotubes it varies from 11 000 MPa to 63 000, we will take some medium value-40 000 MPa) and multiply it to cross-section’s area, in our case rod is cylinder with circular cross-section. If radius of cross-section is 1 meters then its area is 3.14 square meters, multiplying this value to value of tensile strength (40 GPa as said) we will get 125 600 000 000 and this is significantly more than value of applied load-25 500 000. Of course, we should also take into consideration ''factor of safety'' which is generally equal to 2 and this indicates us that for safety the payload’s actual mass should be twice less but in our case as we see the rod will be able to accelerate the payload to above-mentioned speed. By the way, note that if that g-load ''2 550 g'' is almost at the payload’s withstanding limit this is not serious problem for the rod itself (we have already seen that value of tensile strength is much more than value of applied load) and this is clear why: payload generally contains sophisticated equipments (electrical circuit, optics an etc.) that will not be able to withstand very high g-loads while the rod will be made of some continuous solid substance, Carbon nanotubes is this case and of course it will be able to withstand much higher g-loads.<br />
<br />
<br />
What will be the mass of such rod? Knowing its volume (for this purpose its cross-section’s area 3.14 square meters should be multiplied to rod’s length-100 000 meters, we get 314 000 cubic meters) and taking the value of density (this also varies for Carbon nanotubes from 0.037 to 1.34 g/cm<sup>3</sup>, let’s take 0.1 g/cm<sup>3</sup>) we get rod’s mass as 31 400 000 kilograms. This is too heavy for Space Elevator’s modern concepts and for improving this situation we should either use many cabins for raising the rod as single unit or use nuclear energy for feeding the cabins instead of laser/microwave beams or deliver the rod’s parts separately in space and then assemble them (see ''Assembling the Space Catapult''). But if some advanced substances are chosen for this purpose (for example ''Silica aerogel'' the density of which is about 1.9 mg/cm<sup>3</sup>, this is 50 times less than the density of the Carbon nanotubes taken above-0.1 g/cm<sup>3</sup>) than problem may be lightened in spite of the fact that their current tensile strength is quite low-16 kPa for the density of 0.1 g/cm<sup>3</sup> ['''7''']. So, we can conclude that we need the material with the density of ''Aerogels'' and tensile strength of Carbon nanotubes.<br />
<br />
How much energy and time will be needed for the rod to accelerate from zero to desired speed-50 km/sec? The amount of rotational energy of the rotating rod can be calculated by the following formula:<br />
Kinetic Energy<sub>rotational</sub>= (1/2)*I*ω2 <br />
<br />
Where:<br />
<br />
'''I'''=moment of inertia <br />
<br />
'''ω'''=angular velocity<br />
<br />
"I" depends on the shape of the mass under rotation. In the case of a uniform rod rotating from its end (axis of rotation is at the end of the rod) I = (m*L2)/3<br />
<br />
<br />
“ω” = V/R, where V = tangential velocity and R = radius<br />
<br />
In our case ''moment of inertia'' is equal to (31 400 000 kg*100 000 m2)/3=104 666 666 666 666 666<br />
ω is equal to (50 000 m/sec)/100 000 m=0.5<br />
<br />
So, Kinetic Energy<sub>rotational</sub>=(1/2)*104 666 666 666 666 666*(0.52)= 13 083 333 333 333 333.25 Joules<br />
<br />
Now, how much time and what amount of solar panels will be needed for accelerating this rod? The amount of Solar constant near the Earth is approximately equal to 1300 W/m2 ['''8'''], with assuming that ''coefficient of efficiency'' of solar panels is roughly 20 % we get 260 Watts per square meters and we can easily link amount energy (that we have already calculated) and power with the time needed. Particularly, ''Energy'' is equal to ''Power''’s multiplication to ''Time'':<br />
<br />
[[File: Formula - Copy.jpg]] <br />
<br />
So, Time is equal to 13 083 333 333 333 333.25 Joules/260 Watts=50320512820512.8 seconds, or 1 595 652 years. If we take much more area for solar panels, for example 10 millions square meters then 0.1595652 years or approximately 58 days will be needed and we think that this is acceptable time span.<br />
<br />
Actually, the time and energy will be needed a bit more for overcoming static friction in electro motor, for overcoming the rarified atmosphere’s resistance (we know that there no absolute vacuum in space), also we should take into consideration electric motors’ coefficient of efficiency that generally reaches 90-95 %, so some energy loss will occur here also. <br />
<br />
Now, what will be the total mass of solar panels producing the energy for Space Catapult? This depends on mass/power ratio, in near future it is expected that very lightweight designs could likely achieve 1 kg/kW ['''9'''] or 0.260 kg/ 260 W (per 1 square meter), so if for rotating the Space Catapult 10 millions square meters of solar panels are used then their total mass would be equal to 2 600 000 kg. We think that it is too heavy for Space Elevator the mass of which is expected to be equal around several hundred metric tons. If so, we will have to use fewer amounts of solar panels and therefore increase the time needed for accelerating the payload’s speed from zero to designed one. This will not make problems if the rod is accelerated only once and then keeps its constant rotation-for this purpose less energy will be needed and the payload will have to reach the rod’s end by first method as described earlier in this paper (see ''Rod’s plane of rotation towards the Earth'').<br />
<br />
We also need to take into consideration the value of deflection when the rod will be delivered to space by means of Space Elevator (see ''Assembling the Space Catapult''), in this case the thin and long rod will be bent due to its own weight and here we will try to calculate its value. This is quite complex problem that apparently cannot have an unambiguous solution because of many reasons, for example due to various temperatures in atmosphere’s different layers, various humidity and possible wind, but still we will try to calculate the value of ''Deflection'' that will occur in case when the rod’s one end is fastened to Space Elevator’s ascending cabin and the second end is fastened to the transport moving on the land, we discussed this option in above-mentioned section of our paper (see ''Assembling the Space Catapult''). The inclination angle for the rod will vary from 0º (rod is transported horizontally on the ground) to 90º (Space Elevator’s cabins are carrying the rod to space) and here we will discuss some medium case when the rod is semi-elevated in the air, when the angle between rod and ground/cable is equal to 45º. On the engineers’ ''eFunda'' web-site there is online calculator that enables to receive the value of ''Deflection'' (actually that site gives different term for this-''Displacement'') ['''10''']:<br />
<br />
Here we need to enter the relevant values:<br />
<br />
''Length of beam'', ''L'': 100 000 meters<br />
<br />
''Line pressure load on beam'', p: In our case this is the weight per meter length. As we have already mentioned the radius of the rod’s cross-section is 1 meter, so the volume of rod’s 1 meter-length part will be 3.14 cubic meter. In case of using Carbon nanotubes with above-mentioned density-0.1 g/cm<sup>3</sup> the weight will be equal to 314 kg or 3 079 Newton. Since we have got the inclination of 45º we should multiply this value to cos45º- 0.707, so we get 2176 N/m.<br />
<br />
''Young's Modulus'', ''E'': This is equal to 1 000 GPa for Carbon nanotubes ['''11'''] <br />
<br />
''Distance from neutral axis to extreme fibers'', ''c'': In our case it is equal to the radius of the rod-1 meter<br />
<br />
''Moment of Inertia'', ''I'': It is equal to (pi*r<sup>4</sup>)/4, so it is equal to 0.785<br />
<br />
According to these initial data the calculator returns extremely high value of Deflection, much higher than the length of the rod itself: -3.61 × 10<sup>9</sup> meters. This result shows us that with the current materials (Carbon nanotubes in our case) it is impossible to raise the rod as ''one single unit'' to space by means of Space Elevator and we need other materials with less density and more ''Young's Modulus'' (or the rod should be much thicker but this will lead to increasing its mass). Therefore, we have got two options: either we should deliver the parts of that rod and then assemble them in space (we have already discussed this option) or completely different technologies for manufacturing the rod should be developed. Particularly, it would be very good if it was possible to manufacture the rod ''in continuous mode'' in vertical position and then uninterruptedly directly to carry it to space by means of Space Elevator’s cabins. Under such approach there will be no ''Deflection'' and several cabins will be able to deliver the rod in space. <br />
<br />
One note about transporting the rod from its place of manufacture to Space Elevator’s base station. We think that this process should be executed by many transports, in other words we are convinced that if the rod is carried by two trains only (or any other kind of transport) then the rod will continuously touch the ground since the ''Deflection'' occurs in any position-horizontal, inclined or vertical and this circumstance will lead to its damage, that’s why several transports will be needed to hold the rod at as many places as possible.<br />
<br />
=Stabilizing the counterweight=<br />
Stabilizing the Space Elevator’s counterweight is very important question during Space Catapult’s performance. Indeed, when the rod rotates it makes the imaginary circles in space and due to rod’s and payload’s masses the Space Catapult’s ''center of mass'' will be continuously shifted and if the counterweight is not somehow stabilized then it will make problems for accurate aiming to certain point at the celestial sphere. Also, if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable then there will be the danger that the rod may actually hit the cable and cut it. To avoid these problems we need to apply to serious measurements. <br />
<br />
First of all, the electro motor’s own axis can be quite long and this will diminish the chance to failure of the whole system. Actually, we are convinced that counterweight’s (where the electric motor will be placed) size will be quite large, mainly due to solar panels’ sizes and amount (this issue was discussed above), also the electromotor should be quite large and powerful to rotate the rod, and hence there will be enough distance between the rod and Space Elevator’s cable. <br />
<br />
The second serious problem is that the center of gravity of the system is not at the center of rotation, therefore it will be necessary to balance the rotating system when the payload is attached and when it is released.<br />
<br />
We think that the Space Catapult’s rod should not be deployed/directed to one side only but some counterweight of it should also exist. This is necessary since the unilaterally loaded (we mean the rod itself plus payload) rod will cause the counterweight to somersault. In other words, the rod should extend to other side and the ''moments of inertia'' of both sides should be the same as during rotating the rod as after releasing the payload when the rod still rotates. This is easily achievable if some additional, second payload is placed on the rod’s second end. Therefore, the Space Catapult will launch two payloads at the same time to the ''opposite'' directions but at various speeds if the second part/side of the rod is shorter.<br />
<br />
How the second payload should be placed on the rod and should we really send two payloads? Until we have got balanced rod this problem does not arise but as soon as the Space Catapult releases the payload this balance will be violated, how it can be restored? There are two theoretical ways for achieving this: reducing the ''mass'' or reducing the ''length''-with diminishing either one of them the ''moment of inertia'' will be decreased. We think that reducing the mass will be less practicable since this would require placing the second payload (spacecraft or anything else) on the rod’s second part and this cannot be done from the Space Elevator’s cabin-this is the easiest way for delivering the payload from Earth to Space Catapult’s rod; so we would have to (see ''Rod’s plane of rotation towards the Earth'') put the second payload on the electro motor and then send it rod’s second part’s end. This is quite complicated task; therefore we can apply to second approach-put some sliding object that will immediately move to electromotor as soon as the spacecraft is released.<br />
<br />
[[File: MOI.jpg]] <br />
<br />
The next problem that may occur is that when the electro motor rotates the rod this motion will make the Space Elevator to rotate to the opposite direction. The same problem arises when helicopter’s primary blade’s rotation forces the helicopter to rotate to opposite direction and this possible rotation is annulled by ''tail rotor''. We think that for balancing the counterweight the additional motor and rod should be installed and this rod should rotate to opposite direction and if their ''angular momentums'' are equal to each other, then their rotations will cancel each other. More precisely, the following equation should be fulfilled:<br />
<br />
[[File: Angular momentum.png]] <br />
<br />
Where ''m'' is mass of the rod, ''v'' is angular speed and ''L'' is rod’s length, the numbers ''1'' and ''2'' refer to first and second rods correspondingly. For balancing both rods’ rotation the multiplication at both sides of the counterweight should be equal, by the way this circumstance enables us to use the second rod with shorter length and even with less mass but rotating at more angular velocity.<br />
<br />
Such approach will effectively deal with other problem which will arise when the Space Catapult releases the payload(s), at this moment the second motor should instantly diminish its angular velocity to some certain level (an ordinary mechanical brakes could be used for this purpose), in this case ''angular momentums'' for both motors/rods will be equal again and Space Elevator’s counterweight will maintain its attitude in space. See the image below depicting the Space Catapult with two electro motors and rods:<br />
<br />
[[File: Two-rods.jpg]] <br />
<br />
Such approach will justify itself if rod’s plane of rotation is parallel to Space Elevator’s cable, but if this plane is orthogonal to cable (see ''Rod’s plane of rotation towards the Earth'') then the second/balancing electromotor cannot be placed under the counterweight because the cable will be cut when rod touches it. Therefore a bit different approach should used and we need to install two/four/eight electro motors with their own relatively shorter rods rotating to opposite direction. They should be placed at the counterweight’s lower side and on its edge (as we suppose the counterweight should be disc) so that their rods not to touch and cut Space Elevator’s cable. Also, total a''ngular momentums'' from these motors should be equal to the ''angular momentum'' from upper motor and thus the counterweight will not rotate and the Space Elevator’s cable will not be twisted. This situation is presented below:<br />
<br />
[[File: Modified-2.jpg]] <br />
<br />
We think that the array of gyroscopes would be also very useful to be installed at the counterweight since they can maintain the attitude of the whole system and this is important for precise aiming to certain point at the celestial sphere. As for the energy required for gyroscopes’ performance it could be received from the array of solar panels which as a result will generally serve Space Catapult’s precise performance.<br />
<br />
=Space Catapult placed at Lagrangian points-the way for gaining subluminal speeds=<br />
<br />
In our paper we discussed the Space Catapult based on the Space Elevator’s counterweight and concluded that this would be convenient when we intend to deliver the payload to space from the Earth. However, such Space Catapult cannot gain very high speeds and therefore we need to choose other way. It is obvious that we need to keep rod’s plane of rotation orthogonally relative to the ''Earth-Sun connecting line'' and hence we should place the rod on the celestial body which will be in synchronous rotation with the Sun but since there is no such body in the solar system we conclude that the Space Catapult for subluminal speeds (the speeds close to speed of light are in mind) should be placed at such point near the Earth where it will be easy to reach it from our planet and where the rotating rod will not hit the Earth and will be always at the same distance from the Sun to avoid the influence of its tidal forces. The examples of such places are '''Lagrangian''' L<sub>1</sub> and/or L<sub>2</sub> points at 1.5 million km away from the Earth. If the Space Catapult is placed at one of these points then its rod can be always orthogonal to the Sun in principle, at the same time it will never collide with the Earth and also it will be quite close to the Earth since 1.5 million km distance is very negligible in space.<br />
<br />
We have got several notes regarding such approach. First, when we mentioned that the rod’s various parts can be at the same distance from the Sun this strictly speaking is not very true because the Sun can be referred as little point where its gravity “comes out” from while the rod is quite long and its initial part (placed at one of the Lagrangian points) will be attracted stronger than the utmost one (for equal attracting the rod should the arc ''with the same curviness as Sun’s surface'' and not straight line); but still this is better than to direct the rod exactly towards the Sun where the tidal forces will try to tear the rod. Second, the Space Catapult should be placed at Lagrangian L1 point which is closer to the Sun than L2 one and therefore receives by 4 % more energy per area from the Sun. Third, the rod should be in constant rotation, this requires much less energy than accelerating it from zero, then stopping it and accelerating it again. Fourth, the existence of the asteroid belt in the solar system between Mars and Jupiter will somehow restrict the actual length of the rod. Indeed, the Space Catapult should be placed at one of the Lagrangian points at 1 AU distance from the Sun while asteroid belt approximately lays at 2.7 AU, from the simple geometry it is obvious that the length of the rod ''almost reaching'' the asteroid belt can be approximately equal to 390 million km, and if the rod is longer then it may simply hit any asteroid within that belt. For 390 million km length rod and for 100 000 m/sec2 acceleration at rod’s end (where the payload will be attached) the maximal speed that the spacecraft can gain will be approximately equal to 200 000 km/sec (two thirds of the speed of light) and this can be considered as enough for practical interstellar spaceflight. Fifth, the spacecraft should be directly put on the rotating rod’s initial end (near electromotor) and then slide towards the other end with its own rocket engines. To achieve this, the spacecraft will have to cover relatively less distance on the rod and then rod’s circular motion will accelerate the spacecraft further-we have already mentioned this in this paper when speaking about deploying the Lunar Space Catapult. This action-putting the spacecraft on the rod will not be difficult since rod’s angular velocity will be quite low due to rod’s huge length, particularly for 400 million km length rod and for 200 000 km/sec linear speed the rod’s angular velocity will be 0.0000796 revolutions/sec.<br />
<br />
[[File: Lagrangian-point.jpg]] <br />
<br />
We have already mentioned that to avoid the destructive influence of the Sun’s tidal forces the rod’s plane of rotation should be orthogonal to the Earth-Sun connecting line. By the way, note that under such approach we may have to wait one year until the Lagrangian Space Catapult occupies the relevant position towards the certain point at the celestial sphere where the spacecraft should be sent to. But from the other hand it would be useful if it is feasible to rotate this whole structure around the imaginary axis directed towards the ''ecliptic poles'' (depicted as faint green dash line on the image above), the reason if this is the possible danger when the rotating rod may hit Mars or asteroids that orbit around the Sun closer than 2.7 AU distance (for example ''433 Eros'' or ''1036 Ganymed''), hence for avoiding such undesired collision the Lagrangian Space Catapult should be slightly rotated by several degrees clockwise/counterclockwise so that the rod not to collide with any celestial object. We are convinced that rotation by several degrees will be absolutely enough measurement due to rod’s gigantic length and relatively less sizes of the celestial objects in the solar system.<br />
<br />
The next issue that we should discuss refers to stability of the Lagrangian Space Catapult placed at L<sub>1</sub> point. As we see this structure will have enormously gigantic size while the Lagrangian point is relatively little mathematical one in space, so what can be done to be convinced that this structure will remain at that point and do not shift aside? The body placed at one of the Lagrangian points is affected by other celestial objects’ gravity and therefore for achieving the balance the rod needs to have the counterweight with more mass if it (counterweight) is shorter. As we clearly see the rod needs the counterweight for two reasons: not to let the Space Catapult somersault and for maintaining it at the L1 point. We think that it would be very useful if the arrays of solar panels act as counterweight since exactly they can give us energy for rotating the rod. Also, we need the second, shorter, perhaps less massive but faster-rotating rod (again-solar panel arrays) the opposite rotation of which would cancel first rod’s rotation, this issue was discussed in this paper. These arrays of solar panels are depicted on the image shown above. <br />
<br />
How such a gigantic structure as Lagrangian Space Catapult can be assembled in space? In our paper we discussed the possible ways for delivering the rod from the Earth to the Space Elevator’s counterweight, now we will try to show that it is possible ''in principle'' to assemble the extra-long rod in space. <br />
<br />
If it is possible from the technical point of view to manufacture extra-long rod then we can use this approach and make 1.5 million km length rod (this is the distance between the Earth and Lagrangian L<sub>1</sub>/L<sub>2</sub> point) that will be mechanically directed to the base station at L<sub>1</sub> point. The capturing devices there will catch the rod and attach it to the electro motor’s shaft after which the rod should be spun by 90º so that it to be orthogonal to Earth-Sun connecting line (for this purpose the additional mechanisms will be needed), this spin is necessary because L<sub>1</sub> point is located on the Earth-Sun connecting line (that is towards the Sun if we look from the Earth) and when directing the rod from the Moon it will lay ''along'' this line while we need across. After this the rod should be slid to another side and then the next rod should be directed to the Lagrangian Space Catapult where it will be attached to the previous rod and etc. In other words, the extra-long rod will be assembled from one side and its length will “grow” from this side to other one, this is necessary because the distance between Moon (the rod should be manufactured exactly there and not on the Earth due to our planet’s relatively more gravity, atmosphere and problematic space debris belt around it) and L<sub>1</sub> point is constant and rod’s parts cannot be more. Due to whole rod’s and its parts’ lengths (400 million and 1.5 million km correspondingly) we think that about 260-270 such operations will be needed to finish assembling the rod (400/1.5). The process of assembling the Lagrangian Space Catapult is shown on the image below:<br />
<br />
[[File: Lagrangian-point-assemble.jpg]]<br />
<br />
=Conclusion=<br />
<br />
As we have seen, for leaving the Solar system and reaching the remote celestial bodies (stars, nebulas) there is no need to develop advanced and complicated technologies that mostly are not capable for gaining extra high velocities nevertheless. In any case, until the Space Elevator is really built (scheduled for construction by 2031) we have got much time for developing the idea of Space Catapult in technical aspect, like finding appropriate materials for the rod, perfect the ways how the Space Catapult can be assembled in space and etc. The concept of Space Catapult itself is the easiest one, does not need developing neither complex and sophisticated technologies, nor some exotic methods (such as ''Gravitoelectromagnetic toroidal launchers'', ''Antimatter rocket'' and etc.) and can be easily implemented in near future; in other words the Space Catapult is not some sophisticated structure that would need profound science research and the fact that it will enable us to gain whatever high speed will justify its developing and building by the humankind. As for other technologies like Ion Drive, they could be used by the spacecraft during flight for other purposes, for example for correcting/changing the flight direction.<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Space_Elevator<br />
<br />
2. http://www.isec.info/index.php?option=com_content&view=article&id=14&Itemid=9<br />
<br />
3. http://www.space-track.org/perl/geo_report.pl (provided data updates regularly, registering is needed) <br />
<br />
4. http://www.oosa.unvienna.org/pdf/reports/ac105/AC105_720E.pdf page 24 (data as at 21 August, 1997) <br />
<br />
5. http://www.amostech.com/ssw/presentations/Session7/S7-1Molotov.pdf page 16<br />
<br />
6. http://www.esa.int/SPECIALS/ESOC/SEMN2VM5NDF_mg_1_s_b.html <br />
<br />
7. http://eetd.lbl.gov/ecs/aerogels/sa-physical.html<br />
<br />
8. http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant<br />
<br />
9. http://www.you.com.au/news/2005.htm, http://www.spacedaily.com/news/ssp-03b.html<br />
<br />
10. http://www.efunda.com/formulae/solid_mechanics/beams/casestudy_display.cfm?case=simple_uniformload<br />
<br />
11. http://en.wikipedia.org/wiki/Young%27s_modulus<br />
<br />
<br />
'''Appendix''': <br />
<br />
Animation illustrating the payload’s departure from the Lagrangian Space Catapult:<br />
[[File: Lagrangian-point-animation.gif]]</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_5&diff=3673OpenSpace 52013-09-21T13:08:13Z<p>Eagle9: /* The technical aspects regarding the Space Catapult */</p>
<hr />
<div>== '''Space Catapult''' ==<br />
<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
=INTRODUCTION=<br />
<br />
<br />
The new method for sending the spacecrafts in deep space is presented here. The paper describes the long rod rotated by electro motor placed at the Space Elevator’s counterweight and at Lagrangian points. This simple structure will enable the rod to gain high velocity and carry the payload with it. After reaching the desired speed the rod will release the payload that will fly in space along the imaginary circle’s tangent. This structure we called Space Catapult and it should work with the assist of Space Elevator. This latter should be used for carrying the payload from the Earth to Space Catapult’s rod.<br />
<br />
For exploring the outer space the humankind generally uses the rocket engines, mostly chemical-propelled ones. They enable us the explore near-Earth celestial bodies and other planets in the solar system. They even enabled us to send several deep space missions beyond the solar system such as '''Pioneer-10''', '''Pioneer-11''', '''Voyager-1''', '''Voyager-2''', however by means of this technology the flight lasts undesirably long and it seems to be impossible to reach remote celestial bodies in space such as stars, so new technologies are necessary for this purpose. However new technologies do not necessary imply new kind of rocket engines, such as ''Ion Drives'' because they are capable for gaining several ten times higher speeds only, but for remote celestial bodies even they are not suitable. Besides, they need a huge amount of energy to be stored onboard the spacecraft and this will make additional problems. So, high speed should be achieved with absolutely different approach. How this can be done?<br />
<br />
High speed can be easily achieved by means of fast-rotating rod around the electric motor. The motor’s rotational speed can be very high; the rod also can be quite long, hence the rod’s end’s linear speed can be extremely high, absolutely unachievable for any other technologies nowadays. The payload should be fastened at the rod’s end where the linear speed generally reaches maximal value. After reaching the necessary speed the rod will release the payload that will fly along the tangent from the current position. Thus the electric energy can be turned into payload’s speed and its velocity could be as high as we wish (except the ''speed of light'' of course). In principle the '''Space Catapult''' (thus we call this structure) would be the simplest, the most convenient and direct way for converting the energy/electricity into speed and conveying it to payload. <br />
<br />
As we see the Space Catapult is quite uncomplicated structure, however if we wish to gain high speeds we should deploy it in space, not on the Earth. Indeed, our planet is surrounded with dense atmosphere that impedes any quick motion, so if we rotate the rod quickly the atmospheric drag and generated heat would burn it very soon, therefore the Space Catapult should be built and deployed in space only, and as we suppose-at the Space Elevator’s counterweight. In other words, the Space Elevator’s counterweight will operate as Space Catapult. See image below:<br />
[[File:Space-catapult.jpg]]<br />
Generally, what is the Space Elevator ['''1''']['''2''']? According to modern concepts it will be the tall vertical structure built on equator and will have height of several ten thousand kilometers with its thin cable fastened to the base station on the Earth and with counterweight placed higher geostationary orbit. Because of balance between centrifugal force and gravity this structure will be stretched and the cabin will move along its cable carrying the goods into high orbit. After delivering the payload, the cabin will descend and carry the next one.<br />
In Space Elevator’s concepts several solutions have been proposed to act as a counterweight: <br />
<br />
1. Heavy, captured asteroid <br />
<br />
2. Space dock, space station or spaceport positioned past geostationary orbit <br />
<br />
3. Extension of the cable itself far beyond geostationary orbit. <br />
<br />
The third idea has gained more support in recent years due to the relative simplicity of the task and the fact that a payload that went to the end of the counterweight-cable would acquire considerable velocity relative to the Earth, allowing it to be launched into interplanetary space. However this idea cannot be completely shared by us due to following reason: <br />
<br />
It is well-known that the values of both '''Orbital''' and '''Escape Velocities''' decreases with increasing the altitude while the '''tangential velocity''' of Space Elevator’s cable increases. We can see the differences between them from the chart presented below:<br />
[[Image: Cxrili.gif]]<br />
<br />
As we see from this chart the ''tangential velocity'' of the Space Elevator even at its end (144 000 or 200 000 km altitude) is not very high to decrease the necessary time for covering the distance from the Earth to remote celestial bodies significantly. To achieve this, even the longer Space Elevator would be needed (its ''tangential velocity'' is directly proportional to its length) and this circumstance would complicate the technical task for building such Space Elevator. Because of this, there is no necessity to extend the cable itself far beyond geostationary orbit as proposed in the third variant. In any case, we have already seen that by means of Space Catapult it is possible to gain such huge velocities that are absolutely unachievable with other technologies, for example with Space Elevator. Therefore, using the counterweight and placing the Space Catapult there definitely has got some technical sense. <br />
<br />
However, we think that the question where the Space Catapult should be placed needs further discussion. Theoretically, the Space Catapult with its payload and nuclear reactor/solar panel needed for rotating the rod may be mounted not only at the counterweight, but on the Space Elevator’s cabin also that can carry all these goods to space in a usual way, as it should do it according to Space Elevator’s modern concepts. This option is quite possible, however for realizing this we need to know the mass of the payload, nuclear reactor/solar panels’ mass plus Space Catapult’s mass from one hand and Space Elevator’s lifting capacity (this ''must'' be more) from other hand, but these data are not available nowadays, therefore we think that the Space Catapult should be still mounted at the Space Elevator’s counterweight where it will be possible to send the payloads into deep space in ''continuous mode'' at high velocities.<br />
<br />
As we saw the Space Catapult is capable to gain very high velocities; however there is being developed other technologies and they in future will enable the spacecraft to fly at high speeds in space. These are Ion Drive systems, more precisely the most perspective one-''Variable Specific Impulse Magnetoplasma Rocket'' (VASIMR) which still under development can be used in future for deep space missions. Can these engines and Space Catapult be the rivals in space? Since none of them have been built and used in space yet we cannot give a persuasive answer to this question; however still it is possible to underline Space Catapult’s one significant advantage: if the future spacecraft uses the VASIMR (or any other kind of Ion Drive) engine it will definitely need to be equipped with nuclear reactor, otherwise the spacecraft will not be able to gain high speeds, also it will need to carry fuel tanks for this purpose. As for the Space Catapult, it can give much higher speed to spacecraft, besides it will have ''stationery'' power plant (see ''Energy source placed on the Space Elevator’s counterweight'') at the Space Elevator’s counterweight, so the payload will ''not'' have to carry the nuclear reactor onboard and this circumstance will lighten the work for deep space spacecraft. Besides, we should not forget that unlike the spacecrafts equipped with ion drive engines the Space Catapult will need no fuel for gaining high velocities. <br />
<br />
Briefly, Space Catapult’s advantages over any kind of propulsion systems are: <br />
<br />
1. Ability to gain any speed that is absolutely unachievable by means of other kinds of engines. <br />
<br />
2. No need by spacecraft to carry energy source that would make it too heavy and impracticable.<br />
<br />
=The Space Catapult needs long rod=<br />
<br />
When building the Space Catapult at Space Elevator’s counterweight we should install quite long rod there, the shorter the rod is, the easier would be installing it, however we should note that rod cannot be extremely short, let’s say 1 km length or so due to following reason:<br />
<br />
When we are going to send some payload into space, we need not only high velocity, but one certain direction also. The little inaccuracy in direction, inclination in several arcminutes is actually acceptable since the spacecraft would easily balance it with its engines; however great inclination from the initial direction would send the spacecraft into the completely different direction and in such case the whole mission will fail.<br />
<br />
If two Space Catapult’s rods have the length of let’s say 1 kilometer and 10 kilometers, then for giving to payload some certain linear speed (for instance 100 km/sec) these rods should rotate at different angular velocity. It is easy to ascertain that the shorter rod should rotate 10 times faster to gain the same linear speed than the rod with more length. But the faster the rod rotates, the more difficult will be to “catch” the needed moment for releasing the payload from the rod for sending it towards some certain direction. If the rod is too short, then it has to rotate very quickly for gaining some certain linear speed and therefore it will be extremely difficult catching the needed moment for releasing the payload. Hence, too short rod can make problem for sending the payload to some certain direction in space especially at high velocities. So, based on payload’s needed velocity we should find rod’s desired, minimal length that will enable us to send the payload in space to necessary direction without fear that it may yaw from the course. <br />
<br />
However, rod’s length will be crucial for payload’s abilities for withstanding the acceleration also. As an example, we can try to calculate its value which the payload will have to withstand during rod’s rotation. The acceleration of the body rotating at the circle with some constant velocity is calculated by the following formula:<br />
<br />
[[File: Acceleration - Copy.jpg]] <br />
<br />
Where a is acceleration in ''m/sec''<sup>2</sup>, ''v'' is payload’s linear velocity on the circle in ''m/sec'' and ''r'' is radius of the circle in ''meters'', in our case it is equal to rod’s length. Let’s assume that the rod is 100 km length and the electromotor rotates it so that payload’s speed is equal to 50 km/sec, in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design and manufacture the spacecraft’s subsystems (avionic and etc.) capable to withstand such acceleration. This circumstance somehow restricts the speeds that we can achieve, in any case their values actually depends on spacecrafts’ abilities for withstanding g-loads. But what can we do if much higher speeds are needed? The answer directly derives from that formula: the radius should be more; by the way note that this is additional reason why the longer rod is more useful. If we are able to make the extra long rod, then this will enable us to gain much higher velocities. <br />
<br />
What material should be used for manufacturing the rod? It is obvious that if very high speeds are needed the rod should be long and even in this case the acceleration at its end will be quite high, therefore ''sufficiently strong and light materials'' are needed for this purpose and making them is as similar challenge as in case of Space Elevator where the same requirements arises for the cable’s material. The lightness is needed because in case of heavy rod a lot of energy will be needed to rotate it; the strength is needed because in case of lack this property the rod will be destroyed due to great acceleration.<br />
<br />
=The mechanism for holding and releasing the payload=<br />
<br />
How the payload can be held by Space Catapult’s rod during rotation and how it can be released from the rod? We think that using ''electromagnet plus mechanical holding devices'' would be a good solution. More precisely, after the payload is attached to the rod it must be held by means of both methods until the rod accelerates and reaches necessary velocity (it may take even several days), but with approaching the desired speed the mechanical device should release the payload however the electromagnet(s) should still hold it. The explanation of such approach is following: generally the mechanical devices are much slower/sluggish in performance than electronic ones. We have already said that when releasing the payload the extreme accuracy is needed and mechanical devices cannot guarantee ''the exact time of releasing'' the payload unlike electronic ones. That is, it’s unlikely that mechanical devices can release the payload at some certain moment when needed while in case of electromagnet it would be enough to cease electric current there, it would lead to immediate vanishing of the magnetic field and sending the payload along the tangent from the point where the payload would be at the current moment. <br />
<br />
<br />
We think that the ''fastest control system'' would enable to release the payload to certain direction. This system (extremely fast-operating computer plus measuring equipments) should know the current position of the rod’s end, the current speed, the needed direction and be capable for computing the necessary moment for giving the order for diminishing the voltage for electromagnets and hence releasing the payload to desired direction and velocity.<br />
<br />
=Rod’s plane of rotation towards the Earth=<br />
<br />
The Space Catapult’s rod when rotating makes the circular plane/flatness in space and this plane may be horizontal/parallel to Earth surface, that is making the right angle to Space Elevator’s cable or it may be placed along the cable; see the both possible situations here:<br />
<br />
[[File: Planes-of-rotation - Copy.jpg]] <br />
<br />
Both approaches have got their advantages/disadvantages and here we will discuss this question, first of all from the point of view of safety.<br />
<br />
For gaining extremely high velocities quite long rod would be needed, maybe with the length of several thousand kilometers or even more. If such rod is placed ''along'' the Space Elevator’s cable then the rod during rotation will cross many orbits from the ''Medium Earth Orbit'' to ''High'' ones. When rotating, the rod may actually hit any satellite and/or space debris object and such collision can lead to rod’s complete destruction; therefore we should choose such plane which would be much more free from any artificial objects; hence if the rod rotates ''horizontally/parallel'' to Earth’s surface at high enough altitude where the satellites’ population is relatively low then this measurement would justify itself because under such circumstance the rod will not cross satellites’ orbits (rod’s plane of rotation will simply coincide to ''one'' orbit’s path). However, we should also note that this altitude actually depends on the Space Elevator’s proposed length. Indeed, the Space Catapult’s rod should be mounted at the Space Elevator’s counterweight; this counterweight from its side should be placed at the end of the Space Elevator at such altitude where the satellites’ population is as low as possible. This means that Space Elevator’s proposed height should be agreed with mounting Space Catapult on its counterweight. According to various databases the number of man-made objects at high orbits, more precisely beyond geostationary orbit is much less than on the lower orbits ['''3''']['''4''']['''5''']['''6'''], therefore the Space Catapult with its rod should be located at the altitude of 50 000-60 000 km above the sea level. At such altitude the space is almost free and nothing will impede rod’s rapid rotation. Besides, the satellites at high orbits are orbiting around the Earth slower than on the lower orbits (as known any satellite orbits around its primary body slower in apogee than in perigee), therefore if some tracking system is mounted at Space Elevator’s counterweight then it will enable the Space Catapult to avoid undesired collision with satellites during Space Catapult’s performance. In other words, the Space Catapult should operate only when the there are no satellites near its vicinities.<br />
<br />
Now we will try to discuss this question from other side.<br />
<br />
How the payload can be transferred from the Space Elevator’s cabin to the Space Catapult’s rod? One way is following: cabin reaches the counterweight where the payload will be released, then payload will be mechanically conveyed to rod, continues its way ''on the rod'' (like the train rides on the rails) and after reaching rod’s end it stops, the rod begins rotating and after gaining necessary linear speed it releases the payload to needed direction. This method is generally realizable; however it seems to be too complicated and unpromising compare to the second one: the Space Catapult’s rod is stopped in space so that it to be directed downwards to the Earth and be parallel to Space Elevator’s cable. The Space Elevator’s cabin moving along the cable with payload stops at the cable ''near'' the end of the Space Catapult’s rod and releases the payload that will fly to the rod, attaches itself to the rod’s end (here the electromagnets would be useful), the rod begins rotating and after gaining needed linear speed will release the payload to necessary direction.<br />
<br />
This second way seems to be more promising because the first one is much more complicated as we have already said: first of all there would be needed some mechanical devices for transferring the payload from the Space Elevator’s cabin to counterweight, the counterweight should have the hole for the payload to move through it from below (we should not forget that the Space Catapult should be mounted ''at'' the counterweight, not ''beneath'' it), besides the rod should be made so that it to have some conveying surface (rails for instance) the payload to move on it. As we see it would be much more convenient if it is possible to convey the payload from the cabin to the rod directly and this would be feasible under the second method which is depicted below:<br />
<br />
[[File: Convey.jpg]] <br />
<br />
One more aspect regarding Space Catapult’s position. This structure, its rod, its electro motor and etc should be mounted at Space Elevator’s counterweight so that the rod to be placed westwards from the cable. The reason of it is following: when the Space Elevator’s cabin stops and releases the payload (which should fly to Space Catapult’s rod) the current speed of which will/should be more than the value of the ''Orbital/Escape Velocity'' at the current altitude. After releasing the payload will fly westwards and upwards because its orbit will be ellipse, under ellipse the payload will fly higher to apogee and at the speed less than Space Elevator’s current speed at the given altitude, in other words the released payload will “lag behind” the Space Elevator’s cable; therefore payloads’ ''stopping points'' at the cable and Space Catapult’s rod’s length should be calculated and chosen so that the payload to fly directly towards rod’s end. This process would be feasible in both cases-if the rod’s plane of rotation is parallel to Earth’s surface and if it is placed along the cable-but still this would be easier for the payload to achieve the rod’s end if the rod is placed along the cable because at least the distance that the payload should cover in space will be less.<br />
<br />
The length of the Space Catapult’s rod placed at the Space Elevator’s counterweight might vary since for various spaceflight purposes different initial speed will be needed and relatively low speed could be achieved by means of shorter rod. Because of this reason it might be necessary to change Space Catapult’s rod’s length, therefore it would be useful if the rod consists of two parts where the first part would be perpetually attached to electro motor and the second one will be attached to the first part if necessary. For this operation Space Catapult’s rod should be placed along the cable since the relative nearness would make this operation quite easy and it could be accomplished by the crew directly from the Space Elevator’s cabin stopped at the needed altitude. <br />
<br />
For deciding the question how the Space Catapult’s rod should be placed towards the Space Elevator’s cable we should take into consideration one substantial circumstance-to which direction do we plan to send the payload in space by means of Space Catapult? This circumstance will influence deciding this problem due to following reason:<br />
<br />
In case ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and if rod’s plane of rotation is parallel to Earth equator, then this plane will be orthogonal to Earth’s rotation axis. This axis from its side is tilted to ''ecliptic plane'' by 66° 34'. This means that Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 23°26'. Here follows very important consequence: under above-mentioned conditions the rod when rotating will be capable for covering only the part of the ''celestial sphere'' from 0° to 23°26' (counted from ''ecliptic plane'' northwards and southwards to ''Ecliptic poles''). This is about one fourth of the ''celestial sphere'' (23°/90°), this will not make problems if we intend to use the Space Catapult for exploring the solar system’s planets because their orbits’ tilts towards ''ecliptic plane'' do not exceed 7° (for planet Mercury, for other planets this tilt is even less); however we will not be able to send the payload for example to the nearest star ''Alpha Centaurs'' because this star is located at -42 degree according to ''ecliptic coordinate system'' in the celestial sphere.<br />
<br />
The situation will drastically change ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and ''if'' rod’s plane of rotation is orthogonal to Earth’s equator and therefore parallel to Earth’s axis of rotation. We have already discussed this option when we mentioned that the rod should be placed westwards from the cable and explained why it would be useful-for delivering the payload from Space Elevator’s cabin to Space Catapult’s rod. Under such conditions the Space Catapult will be capable to aim to any point on the ''celestial sphere''. Indeed, the Earth with the Space Elevator rotates around its axis and Space Elevator’s counterweight draws an imaginary circle in space. This circle is tilted to ''ecliptic plane'' at 23°26' and crosses this plane in two point called ''ascending'' and ''descending nodes''. The other points that are 90° away from these nodes we call point(s) of ''maximum elevation/depression'' (relative to ''ecliptic plane''). When the Space Elevator is at a''scending/descending node'' its rod and hence the payload can be directed to any point from 0º to 66º on the celestial sphere northwards and southwards from ecliptic plane. This makes about 75 % of celestial sphere. See the image depicting this situation:<br />
<br />
[[File: Node.jpg]]<br />
<br />
But when the space Elevator reaches the points of ''maximum elevation/depression'' then its rod during rapid rotation may be directed to any point from southern ''Ecliptic pole'' to ''Northern pole'' at the celestial sphere because at these points rod’s ''plane of rotation'' is orthogonal to ''ecliptic plane'' and thus the rotating rod can aim to ecliptic poles as well as other points. See this situation below:<br />
<br />
[[File: Elevation.jpg]] <br />
<br />
The situation will be similar if the Space Catapult’s rod is orthogonally placed towards cable. Under such approach Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 66° 34' and the Space Catapult will be capable to cover ''three fourths'' (66°/90°) of the ''celestial'' ''sphere'' when the Space Elevator is at the points of ''maximum elevation/depression'' and the whole celestial sphere when the Space Elevator is at ascending/descending nodes. For aiming the needed point on the celestial sphere the Earth should occupy the appropriate attitude towards the stars during the revolution around its axis, the same thing should be done under previous case described in the paragraph above. <br />
<br />
In conclusion, thinking about rod’s plane of rotation towards the Earth, we should note one important difference between above-mentioned approaches: if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, then in case of emergency during Space Catapult’s performance (for example if the Space Catapult’s rod is cut by sudden meteorite bombardment) the rod’s part with the payload may simply crash to the Earth at huge velocity if the rod at this moment is directed to the Earth. This cannot happen if Space Catapult’s rod’s plane of rotation is orthogonal to Space Elevator’s cable because payload’s rotational path will not be directed towards the Earth and hence its flying trajectory will never cross the Earth.<br />
<br />
=Braking the Space Catapult’s rod=<br />
<br />
After releasing the payload at necessary speed and direction, the Space Catapult’s rod will have a huge angular velocity that needs to be decreased to zero in order the Space Catapult’s rod to get another payload in motionless position and then to send it to space. <br />
What methods can we use to reduce Space Catapult’s rod’s rotation to zero? There are several possible ways: <br />
<br />
1. The electromotor designed for accelerating the rod may actually play a role of brakes, more precisely after releasing the payload to space the electromotor should operate/rotate in the opposite direction, hence rod’s rotational speed will be diminished to zero after that electromotor will stop operating. Under such method a bit less energy will be spent for decelerating the rod than in case of accelerating because when decelerating the rod is free from payload. <br />
<br />
2. An ordinary mechanical brakes, however due to electro motor’s and rod’s sizes a huge brake(s) would be needed to be installed on the Space Elevator’s counterweight and this circumstance would make additional problems from the engineering point of view. Nevertheless, we should admit that under such method we would not need as much energy as during accelerating; on the contrary, in this process the heat will be emitted as it generally happens during braking. <br />
<br />
3. For decelerating the rod we can use the well-known phenomenon in physics-''electromagnetic induction'': when the c''onductor/ closed circuit'' moves into the magnetic field the electric current is generated there. In case of Space Catapult we can use this phenomenon in the following manner: the conductor should be wrapped around the whole length of the rod like a helix and there should be possibility that this conductor to be turned into the ''closed circuit'' by means of mechanically connecting its ends (see the image below). After releasing the payload at necessary speed and direction this circuit should be closed, then according to ''electromagnetic induction'' the electric current will be generated in the conductor and the energy of this electric current will come from rod’s kinetic energy. Therefore, inducted electric current in the enclosed circuit will force this circuit and rod to lose kinetic energy and speed. The part of the generated electric current will be spent in prevailing conductor’s electric resistance:<br />
<br />
[[File: Helix.jpg]] <br />
<br />
The advantage of this method is that for decelerating the rod no energy will be required, as for drawback-much time will be required for this purpose because at the altitude of several ten thousand kilometers the Earth’s magnetic field is quite weak and the effect described in the paragraph above will need much time to operate and give necessary result. <br />
<br />
4. The above-described third method could be realized in a bit different way: if the conductor wrapped around the rod is a closed circuit and if we conduct the electricity there then the electric current will generate its own magnetic field that will counteract with Earth’s one. More precisely, according to ''Lenz's law'' induced current’s magnetic field will be in such a direction as to oppose the motion or change causing it, in other words induced current’s magnetic field will counteract outer magnetic field’s any change and this will cause decelerating rod’s rotation and finally its stopping. <br />
<br />
5. The obvious disadvantage of the third and fourth method described above is weakness of the Earth’s magnetic field because of which decelerating the rod may be delayed in time. For solving this problem we can create artificial magnetic field by means of electromagnets. Particularly, one electromagnet should be placed at the Space Elevator’s counterweight, very close to Space Catapult’s rod. The second electromagnet should be placed directly on the Space Catapult’s rod close to first electromagnet (actually, instead of this second electromagnet there could be used the conductor wrapped around the rod as we described above in previous methods). The reason of this nearness is that magnetic field generally weakens directly proportional to distance’s third power and much time will be needed for decelerating Space Catapult’s rod if two electromagnets are far from each other.<br />
<br />
This method probably will consume the most amount of energy but at the same time it will be the most effective because it does not depend on outer factors such as Earth’s magnetic field which is quite weak at the altitude of several ten thousand kilometers above the sea level. <br />
<br />
Eventually, which methods for decelerating the Space Catapult’s rod would be the best? As we see each one of them have got their advantages and disadvantages. We can state that we should choose one of them according to spaceflight’s profile and goal. Particularly, if we decide to send the spacecraft into the deep space mission where especially high speed is necessary then in this case ''longer/more massive'' rod would be needed rotating at very high speed. Under such circumstance much energy will be needed for accelerating/decelerating the rod. We should also take into consideration the fact how frequently the Space Catapult will operate, in other words how mane payloads it will have to send into space per some certain amount of time, week/month and etc. If time interval between two following missions is relatively high then we should choose the method that will consume less energy and more time for decelerating the rod. On the contrary, if the Space Catapult has to send payloads very often then we should choose the method that will consume more energy and enable the rod to decelerate faster. In other words, we should find ''golden mean'' between consuming time and energy. We should also take into account how much energy supply will be produced at the Space Elevator’s counterweight (see ''Energy source placed on the Space Elevator’s counterweight'') and what part of this energy can we spend for accelerating/decelerating the rod.<br />
<br />
The rod’s rotations can be decelerated much faster than accelerated; the reason of it is that when accelerating the rod has got some sophisticated device as payload and generally unmanned spacecrafts are capable to high g-loads, but still for them some restrictions exist. After the payload is released at needed direction and speed, the rod can decelerate much faster because the rod itself is quite simple device without any complex and sophisticated details. <br />
<br />
We can actually use several methods, such as the third one and then the first/fifth ones. This would be justified because of following reason: as we have already said when decelerating with the third/forth method the problem of weakness of the Earth’s magnetic field would occur, therefore much time would be necessary for described method(s) to perform and give us result. However, we should note that in the beginning when the rod rotates very quickly this method would still operate strong enough. This derives from Faraday's law of induction stating that “the electromotive force generated is proportional ''to the rate of change of the magnetic flux''”. Therefore, in the beginning when the rod is rotating very quickly we can use the third/forth method(s) and when the rod significantly brakes we can apply to the first/fifth ones-they do not depend on Earth magnetic field. In other words, such approach would greatly help us in finding the golden mean between spending energy and time necessary for decelerating the rod. <br />
<br />
And finally: after releasing the payload the Space Catapult’s rod can actually give us energy. More precisely, the electro motor itself can serve as electric generator also since we know that the same machine can operate as electric motor if it is fed with electricity and as generator for electricity if its rotor is rotated by other machines. Therefore after releasing the payload when the electro motor’s rotor is rotating very quickly it can give us energy, in result of which the rod will lose its kinetic energy and speed, as for generated energy it can be sent downwards to the Earth for our terrestrial needs (see the next section in this paper) or stored onboard the Space Elevator’s counterweight. This approach has got one substantial advantage: it does not imply additional mass (wrapped wire) that will cause problems because rotating heavier rod would consume more energy.<br />
<br />
=Energy source placed on the Space Elevator’s counterweight=<br />
<br />
As well-known, the Space Elevator’s cabin needs energy when moving along the cable and it can get it from the Earth by means of various ways, such as: laser beam, microwaves, through the cable itself and etc. On the other hand, Space Catapult also needs much energy for rotating the rod and for this purpose some energy source should be placed on the Space Elevator’s counterweight, presumably solar panels array. Doing this would demand additional funding and engineering work and this undertaking should be justified, so how can we prove that placing energy source on the counterweight would be necessary and useful? We should not forget that the energy generally could be simply transmitted from the Earth without carrying any material for energy source on counterweight; so we can justify this undertaking if we declare/prove that: <br />
<br />
1. Energy source should be designed for ''both'' Space Elevator’s cabin and Space Catapult’s rod. We can imagine it as array of numerous solar panels producing enough energy for both above-mentioned constructions. For this purpose solar panels would be better solution than nuclear reactor because they do not need nuclear fuel to be carried from the Earth to counterweight, also they are capable for producing energy in a continuous mode. By the way this circumstance will enable us to send the payload to space by Space Catapult whenever we want without depending existence nuclear fuel at the counterweight. <br />
<br />
2. Transmitting energy from the counterweight (“from above”) is better and advantageous than doing the same thing from Earth (“from below”). Indeed, when we try to transmit energy (laser or microwave beam) from the Earth to ascending cabin, the part of energy is inevitably lost and dispersed in the Earth’s atmosphere and (this is point of the question) this continues during the whole process of ascent. On the contrary, when transmitting the energy from counterweight to cabin the energy will be lost only on the little part of this voyage, more specifically until the cabin leaves the atmosphere (100 km in height) and when cabin leaves it the energy will be transmitted in vacuum without loss. <br />
<br />
3. For receiving the energy from the Earth the huge solar panels (in case of laser beam) or antennas (in case of microwaves) will be needed to be mounted on the counterweight and this is additional mass and additional engineering work.<br />
<br />
We think that these arguments given above are enough for shoving that placing energy source on the Space Elevator’s counterweight have advantages over transmitting energy from the Earth and as conclusion we can state that energy source on counterweight would serve both space transportation systems-Space Elevator and Space catapult. <br />
<br />
As addition, we could use the energy produced on the counterweight for terrestrial needs also. Indeed, there have been developed numerous projects for receiving energy from space since 60-ies implying producing it by means of solar panels and then transmitting to the Earth. Combining all these three goals we can conclude that placing solar power plant on the Space Elevator’s counterweight would be triply useful and advantageous. In other words, when the Space Catapult and Space Elevator do not function, the energy produced on the counterweight should be directly transmitted to the Earth for our terrestrial needs and thus the idea of Space Elevator, Space Catapult and space power plant will be combined in one project.<br />
<br />
=Assembling the Space Catapult=<br />
<br />
Assembling in space such a huge structure as Space Catapult will not be an easy task from the technical point of view and definitely needs special engineering approach. Besides, we think that Space Catapult’s rod should be mounted at the Space Elevator’s counterweight separately from every other parts of the Space Catapult (e.g. electro motor and etc.); this circumstance is caused by rod’s gigantic sizes. More precisely, electric motor and plus any other equipments necessary for Space Catapult’s performance should be delivered to space by means of Space Elevator in a usual way; as for Space Catapult’s rod, it is a different matter and it should be delivered and mounted separately in the end. <br />
<br />
Eventually, Space Catapult’s rod will be quite long, perhaps much more than 100 kilometers. It is obvious that delivering such a long rod as ''one single unit'' would be quite difficult task; also it is possible that due to its total mass the Space Elevator’s cabin will not be able to deliver such rod at all, but we have already mentioned that the Space Catapult may have the rod with various length; more precisely the rod may consist of two/more parts. In such case these parts should be delivered towards the counterweight separately and then assembled. <br />
<br />
But the Space Elevator’s cabin can actually deliver the Space Catapult’s rod as ''one single unit'' in space. We think that this would depend only on rod’s mass. The Space Elevator’s lifting capacity is not well-known yet; however apparently it will not exceed one hundred metric tons and if Space Catapult’s rod is made of extra light material then cabin will be able to deliver it in space and in such case the following question will arise: how the cabin will deliver such a huge object in space without any damage?<br />
<br />
This can be done by means of two cabins. Generally, Space Elevator’s conception implies only one cabin moving along the cable, but for some special purpose (like delivering Space Catapult’s rod in space) we can use the second cabin also that will descend downwards after finishing its job and will not participate in Space Elevator’s further performance. As for the process of delivering the rod, we can imagine it in a following manner: at first the rod will be placed horizontally on the Earth (thus it must be manufactured and then transported to the Space Elevator’s base station), then the Space Elevator’s first cabin will carry rod’s one end along the cable while the rod’s second end will be moved on the Earth so that the rod to take more and more vertical position. When the rod is in vertical position the second cabin will capture rod’s second end and will carry it in space. We think that without the second cabin it would be quite difficult for one cabin only to carry long/heavy rod because the rod may actually shake and crash to the Space Elevator’s cable and this is absolutely undesirable. <br />
<br />
So, as we see in principle it looks to be quite easy, however the assembling may complicate due to rod’s length. In this case it would be better to carry not the rod as ''one single unit'' but its parts and then to assemble them in space in the following manner: ''two'' cabins will carry the first part as described above, when this part is delivered to space and temporarily hung at the cable the next two cabins will carry the second part that will be attached to the first one from below; the other parts will be delivered to space and assembled into the rod in the same way. <br />
<br />
The obvious disadvantage of the above-described method is that each part needs two cabins on the Space Elevator’s cable, besides the humans will be needed for assembling the rod from these parts in the atmosphere’s upper layers; therefore we think that the first way-delivering the rod into space as one single unit still would be easier and more realistic; besides we should take into consideration the fact that if the rod is assembled the additional devices will be needed ''on the rod itself'' for joining these parts and this circumstance would lead to increasing the rod’s total mass and this is undesirable. See the image showing assembling process:<br />
<br />
[[File: Assembling.jpg]] <br />
<br />
Whatever design/structure the rod has-assembled from several parts or as one single unit, it must be delivered to its destination-Space Elevator’s counterweight and must be fastened to electro motor’s own axis. But the problem is that the rod will be quite long and also the fact that Space Catapult’s electro motor will be placed at counterweight’s upper side (or at the ''lateral'' side if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), so it will be necessary the rod coming from below to be moved to counterweight’s upper/lateral side, besides the rod should be docked with electro motor’s axis as accurately as possible. How is it possible to realize such complex engineering operation? Here we can indicate one possible theoretical way: <br />
<br />
The rod will be parallel to Space Elevator’s cable when carried by cabin, but later the cabin’s mechanisms should rotate it so that the rod to be orthogonal to Space Elevator’s cable (this will not be necessary if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), exactly in this position the rod should be delivered to counterweight, besides the rod when moving along the cable should be shifted a bit upwards (relative to the Earth) than the cabin itself. Under such conditions we will easily achieve docking the rod to electro motor’s own axis which from its side should have some trapping device (magnetic for example) to “catch” the rod and thus guarantee docking the rod to electro motor and finishing assembling the Space Catapult as a whole. But if the rod’s plane of rotation is parallel to cable then assembling process will be much easier because the ascending rod may directly dock to electro motor’s own axis. See the image showing this process:<br />
<br />
[[File: Deliver - Copy.jpg]] <br />
<br />
We think that it would be useful if one Space Elevator is built specially for Space Catapult with its base station located on the land, not the ocean. This would be justified because transporting Space Catapult’s rod from its place of manufacture to Space Elevator’s base station should occur on the land by means of several transports simultaneously (due to rod’s great length), this will enable us to deliver the rod to its destination without any damage while this kind of operation is hardly possible on the water.<br />
<br />
=The technical aspects regarding the Space Catapult=<br />
<br />
As an example, we can try to calculate/ascertain all possible kinds of aspects regarding the rod with some certain mass and sizes, for example we can assume the Space Catapult has got 100 km length rod. <br />
<br />
The circumference of the circle that this rod’s end will draw in space will be equal to 2πr=628 km. As we have already mentioned payload’s abilities for withstanding the g-load is restricted, so if the electromotor rotates the rod so that payload’s speed is equal to 50 km/sec (this means that it will take 12.56 seconds for the rod to make one complete revolution), in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design the spacecraft that will withstand such acceleration, but what about the rod itself? Which material can be used for designing this rod, what will be its mass and how much energy and time will be needed for the rod to reach this velocity? <br />
<br />
For manufacturing the rod we should choose the material with very low density and highest value of strength. Currently, the ''Carbon nanotubes'' are the best candidates for this purpose. What will the mass of the rod made of this material? This depends on width also and it should be as less as possible (otherwise the rod will be too heavy and too wide for transporting from manufacture place to Space Elevator’s base station and for delivering it to space by means of Space Elevator) but from the other hand the ''applied load'' will not let us to design very narrow rod.<br />
<br />
Let’s assume that we intend to launch the payload with the mass of 10 000 kg (during calculation we will use ''SI system'' only). To clarify what kind of material will be able to withstand the acceleration we should calculate and then compare two values: the ''applied load'' and ''tensile strength''. For calculating the first one we should multiply g-load (which we already know-2 550 g) to its mass-10 000 kg, we will get 25 500 000. As for calculating tensile strength, we should take its values (for Carbon nanotubes it varies from 11 000 MPa to 63 000, we will take some medium value-40 000 MPa) and multiply it to cross-section’s area, in our case rod is cylinder with circular cross-section. If radius of cross-section is 1 meters then its area is 3.14 square meters, multiplying this value to value of tensile strength (40 GPa as said) we will get 125 600 000 000 and this is significantly more than value of applied load-25 500 000. Of course, we should also take into consideration ''factor of safety'' which is generally equal to 2 and this indicates us that for safety the payload’s actual mass should be twice less but in our case as we see the rod will be able to accelerate the payload to above-mentioned speed. By the way, note that if that g-load ''2 550 g'' is almost at the payload’s withstanding limit this is not serious problem for the rod itself (we have already seen that value of tensile strength is much more than value of applied load) and this is clear why: payload generally contains sophisticated equipments (electrical circuit, optics an etc.) that will not be able to withstand very high g-loads while the rod will be made of some continuous solid substance, Carbon nanotubes is this case and of course it will be able to withstand much higher g-loads.<br />
<br />
<br />
What will be the mass of such rod? Knowing its volume (for this purpose its cross-section’s area 3.14 square meters should be multiplied to rod’s length-100 000 meters, we get 314 000 cubic meters) and taking the value of density (this also varies for Carbon nanotubes from 0.037 to 1.34 g/cm<sup>3</sup>, let’s take 0.1 g/cm<sup>3</sup>) we get rod’s mass as 31 400 000 kilograms. This is too heavy for Space Elevator’s modern concepts and for improving this situation we should either use many cabins for raising the rod as single unit or use nuclear energy for feeding the cabins instead of laser/microwave beams or deliver the rod’s parts separately in space and then assemble them (see ''Assembling the Space Catapult''). But if some advanced substances are chosen for this purpose (for example ''Silica aerogel'' the density of which is about 1.9 mg/cm<sup>3</sup>, this is 50 times less than the density of the Carbon nanotubes taken above-0.1 g/cm<sup>3</sup>) than problem may be lightened in spite of the fact that their current tensile strength is quite low-16 kPa for the density of 0.1 g/cm<sup>3</sup> ['''7''']. So, we can conclude that we need the material with the density of ''Aerogels'' and tensile strength of Carbon nanotubes.<br />
<br />
How much energy and time will be needed for the rod to accelerate from zero to desired speed-50 km/sec? The amount of rotational energy of the rotating rod can be calculated by the following formula:<br />
Kinetic Energy<sub>rotational</sub>= (1/2)*I*ω2 <br />
<br />
Where:<br />
<br />
'''I'''=moment of inertia <br />
<br />
'''ω'''=angular velocity<br />
<br />
"I" depends on the shape of the mass under rotation. In the case of a uniform rod rotating from its end (axis of rotation is at the end of the rod) I = (m*L2)/3<br />
<br />
<br />
“ω” = V/R, where V = tangential velocity and R = radius<br />
<br />
In our case ''moment of inertia'' is equal to (31 400 000 kg*100 000 m2)/3=104 666 666 666 666 666<br />
ω is equal to (50 000 m/sec)/100 000 m=0.5<br />
<br />
So, Kinetic Energy<sub>rotational</sub>=(1/2)*104 666 666 666 666 666*(0.52)= 13 083 333 333 333 333.25 Joules<br />
<br />
Now, how much time and what amount of solar panels will be needed for accelerating this rod? The amount of Solar constant near the Earth is approximately equal to 1300 W/m2 ['''8'''], with assuming that ''coefficient of efficiency'' of solar panels is roughly 20 % we get 260 Watts per square meters and we can easily link amount energy (that we have already calculated) and power with the time needed. Particularly, ''Energy'' is equal to ''Power''’s multiplication to ''Time'':<br />
<br />
[[File: Formula - Copy.jpg]] <br />
<br />
So, Time is equal to 13 083 333 333 333 333.25 Joules/260 Watts=50320512820512.8 seconds, or 1 595 652 years. If we take much more area for solar panels, for example 10 millions square meters then 0.1595652 years or approximately 58 days will be needed and we think that this is acceptable time span.<br />
<br />
Actually, the time and energy will be needed a bit more for overcoming static friction in electro motor, for overcoming the rarified atmosphere’s resistance (we know that there no absolute vacuum in space), also we should take into consideration electric motors’ coefficient of efficiency that generally reaches 90-95 %, so some energy loss will occur here also. <br />
<br />
Now, what will be the total mass of solar panels producing the energy for Space Catapult? This depends on mass/power ratio, in near future it is expected that very lightweight designs could likely achieve 1 kg/kW ['''9'''] or 0.260 kg/ 260 W (per 1 square meter), so if for rotating the Space Catapult 10 millions square meters of solar panels are used then their total mass would be equal to 2 600 000 kg. We think that it is too heavy for Space Elevator the mass of which is expected to be equal around several hundred metric tons. If so, we will have to use fewer amounts of solar panels and therefore increase the time needed for accelerating the payload’s speed from zero to designed one. This will not make problems if the rod is accelerated only once and then keeps its constant rotation-for this purpose less energy will be needed and the payload will have to reach the rod’s end by first method as described earlier in this paper (see ''Rod’s plane of rotation towards the Earth'').<br />
<br />
We also need to take into consideration the value of deflection when the rod will be delivered to space by means of Space Elevator (see ''Assembling the Space Catapult''), in this case the thin and long rod will be bent due to its own weight and here we will try to calculate its value. This is quite complex problem that apparently cannot have an unambiguous solution because of many reasons, for example due to various temperatures in atmosphere’s different layers, various humidity and possible wind, but still we will try to calculate the value of ''Deflection'' that will occur in case when the rod’s one end is fastened to Space Elevator’s ascending cabin and the second end is fastened to the transport moving on the land, we discussed this option in above-mentioned section of our paper (see ''Assembling the Space Catapult''). The inclination angle for the rod will vary from 0º (rod is transported horizontally on the ground) to 90º (Space Elevator’s cabins are carrying the rod to space) and here we will discuss some medium case when the rod is semi-elevated in the air, when the angle between rod and ground/cable is equal to 45º. On the engineers’ ''eFunda'' web-site there is online calculator that enables to receive the value of ''Deflection'' (actually that site gives different term for this-''Displacement'') ['''10''']:<br />
<br />
Here we need to enter the relevant values:<br />
<br />
''Length of beam'', ''L'': 100 000 meters<br />
<br />
''Line pressure load on beam'', p: In our case this is the weight per meter length. As we have already mentioned the radius of the rod’s cross-section is 1 meter, so the volume of rod’s 1 meter-length part will be 3.14 cubic meter. In case of using Carbon nanotubes with above-mentioned density-0.1 g/cm<sup>3</sup> the weight will be equal to 314 kg or 3 079 Newton. Since we have got the inclination of 45º we should multiply this value to cos45º- 0.707, so we get 2176 N/m.<br />
<br />
''Young's Modulus'', ''E'': This is equal to 1 000 GPa for Carbon nanotubes [11] <br />
<br />
''Distance from neutral axis to extreme fibers'', ''c'': In our case it is equal to the radius of the rod-1 meter<br />
<br />
''Moment of Inertia'', ''I'': It is equal to (pi*r<sup>4</sup>)/4, so it is equal to 0.785<br />
<br />
According to these initial data the calculator returns extremely high value of Deflection, much higher than the length of the rod itself: -3.61 × 10<sup>9</sup> meters. This result shows us that with the current materials (Carbon nanotubes in our case) it is impossible to raise the rod as ''one single unit'' to space by means of Space Elevator and we need other materials with less density and more ''Young's Modulus'' (or the rod should be much thicker but this will lead to increasing its mass). Therefore, we have got two options: either we should deliver the parts of that rod and then assemble them in space (we have already discussed this option) or completely different technologies for manufacturing the rod should be developed. Particularly, it would be very good if it was possible to manufacture the rod ''in continuous mode'' in vertical position and then uninterruptedly directly to carry it to space by means of Space Elevator’s cabins. Under such approach there will be no ''Deflection'' and several cabins will be able to deliver the rod in space. <br />
<br />
One note about transporting the rod from its place of manufacture to Space Elevator’s base station. We think that this process should be executed by many transports, in other words we are convinced that if the rod is carried by two trains only (or any other kind of transport) then the rod will continuously touch the ground since the ''Deflection'' occurs in any position-horizontal, inclined or vertical and this circumstance will lead to its damage, that’s why several transports will be needed to hold the rod at as many places as possible.<br />
<br />
=Stabilizing the counterweight=<br />
Stabilizing the Space Elevator’s counterweight is very important question during Space Catapult’s performance. Indeed, when the rod rotates it makes the imaginary circles in space and due to rod’s and payload’s masses the Space Catapult’s ''center of mass'' will be continuously shifted and if the counterweight is not somehow stabilized then it will make problems for accurate aiming to certain point at the celestial sphere. Also, if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable then there will be the danger that the rod may actually hit the cable and cut it. To avoid these problems we need to apply to serious measurements. <br />
<br />
First of all, the electro motor’s own axis can be quite long and this will diminish the chance to failure of the whole system. Actually, we are convinced that counterweight’s (where the electric motor will be placed) size will be quite large, mainly due to solar panels’ sizes and amount (this issue was discussed above), also the electromotor should be quite large and powerful to rotate the rod, and hence there will be enough distance between the rod and Space Elevator’s cable. <br />
<br />
The second serious problem is that the center of gravity of the system is not at the center of rotation, therefore it will be necessary to balance the rotating system when the payload is attached and when it is released.<br />
<br />
We think that the Space Catapult’s rod should not be deployed/directed to one side only but some counterweight of it should also exist. This is necessary since the unilaterally loaded (we mean the rod itself plus payload) rod will cause the counterweight to somersault. In other words, the rod should extend to other side and the ''moments of inertia'' of both sides should be the same as during rotating the rod as after releasing the payload when the rod still rotates. This is easily achievable if some additional, second payload is placed on the rod’s second end. Therefore, the Space Catapult will launch two payloads at the same time to the ''opposite'' directions but at various speeds if the second part/side of the rod is shorter.<br />
<br />
How the second payload should be placed on the rod and should we really send two payloads? Until we have got balanced rod this problem does not arise but as soon as the Space Catapult releases the payload this balance will be violated, how it can be restored? There are two theoretical ways for achieving this: reducing the ''mass'' or reducing the ''length''-with diminishing either one of them the ''moment of inertia'' will be decreased. We think that reducing the mass will be less practicable since this would require placing the second payload (spacecraft or anything else) on the rod’s second part and this cannot be done from the Space Elevator’s cabin-this is the easiest way for delivering the payload from Earth to Space Catapult’s rod; so we would have to (see ''Rod’s plane of rotation towards the Earth'') put the second payload on the electro motor and then send it rod’s second part’s end. This is quite complicated task; therefore we can apply to second approach-put some sliding object that will immediately move to electromotor as soon as the spacecraft is released.<br />
<br />
[[File: MOI.jpg]] <br />
<br />
The next problem that may occur is that when the electro motor rotates the rod this motion will make the Space Elevator to rotate to the opposite direction. The same problem arises when helicopter’s primary blade’s rotation forces the helicopter to rotate to opposite direction and this possible rotation is annulled by ''tail rotor''. We think that for balancing the counterweight the additional motor and rod should be installed and this rod should rotate to opposite direction and if their ''angular momentums'' are equal to each other, then their rotations will cancel each other. More precisely, the following equation should be fulfilled:<br />
<br />
[[File: Angular momentum.png]] <br />
<br />
Where ''m'' is mass of the rod, ''v'' is angular speed and ''L'' is rod’s length, the numbers ''1'' and ''2'' refer to first and second rods correspondingly. For balancing both rods’ rotation the multiplication at both sides of the counterweight should be equal, by the way this circumstance enables us to use the second rod with shorter length and even with less mass but rotating at more angular velocity.<br />
<br />
Such approach will effectively deal with other problem which will arise when the Space Catapult releases the payload(s), at this moment the second motor should instantly diminish its angular velocity to some certain level (an ordinary mechanical brakes could be used for this purpose), in this case ''angular momentums'' for both motors/rods will be equal again and Space Elevator’s counterweight will maintain its attitude in space. See the image below depicting the Space Catapult with two electro motors and rods:<br />
<br />
[[File: Two-rods.jpg]] <br />
<br />
Such approach will justify itself if rod’s plane of rotation is parallel to Space Elevator’s cable, but if this plane is orthogonal to cable (see ''Rod’s plane of rotation towards the Earth'') then the second/balancing electromotor cannot be placed under the counterweight because the cable will be cut when rod touches it. Therefore a bit different approach should used and we need to install two/four/eight electro motors with their own relatively shorter rods rotating to opposite direction. They should be placed at the counterweight’s lower side and on its edge (as we suppose the counterweight should be disc) so that their rods not to touch and cut Space Elevator’s cable. Also, total a''ngular momentums'' from these motors should be equal to the ''angular momentum'' from upper motor and thus the counterweight will not rotate and the Space Elevator’s cable will not be twisted. This situation is presented below:<br />
<br />
[[File: Modified-2.jpg]] <br />
<br />
We think that the array of gyroscopes would be also very useful to be installed at the counterweight since they can maintain the attitude of the whole system and this is important for precise aiming to certain point at the celestial sphere. As for the energy required for gyroscopes’ performance it could be received from the array of solar panels which as a result will generally serve Space Catapult’s precise performance.<br />
<br />
=Space Catapult placed at Lagrangian points-the way for gaining subluminal speeds=<br />
<br />
In our paper we discussed the Space Catapult based on the Space Elevator’s counterweight and concluded that this would be convenient when we intend to deliver the payload to space from the Earth. However, such Space Catapult cannot gain very high speeds and therefore we need to choose other way. It is obvious that we need to keep rod’s plane of rotation orthogonally relative to the ''Earth-Sun connecting line'' and hence we should place the rod on the celestial body which will be in synchronous rotation with the Sun but since there is no such body in the solar system we conclude that the Space Catapult for subluminal speeds (the speeds close to speed of light are in mind) should be placed at such point near the Earth where it will be easy to reach it from our planet and where the rotating rod will not hit the Earth and will be always at the same distance from the Sun to avoid the influence of its tidal forces. The examples of such places are '''Lagrangian''' L<sub>1</sub> and/or L<sub>2</sub> points at 1.5 million km away from the Earth. If the Space Catapult is placed at one of these points then its rod can be always orthogonal to the Sun in principle, at the same time it will never collide with the Earth and also it will be quite close to the Earth since 1.5 million km distance is very negligible in space.<br />
<br />
We have got several notes regarding such approach. First, when we mentioned that the rod’s various parts can be at the same distance from the Sun this strictly speaking is not very true because the Sun can be referred as little point where its gravity “comes out” from while the rod is quite long and its initial part (placed at one of the Lagrangian points) will be attracted stronger than the utmost one (for equal attracting the rod should the arc ''with the same curviness as Sun’s surface'' and not straight line); but still this is better than to direct the rod exactly towards the Sun where the tidal forces will try to tear the rod. Second, the Space Catapult should be placed at Lagrangian L1 point which is closer to the Sun than L2 one and therefore receives by 4 % more energy per area from the Sun. Third, the rod should be in constant rotation, this requires much less energy than accelerating it from zero, then stopping it and accelerating it again. Fourth, the existence of the asteroid belt in the solar system between Mars and Jupiter will somehow restrict the actual length of the rod. Indeed, the Space Catapult should be placed at one of the Lagrangian points at 1 AU distance from the Sun while asteroid belt approximately lays at 2.7 AU, from the simple geometry it is obvious that the length of the rod ''almost reaching'' the asteroid belt can be approximately equal to 390 million km, and if the rod is longer then it may simply hit any asteroid within that belt. For 390 million km length rod and for 100 000 m/sec2 acceleration at rod’s end (where the payload will be attached) the maximal speed that the spacecraft can gain will be approximately equal to 200 000 km/sec (two thirds of the speed of light) and this can be considered as enough for practical interstellar spaceflight. Fifth, the spacecraft should be directly put on the rotating rod’s initial end (near electromotor) and then slide towards the other end with its own rocket engines. To achieve this, the spacecraft will have to cover relatively less distance on the rod and then rod’s circular motion will accelerate the spacecraft further-we have already mentioned this in this paper when speaking about deploying the Lunar Space Catapult. This action-putting the spacecraft on the rod will not be difficult since rod’s angular velocity will be quite low due to rod’s huge length, particularly for 400 million km length rod and for 200 000 km/sec linear speed the rod’s angular velocity will be 0.0000796 revolutions/sec.<br />
<br />
[[File: Lagrangian-point.jpg]] <br />
<br />
We have already mentioned that to avoid the destructive influence of the Sun’s tidal forces the rod’s plane of rotation should be orthogonal to the Earth-Sun connecting line. By the way, note that under such approach we may have to wait one year until the Lagrangian Space Catapult occupies the relevant position towards the certain point at the celestial sphere where the spacecraft should be sent to. But from the other hand it would be useful if it is feasible to rotate this whole structure around the imaginary axis directed towards the ''ecliptic poles'' (depicted as faint green dash line on the image above), the reason if this is the possible danger when the rotating rod may hit Mars or asteroids that orbit around the Sun closer than 2.7 AU distance (for example ''433 Eros'' or ''1036 Ganymed''), hence for avoiding such undesired collision the Lagrangian Space Catapult should be slightly rotated by several degrees clockwise/counterclockwise so that the rod not to collide with any celestial object. We are convinced that rotation by several degrees will be absolutely enough measurement due to rod’s gigantic length and relatively less sizes of the celestial objects in the solar system.<br />
<br />
The next issue that we should discuss refers to stability of the Lagrangian Space Catapult placed at L<sub>1</sub> point. As we see this structure will have enormously gigantic size while the Lagrangian point is relatively little mathematical one in space, so what can be done to be convinced that this structure will remain at that point and do not shift aside? The body placed at one of the Lagrangian points is affected by other celestial objects’ gravity and therefore for achieving the balance the rod needs to have the counterweight with more mass if it (counterweight) is shorter. As we clearly see the rod needs the counterweight for two reasons: not to let the Space Catapult somersault and for maintaining it at the L1 point. We think that it would be very useful if the arrays of solar panels act as counterweight since exactly they can give us energy for rotating the rod. Also, we need the second, shorter, perhaps less massive but faster-rotating rod (again-solar panel arrays) the opposite rotation of which would cancel first rod’s rotation, this issue was discussed in this paper. These arrays of solar panels are depicted on the image shown above. <br />
<br />
How such a gigantic structure as Lagrangian Space Catapult can be assembled in space? In our paper we discussed the possible ways for delivering the rod from the Earth to the Space Elevator’s counterweight, now we will try to show that it is possible ''in principle'' to assemble the extra-long rod in space. <br />
<br />
If it is possible from the technical point of view to manufacture extra-long rod then we can use this approach and make 1.5 million km length rod (this is the distance between the Earth and Lagrangian L<sub>1</sub>/L<sub>2</sub> point) that will be mechanically directed to the base station at L<sub>1</sub> point. The capturing devices there will catch the rod and attach it to the electro motor’s shaft after which the rod should be spun by 90º so that it to be orthogonal to Earth-Sun connecting line (for this purpose the additional mechanisms will be needed), this spin is necessary because L<sub>1</sub> point is located on the Earth-Sun connecting line (that is towards the Sun if we look from the Earth) and when directing the rod from the Moon it will lay ''along'' this line while we need across. After this the rod should be slid to another side and then the next rod should be directed to the Lagrangian Space Catapult where it will be attached to the previous rod and etc. In other words, the extra-long rod will be assembled from one side and its length will “grow” from this side to other one, this is necessary because the distance between Moon (the rod should be manufactured exactly there and not on the Earth due to our planet’s relatively more gravity, atmosphere and problematic space debris belt around it) and L<sub>1</sub> point is constant and rod’s parts cannot be more. Due to whole rod’s and its parts’ lengths (400 million and 1.5 million km correspondingly) we think that about 260-270 such operations will be needed to finish assembling the rod (400/1.5). The process of assembling the Lagrangian Space Catapult is shown on the image below:<br />
<br />
[[File: Lagrangian-point-assemble.jpg]]<br />
<br />
=Conclusion=<br />
<br />
As we have seen, for leaving the Solar system and reaching the remote celestial bodies (stars, nebulas) there is no need to develop advanced and complicated technologies that mostly are not capable for gaining extra high velocities nevertheless. In any case, until the Space Elevator is really built (scheduled for construction by 2031) we have got much time for developing the idea of Space Catapult in technical aspect, like finding appropriate materials for the rod, perfect the ways how the Space Catapult can be assembled in space and etc. The concept of Space Catapult itself is the easiest one, does not need developing neither complex and sophisticated technologies, nor some exotic methods (such as ''Gravitoelectromagnetic toroidal launchers'', ''Antimatter rocket'' and etc.) and can be easily implemented in near future; in other words the Space Catapult is not some sophisticated structure that would need profound science research and the fact that it will enable us to gain whatever high speed will justify its developing and building by the humankind. As for other technologies like Ion Drive, they could be used by the spacecraft during flight for other purposes, for example for correcting/changing the flight direction.<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Space_Elevator<br />
<br />
2. http://www.isec.info/index.php?option=com_content&view=article&id=14&Itemid=9<br />
<br />
3. http://www.space-track.org/perl/geo_report.pl (provided data updates regularly, registering is needed) <br />
<br />
4. http://www.oosa.unvienna.org/pdf/reports/ac105/AC105_720E.pdf page 24 (data as at 21 August, 1997) <br />
<br />
5. http://www.amostech.com/ssw/presentations/Session7/S7-1Molotov.pdf page 16<br />
<br />
6. http://www.esa.int/SPECIALS/ESOC/SEMN2VM5NDF_mg_1_s_b.html <br />
<br />
7. http://eetd.lbl.gov/ecs/aerogels/sa-physical.html<br />
<br />
8. http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant<br />
<br />
9. http://www.you.com.au/news/2005.htm, http://www.spacedaily.com/news/ssp-03b.html<br />
<br />
10. http://www.efunda.com/formulae/solid_mechanics/beams/casestudy_display.cfm?case=simple_uniformload<br />
<br />
11. http://en.wikipedia.org/wiki/Young%27s_modulus<br />
<br />
<br />
'''Appendix''': <br />
<br />
Animation illustrating the payload’s departure from the Lagrangian Space Catapult:<br />
[[File: Lagrangian-point-animation.gif]]</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_5&diff=3672OpenSpace 52013-09-21T13:06:13Z<p>Eagle9: </p>
<hr />
<div>== '''Space Catapult''' ==<br />
<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
=INTRODUCTION=<br />
<br />
<br />
The new method for sending the spacecrafts in deep space is presented here. The paper describes the long rod rotated by electro motor placed at the Space Elevator’s counterweight and at Lagrangian points. This simple structure will enable the rod to gain high velocity and carry the payload with it. After reaching the desired speed the rod will release the payload that will fly in space along the imaginary circle’s tangent. This structure we called Space Catapult and it should work with the assist of Space Elevator. This latter should be used for carrying the payload from the Earth to Space Catapult’s rod.<br />
<br />
For exploring the outer space the humankind generally uses the rocket engines, mostly chemical-propelled ones. They enable us the explore near-Earth celestial bodies and other planets in the solar system. They even enabled us to send several deep space missions beyond the solar system such as '''Pioneer-10''', '''Pioneer-11''', '''Voyager-1''', '''Voyager-2''', however by means of this technology the flight lasts undesirably long and it seems to be impossible to reach remote celestial bodies in space such as stars, so new technologies are necessary for this purpose. However new technologies do not necessary imply new kind of rocket engines, such as ''Ion Drives'' because they are capable for gaining several ten times higher speeds only, but for remote celestial bodies even they are not suitable. Besides, they need a huge amount of energy to be stored onboard the spacecraft and this will make additional problems. So, high speed should be achieved with absolutely different approach. How this can be done?<br />
<br />
High speed can be easily achieved by means of fast-rotating rod around the electric motor. The motor’s rotational speed can be very high; the rod also can be quite long, hence the rod’s end’s linear speed can be extremely high, absolutely unachievable for any other technologies nowadays. The payload should be fastened at the rod’s end where the linear speed generally reaches maximal value. After reaching the necessary speed the rod will release the payload that will fly along the tangent from the current position. Thus the electric energy can be turned into payload’s speed and its velocity could be as high as we wish (except the ''speed of light'' of course). In principle the '''Space Catapult''' (thus we call this structure) would be the simplest, the most convenient and direct way for converting the energy/electricity into speed and conveying it to payload. <br />
<br />
As we see the Space Catapult is quite uncomplicated structure, however if we wish to gain high speeds we should deploy it in space, not on the Earth. Indeed, our planet is surrounded with dense atmosphere that impedes any quick motion, so if we rotate the rod quickly the atmospheric drag and generated heat would burn it very soon, therefore the Space Catapult should be built and deployed in space only, and as we suppose-at the Space Elevator’s counterweight. In other words, the Space Elevator’s counterweight will operate as Space Catapult. See image below:<br />
[[File:Space-catapult.jpg]]<br />
Generally, what is the Space Elevator ['''1''']['''2''']? According to modern concepts it will be the tall vertical structure built on equator and will have height of several ten thousand kilometers with its thin cable fastened to the base station on the Earth and with counterweight placed higher geostationary orbit. Because of balance between centrifugal force and gravity this structure will be stretched and the cabin will move along its cable carrying the goods into high orbit. After delivering the payload, the cabin will descend and carry the next one.<br />
In Space Elevator’s concepts several solutions have been proposed to act as a counterweight: <br />
<br />
1. Heavy, captured asteroid <br />
<br />
2. Space dock, space station or spaceport positioned past geostationary orbit <br />
<br />
3. Extension of the cable itself far beyond geostationary orbit. <br />
<br />
The third idea has gained more support in recent years due to the relative simplicity of the task and the fact that a payload that went to the end of the counterweight-cable would acquire considerable velocity relative to the Earth, allowing it to be launched into interplanetary space. However this idea cannot be completely shared by us due to following reason: <br />
<br />
It is well-known that the values of both '''Orbital''' and '''Escape Velocities''' decreases with increasing the altitude while the '''tangential velocity''' of Space Elevator’s cable increases. We can see the differences between them from the chart presented below:<br />
[[Image: Cxrili.gif]]<br />
<br />
As we see from this chart the ''tangential velocity'' of the Space Elevator even at its end (144 000 or 200 000 km altitude) is not very high to decrease the necessary time for covering the distance from the Earth to remote celestial bodies significantly. To achieve this, even the longer Space Elevator would be needed (its ''tangential velocity'' is directly proportional to its length) and this circumstance would complicate the technical task for building such Space Elevator. Because of this, there is no necessity to extend the cable itself far beyond geostationary orbit as proposed in the third variant. In any case, we have already seen that by means of Space Catapult it is possible to gain such huge velocities that are absolutely unachievable with other technologies, for example with Space Elevator. Therefore, using the counterweight and placing the Space Catapult there definitely has got some technical sense. <br />
<br />
However, we think that the question where the Space Catapult should be placed needs further discussion. Theoretically, the Space Catapult with its payload and nuclear reactor/solar panel needed for rotating the rod may be mounted not only at the counterweight, but on the Space Elevator’s cabin also that can carry all these goods to space in a usual way, as it should do it according to Space Elevator’s modern concepts. This option is quite possible, however for realizing this we need to know the mass of the payload, nuclear reactor/solar panels’ mass plus Space Catapult’s mass from one hand and Space Elevator’s lifting capacity (this ''must'' be more) from other hand, but these data are not available nowadays, therefore we think that the Space Catapult should be still mounted at the Space Elevator’s counterweight where it will be possible to send the payloads into deep space in ''continuous mode'' at high velocities.<br />
<br />
As we saw the Space Catapult is capable to gain very high velocities; however there is being developed other technologies and they in future will enable the spacecraft to fly at high speeds in space. These are Ion Drive systems, more precisely the most perspective one-''Variable Specific Impulse Magnetoplasma Rocket'' (VASIMR) which still under development can be used in future for deep space missions. Can these engines and Space Catapult be the rivals in space? Since none of them have been built and used in space yet we cannot give a persuasive answer to this question; however still it is possible to underline Space Catapult’s one significant advantage: if the future spacecraft uses the VASIMR (or any other kind of Ion Drive) engine it will definitely need to be equipped with nuclear reactor, otherwise the spacecraft will not be able to gain high speeds, also it will need to carry fuel tanks for this purpose. As for the Space Catapult, it can give much higher speed to spacecraft, besides it will have ''stationery'' power plant (see ''Energy source placed on the Space Elevator’s counterweight'') at the Space Elevator’s counterweight, so the payload will ''not'' have to carry the nuclear reactor onboard and this circumstance will lighten the work for deep space spacecraft. Besides, we should not forget that unlike the spacecrafts equipped with ion drive engines the Space Catapult will need no fuel for gaining high velocities. <br />
<br />
Briefly, Space Catapult’s advantages over any kind of propulsion systems are: <br />
<br />
1. Ability to gain any speed that is absolutely unachievable by means of other kinds of engines. <br />
<br />
2. No need by spacecraft to carry energy source that would make it too heavy and impracticable.<br />
<br />
=The Space Catapult needs long rod=<br />
<br />
When building the Space Catapult at Space Elevator’s counterweight we should install quite long rod there, the shorter the rod is, the easier would be installing it, however we should note that rod cannot be extremely short, let’s say 1 km length or so due to following reason:<br />
<br />
When we are going to send some payload into space, we need not only high velocity, but one certain direction also. The little inaccuracy in direction, inclination in several arcminutes is actually acceptable since the spacecraft would easily balance it with its engines; however great inclination from the initial direction would send the spacecraft into the completely different direction and in such case the whole mission will fail.<br />
<br />
If two Space Catapult’s rods have the length of let’s say 1 kilometer and 10 kilometers, then for giving to payload some certain linear speed (for instance 100 km/sec) these rods should rotate at different angular velocity. It is easy to ascertain that the shorter rod should rotate 10 times faster to gain the same linear speed than the rod with more length. But the faster the rod rotates, the more difficult will be to “catch” the needed moment for releasing the payload from the rod for sending it towards some certain direction. If the rod is too short, then it has to rotate very quickly for gaining some certain linear speed and therefore it will be extremely difficult catching the needed moment for releasing the payload. Hence, too short rod can make problem for sending the payload to some certain direction in space especially at high velocities. So, based on payload’s needed velocity we should find rod’s desired, minimal length that will enable us to send the payload in space to necessary direction without fear that it may yaw from the course. <br />
<br />
However, rod’s length will be crucial for payload’s abilities for withstanding the acceleration also. As an example, we can try to calculate its value which the payload will have to withstand during rod’s rotation. The acceleration of the body rotating at the circle with some constant velocity is calculated by the following formula:<br />
<br />
[[File: Acceleration - Copy.jpg]] <br />
<br />
Where a is acceleration in ''m/sec''<sup>2</sup>, ''v'' is payload’s linear velocity on the circle in ''m/sec'' and ''r'' is radius of the circle in ''meters'', in our case it is equal to rod’s length. Let’s assume that the rod is 100 km length and the electromotor rotates it so that payload’s speed is equal to 50 km/sec, in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design and manufacture the spacecraft’s subsystems (avionic and etc.) capable to withstand such acceleration. This circumstance somehow restricts the speeds that we can achieve, in any case their values actually depends on spacecrafts’ abilities for withstanding g-loads. But what can we do if much higher speeds are needed? The answer directly derives from that formula: the radius should be more; by the way note that this is additional reason why the longer rod is more useful. If we are able to make the extra long rod, then this will enable us to gain much higher velocities. <br />
<br />
What material should be used for manufacturing the rod? It is obvious that if very high speeds are needed the rod should be long and even in this case the acceleration at its end will be quite high, therefore ''sufficiently strong and light materials'' are needed for this purpose and making them is as similar challenge as in case of Space Elevator where the same requirements arises for the cable’s material. The lightness is needed because in case of heavy rod a lot of energy will be needed to rotate it; the strength is needed because in case of lack this property the rod will be destroyed due to great acceleration.<br />
<br />
=The mechanism for holding and releasing the payload=<br />
<br />
How the payload can be held by Space Catapult’s rod during rotation and how it can be released from the rod? We think that using ''electromagnet plus mechanical holding devices'' would be a good solution. More precisely, after the payload is attached to the rod it must be held by means of both methods until the rod accelerates and reaches necessary velocity (it may take even several days), but with approaching the desired speed the mechanical device should release the payload however the electromagnet(s) should still hold it. The explanation of such approach is following: generally the mechanical devices are much slower/sluggish in performance than electronic ones. We have already said that when releasing the payload the extreme accuracy is needed and mechanical devices cannot guarantee ''the exact time of releasing'' the payload unlike electronic ones. That is, it’s unlikely that mechanical devices can release the payload at some certain moment when needed while in case of electromagnet it would be enough to cease electric current there, it would lead to immediate vanishing of the magnetic field and sending the payload along the tangent from the point where the payload would be at the current moment. <br />
<br />
<br />
We think that the ''fastest control system'' would enable to release the payload to certain direction. This system (extremely fast-operating computer plus measuring equipments) should know the current position of the rod’s end, the current speed, the needed direction and be capable for computing the necessary moment for giving the order for diminishing the voltage for electromagnets and hence releasing the payload to desired direction and velocity.<br />
<br />
=Rod’s plane of rotation towards the Earth=<br />
<br />
The Space Catapult’s rod when rotating makes the circular plane/flatness in space and this plane may be horizontal/parallel to Earth surface, that is making the right angle to Space Elevator’s cable or it may be placed along the cable; see the both possible situations here:<br />
<br />
[[File: Planes-of-rotation - Copy.jpg]] <br />
<br />
Both approaches have got their advantages/disadvantages and here we will discuss this question, first of all from the point of view of safety.<br />
<br />
For gaining extremely high velocities quite long rod would be needed, maybe with the length of several thousand kilometers or even more. If such rod is placed ''along'' the Space Elevator’s cable then the rod during rotation will cross many orbits from the ''Medium Earth Orbit'' to ''High'' ones. When rotating, the rod may actually hit any satellite and/or space debris object and such collision can lead to rod’s complete destruction; therefore we should choose such plane which would be much more free from any artificial objects; hence if the rod rotates ''horizontally/parallel'' to Earth’s surface at high enough altitude where the satellites’ population is relatively low then this measurement would justify itself because under such circumstance the rod will not cross satellites’ orbits (rod’s plane of rotation will simply coincide to ''one'' orbit’s path). However, we should also note that this altitude actually depends on the Space Elevator’s proposed length. Indeed, the Space Catapult’s rod should be mounted at the Space Elevator’s counterweight; this counterweight from its side should be placed at the end of the Space Elevator at such altitude where the satellites’ population is as low as possible. This means that Space Elevator’s proposed height should be agreed with mounting Space Catapult on its counterweight. According to various databases the number of man-made objects at high orbits, more precisely beyond geostationary orbit is much less than on the lower orbits ['''3''']['''4''']['''5''']['''6'''], therefore the Space Catapult with its rod should be located at the altitude of 50 000-60 000 km above the sea level. At such altitude the space is almost free and nothing will impede rod’s rapid rotation. Besides, the satellites at high orbits are orbiting around the Earth slower than on the lower orbits (as known any satellite orbits around its primary body slower in apogee than in perigee), therefore if some tracking system is mounted at Space Elevator’s counterweight then it will enable the Space Catapult to avoid undesired collision with satellites during Space Catapult’s performance. In other words, the Space Catapult should operate only when the there are no satellites near its vicinities.<br />
<br />
Now we will try to discuss this question from other side.<br />
<br />
How the payload can be transferred from the Space Elevator’s cabin to the Space Catapult’s rod? One way is following: cabin reaches the counterweight where the payload will be released, then payload will be mechanically conveyed to rod, continues its way ''on the rod'' (like the train rides on the rails) and after reaching rod’s end it stops, the rod begins rotating and after gaining necessary linear speed it releases the payload to needed direction. This method is generally realizable; however it seems to be too complicated and unpromising compare to the second one: the Space Catapult’s rod is stopped in space so that it to be directed downwards to the Earth and be parallel to Space Elevator’s cable. The Space Elevator’s cabin moving along the cable with payload stops at the cable ''near'' the end of the Space Catapult’s rod and releases the payload that will fly to the rod, attaches itself to the rod’s end (here the electromagnets would be useful), the rod begins rotating and after gaining needed linear speed will release the payload to necessary direction.<br />
<br />
This second way seems to be more promising because the first one is much more complicated as we have already said: first of all there would be needed some mechanical devices for transferring the payload from the Space Elevator’s cabin to counterweight, the counterweight should have the hole for the payload to move through it from below (we should not forget that the Space Catapult should be mounted ''at'' the counterweight, not ''beneath'' it), besides the rod should be made so that it to have some conveying surface (rails for instance) the payload to move on it. As we see it would be much more convenient if it is possible to convey the payload from the cabin to the rod directly and this would be feasible under the second method which is depicted below:<br />
<br />
[[File: Convey.jpg]] <br />
<br />
One more aspect regarding Space Catapult’s position. This structure, its rod, its electro motor and etc should be mounted at Space Elevator’s counterweight so that the rod to be placed westwards from the cable. The reason of it is following: when the Space Elevator’s cabin stops and releases the payload (which should fly to Space Catapult’s rod) the current speed of which will/should be more than the value of the ''Orbital/Escape Velocity'' at the current altitude. After releasing the payload will fly westwards and upwards because its orbit will be ellipse, under ellipse the payload will fly higher to apogee and at the speed less than Space Elevator’s current speed at the given altitude, in other words the released payload will “lag behind” the Space Elevator’s cable; therefore payloads’ ''stopping points'' at the cable and Space Catapult’s rod’s length should be calculated and chosen so that the payload to fly directly towards rod’s end. This process would be feasible in both cases-if the rod’s plane of rotation is parallel to Earth’s surface and if it is placed along the cable-but still this would be easier for the payload to achieve the rod’s end if the rod is placed along the cable because at least the distance that the payload should cover in space will be less.<br />
<br />
The length of the Space Catapult’s rod placed at the Space Elevator’s counterweight might vary since for various spaceflight purposes different initial speed will be needed and relatively low speed could be achieved by means of shorter rod. Because of this reason it might be necessary to change Space Catapult’s rod’s length, therefore it would be useful if the rod consists of two parts where the first part would be perpetually attached to electro motor and the second one will be attached to the first part if necessary. For this operation Space Catapult’s rod should be placed along the cable since the relative nearness would make this operation quite easy and it could be accomplished by the crew directly from the Space Elevator’s cabin stopped at the needed altitude. <br />
<br />
For deciding the question how the Space Catapult’s rod should be placed towards the Space Elevator’s cable we should take into consideration one substantial circumstance-to which direction do we plan to send the payload in space by means of Space Catapult? This circumstance will influence deciding this problem due to following reason:<br />
<br />
In case ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and if rod’s plane of rotation is parallel to Earth equator, then this plane will be orthogonal to Earth’s rotation axis. This axis from its side is tilted to ''ecliptic plane'' by 66° 34'. This means that Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 23°26'. Here follows very important consequence: under above-mentioned conditions the rod when rotating will be capable for covering only the part of the ''celestial sphere'' from 0° to 23°26' (counted from ''ecliptic plane'' northwards and southwards to ''Ecliptic poles''). This is about one fourth of the ''celestial sphere'' (23°/90°), this will not make problems if we intend to use the Space Catapult for exploring the solar system’s planets because their orbits’ tilts towards ''ecliptic plane'' do not exceed 7° (for planet Mercury, for other planets this tilt is even less); however we will not be able to send the payload for example to the nearest star ''Alpha Centaurs'' because this star is located at -42 degree according to ''ecliptic coordinate system'' in the celestial sphere.<br />
<br />
The situation will drastically change ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and ''if'' rod’s plane of rotation is orthogonal to Earth’s equator and therefore parallel to Earth’s axis of rotation. We have already discussed this option when we mentioned that the rod should be placed westwards from the cable and explained why it would be useful-for delivering the payload from Space Elevator’s cabin to Space Catapult’s rod. Under such conditions the Space Catapult will be capable to aim to any point on the ''celestial sphere''. Indeed, the Earth with the Space Elevator rotates around its axis and Space Elevator’s counterweight draws an imaginary circle in space. This circle is tilted to ''ecliptic plane'' at 23°26' and crosses this plane in two point called ''ascending'' and ''descending nodes''. The other points that are 90° away from these nodes we call point(s) of ''maximum elevation/depression'' (relative to ''ecliptic plane''). When the Space Elevator is at a''scending/descending node'' its rod and hence the payload can be directed to any point from 0º to 66º on the celestial sphere northwards and southwards from ecliptic plane. This makes about 75 % of celestial sphere. See the image depicting this situation:<br />
<br />
[[File: Node.jpg]]<br />
<br />
But when the space Elevator reaches the points of ''maximum elevation/depression'' then its rod during rapid rotation may be directed to any point from southern ''Ecliptic pole'' to ''Northern pole'' at the celestial sphere because at these points rod’s ''plane of rotation'' is orthogonal to ''ecliptic plane'' and thus the rotating rod can aim to ecliptic poles as well as other points. See this situation below:<br />
<br />
[[File: Elevation.jpg]] <br />
<br />
The situation will be similar if the Space Catapult’s rod is orthogonally placed towards cable. Under such approach Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 66° 34' and the Space Catapult will be capable to cover ''three fourths'' (66°/90°) of the ''celestial'' ''sphere'' when the Space Elevator is at the points of ''maximum elevation/depression'' and the whole celestial sphere when the Space Elevator is at ascending/descending nodes. For aiming the needed point on the celestial sphere the Earth should occupy the appropriate attitude towards the stars during the revolution around its axis, the same thing should be done under previous case described in the paragraph above. <br />
<br />
In conclusion, thinking about rod’s plane of rotation towards the Earth, we should note one important difference between above-mentioned approaches: if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, then in case of emergency during Space Catapult’s performance (for example if the Space Catapult’s rod is cut by sudden meteorite bombardment) the rod’s part with the payload may simply crash to the Earth at huge velocity if the rod at this moment is directed to the Earth. This cannot happen if Space Catapult’s rod’s plane of rotation is orthogonal to Space Elevator’s cable because payload’s rotational path will not be directed towards the Earth and hence its flying trajectory will never cross the Earth.<br />
<br />
=Braking the Space Catapult’s rod=<br />
<br />
After releasing the payload at necessary speed and direction, the Space Catapult’s rod will have a huge angular velocity that needs to be decreased to zero in order the Space Catapult’s rod to get another payload in motionless position and then to send it to space. <br />
What methods can we use to reduce Space Catapult’s rod’s rotation to zero? There are several possible ways: <br />
<br />
1. The electromotor designed for accelerating the rod may actually play a role of brakes, more precisely after releasing the payload to space the electromotor should operate/rotate in the opposite direction, hence rod’s rotational speed will be diminished to zero after that electromotor will stop operating. Under such method a bit less energy will be spent for decelerating the rod than in case of accelerating because when decelerating the rod is free from payload. <br />
<br />
2. An ordinary mechanical brakes, however due to electro motor’s and rod’s sizes a huge brake(s) would be needed to be installed on the Space Elevator’s counterweight and this circumstance would make additional problems from the engineering point of view. Nevertheless, we should admit that under such method we would not need as much energy as during accelerating; on the contrary, in this process the heat will be emitted as it generally happens during braking. <br />
<br />
3. For decelerating the rod we can use the well-known phenomenon in physics-''electromagnetic induction'': when the c''onductor/ closed circuit'' moves into the magnetic field the electric current is generated there. In case of Space Catapult we can use this phenomenon in the following manner: the conductor should be wrapped around the whole length of the rod like a helix and there should be possibility that this conductor to be turned into the ''closed circuit'' by means of mechanically connecting its ends (see the image below). After releasing the payload at necessary speed and direction this circuit should be closed, then according to ''electromagnetic induction'' the electric current will be generated in the conductor and the energy of this electric current will come from rod’s kinetic energy. Therefore, inducted electric current in the enclosed circuit will force this circuit and rod to lose kinetic energy and speed. The part of the generated electric current will be spent in prevailing conductor’s electric resistance:<br />
<br />
[[File: Helix.jpg]] <br />
<br />
The advantage of this method is that for decelerating the rod no energy will be required, as for drawback-much time will be required for this purpose because at the altitude of several ten thousand kilometers the Earth’s magnetic field is quite weak and the effect described in the paragraph above will need much time to operate and give necessary result. <br />
<br />
4. The above-described third method could be realized in a bit different way: if the conductor wrapped around the rod is a closed circuit and if we conduct the electricity there then the electric current will generate its own magnetic field that will counteract with Earth’s one. More precisely, according to ''Lenz's law'' induced current’s magnetic field will be in such a direction as to oppose the motion or change causing it, in other words induced current’s magnetic field will counteract outer magnetic field’s any change and this will cause decelerating rod’s rotation and finally its stopping. <br />
<br />
5. The obvious disadvantage of the third and fourth method described above is weakness of the Earth’s magnetic field because of which decelerating the rod may be delayed in time. For solving this problem we can create artificial magnetic field by means of electromagnets. Particularly, one electromagnet should be placed at the Space Elevator’s counterweight, very close to Space Catapult’s rod. The second electromagnet should be placed directly on the Space Catapult’s rod close to first electromagnet (actually, instead of this second electromagnet there could be used the conductor wrapped around the rod as we described above in previous methods). The reason of this nearness is that magnetic field generally weakens directly proportional to distance’s third power and much time will be needed for decelerating Space Catapult’s rod if two electromagnets are far from each other.<br />
<br />
This method probably will consume the most amount of energy but at the same time it will be the most effective because it does not depend on outer factors such as Earth’s magnetic field which is quite weak at the altitude of several ten thousand kilometers above the sea level. <br />
<br />
Eventually, which methods for decelerating the Space Catapult’s rod would be the best? As we see each one of them have got their advantages and disadvantages. We can state that we should choose one of them according to spaceflight’s profile and goal. Particularly, if we decide to send the spacecraft into the deep space mission where especially high speed is necessary then in this case ''longer/more massive'' rod would be needed rotating at very high speed. Under such circumstance much energy will be needed for accelerating/decelerating the rod. We should also take into consideration the fact how frequently the Space Catapult will operate, in other words how mane payloads it will have to send into space per some certain amount of time, week/month and etc. If time interval between two following missions is relatively high then we should choose the method that will consume less energy and more time for decelerating the rod. On the contrary, if the Space Catapult has to send payloads very often then we should choose the method that will consume more energy and enable the rod to decelerate faster. In other words, we should find ''golden mean'' between consuming time and energy. We should also take into account how much energy supply will be produced at the Space Elevator’s counterweight (see ''Energy source placed on the Space Elevator’s counterweight'') and what part of this energy can we spend for accelerating/decelerating the rod.<br />
<br />
The rod’s rotations can be decelerated much faster than accelerated; the reason of it is that when accelerating the rod has got some sophisticated device as payload and generally unmanned spacecrafts are capable to high g-loads, but still for them some restrictions exist. After the payload is released at needed direction and speed, the rod can decelerate much faster because the rod itself is quite simple device without any complex and sophisticated details. <br />
<br />
We can actually use several methods, such as the third one and then the first/fifth ones. This would be justified because of following reason: as we have already said when decelerating with the third/forth method the problem of weakness of the Earth’s magnetic field would occur, therefore much time would be necessary for described method(s) to perform and give us result. However, we should note that in the beginning when the rod rotates very quickly this method would still operate strong enough. This derives from Faraday's law of induction stating that “the electromotive force generated is proportional ''to the rate of change of the magnetic flux''”. Therefore, in the beginning when the rod is rotating very quickly we can use the third/forth method(s) and when the rod significantly brakes we can apply to the first/fifth ones-they do not depend on Earth magnetic field. In other words, such approach would greatly help us in finding the golden mean between spending energy and time necessary for decelerating the rod. <br />
<br />
And finally: after releasing the payload the Space Catapult’s rod can actually give us energy. More precisely, the electro motor itself can serve as electric generator also since we know that the same machine can operate as electric motor if it is fed with electricity and as generator for electricity if its rotor is rotated by other machines. Therefore after releasing the payload when the electro motor’s rotor is rotating very quickly it can give us energy, in result of which the rod will lose its kinetic energy and speed, as for generated energy it can be sent downwards to the Earth for our terrestrial needs (see the next section in this paper) or stored onboard the Space Elevator’s counterweight. This approach has got one substantial advantage: it does not imply additional mass (wrapped wire) that will cause problems because rotating heavier rod would consume more energy.<br />
<br />
=Energy source placed on the Space Elevator’s counterweight=<br />
<br />
As well-known, the Space Elevator’s cabin needs energy when moving along the cable and it can get it from the Earth by means of various ways, such as: laser beam, microwaves, through the cable itself and etc. On the other hand, Space Catapult also needs much energy for rotating the rod and for this purpose some energy source should be placed on the Space Elevator’s counterweight, presumably solar panels array. Doing this would demand additional funding and engineering work and this undertaking should be justified, so how can we prove that placing energy source on the counterweight would be necessary and useful? We should not forget that the energy generally could be simply transmitted from the Earth without carrying any material for energy source on counterweight; so we can justify this undertaking if we declare/prove that: <br />
<br />
1. Energy source should be designed for ''both'' Space Elevator’s cabin and Space Catapult’s rod. We can imagine it as array of numerous solar panels producing enough energy for both above-mentioned constructions. For this purpose solar panels would be better solution than nuclear reactor because they do not need nuclear fuel to be carried from the Earth to counterweight, also they are capable for producing energy in a continuous mode. By the way this circumstance will enable us to send the payload to space by Space Catapult whenever we want without depending existence nuclear fuel at the counterweight. <br />
<br />
2. Transmitting energy from the counterweight (“from above”) is better and advantageous than doing the same thing from Earth (“from below”). Indeed, when we try to transmit energy (laser or microwave beam) from the Earth to ascending cabin, the part of energy is inevitably lost and dispersed in the Earth’s atmosphere and (this is point of the question) this continues during the whole process of ascent. On the contrary, when transmitting the energy from counterweight to cabin the energy will be lost only on the little part of this voyage, more specifically until the cabin leaves the atmosphere (100 km in height) and when cabin leaves it the energy will be transmitted in vacuum without loss. <br />
<br />
3. For receiving the energy from the Earth the huge solar panels (in case of laser beam) or antennas (in case of microwaves) will be needed to be mounted on the counterweight and this is additional mass and additional engineering work.<br />
<br />
We think that these arguments given above are enough for shoving that placing energy source on the Space Elevator’s counterweight have advantages over transmitting energy from the Earth and as conclusion we can state that energy source on counterweight would serve both space transportation systems-Space Elevator and Space catapult. <br />
<br />
As addition, we could use the energy produced on the counterweight for terrestrial needs also. Indeed, there have been developed numerous projects for receiving energy from space since 60-ies implying producing it by means of solar panels and then transmitting to the Earth. Combining all these three goals we can conclude that placing solar power plant on the Space Elevator’s counterweight would be triply useful and advantageous. In other words, when the Space Catapult and Space Elevator do not function, the energy produced on the counterweight should be directly transmitted to the Earth for our terrestrial needs and thus the idea of Space Elevator, Space Catapult and space power plant will be combined in one project.<br />
<br />
=Assembling the Space Catapult=<br />
<br />
Assembling in space such a huge structure as Space Catapult will not be an easy task from the technical point of view and definitely needs special engineering approach. Besides, we think that Space Catapult’s rod should be mounted at the Space Elevator’s counterweight separately from every other parts of the Space Catapult (e.g. electro motor and etc.); this circumstance is caused by rod’s gigantic sizes. More precisely, electric motor and plus any other equipments necessary for Space Catapult’s performance should be delivered to space by means of Space Elevator in a usual way; as for Space Catapult’s rod, it is a different matter and it should be delivered and mounted separately in the end. <br />
<br />
Eventually, Space Catapult’s rod will be quite long, perhaps much more than 100 kilometers. It is obvious that delivering such a long rod as ''one single unit'' would be quite difficult task; also it is possible that due to its total mass the Space Elevator’s cabin will not be able to deliver such rod at all, but we have already mentioned that the Space Catapult may have the rod with various length; more precisely the rod may consist of two/more parts. In such case these parts should be delivered towards the counterweight separately and then assembled. <br />
<br />
But the Space Elevator’s cabin can actually deliver the Space Catapult’s rod as ''one single unit'' in space. We think that this would depend only on rod’s mass. The Space Elevator’s lifting capacity is not well-known yet; however apparently it will not exceed one hundred metric tons and if Space Catapult’s rod is made of extra light material then cabin will be able to deliver it in space and in such case the following question will arise: how the cabin will deliver such a huge object in space without any damage?<br />
<br />
This can be done by means of two cabins. Generally, Space Elevator’s conception implies only one cabin moving along the cable, but for some special purpose (like delivering Space Catapult’s rod in space) we can use the second cabin also that will descend downwards after finishing its job and will not participate in Space Elevator’s further performance. As for the process of delivering the rod, we can imagine it in a following manner: at first the rod will be placed horizontally on the Earth (thus it must be manufactured and then transported to the Space Elevator’s base station), then the Space Elevator’s first cabin will carry rod’s one end along the cable while the rod’s second end will be moved on the Earth so that the rod to take more and more vertical position. When the rod is in vertical position the second cabin will capture rod’s second end and will carry it in space. We think that without the second cabin it would be quite difficult for one cabin only to carry long/heavy rod because the rod may actually shake and crash to the Space Elevator’s cable and this is absolutely undesirable. <br />
<br />
So, as we see in principle it looks to be quite easy, however the assembling may complicate due to rod’s length. In this case it would be better to carry not the rod as ''one single unit'' but its parts and then to assemble them in space in the following manner: ''two'' cabins will carry the first part as described above, when this part is delivered to space and temporarily hung at the cable the next two cabins will carry the second part that will be attached to the first one from below; the other parts will be delivered to space and assembled into the rod in the same way. <br />
<br />
The obvious disadvantage of the above-described method is that each part needs two cabins on the Space Elevator’s cable, besides the humans will be needed for assembling the rod from these parts in the atmosphere’s upper layers; therefore we think that the first way-delivering the rod into space as one single unit still would be easier and more realistic; besides we should take into consideration the fact that if the rod is assembled the additional devices will be needed ''on the rod itself'' for joining these parts and this circumstance would lead to increasing the rod’s total mass and this is undesirable. See the image showing assembling process:<br />
<br />
[[File: Assembling.jpg]] <br />
<br />
Whatever design/structure the rod has-assembled from several parts or as one single unit, it must be delivered to its destination-Space Elevator’s counterweight and must be fastened to electro motor’s own axis. But the problem is that the rod will be quite long and also the fact that Space Catapult’s electro motor will be placed at counterweight’s upper side (or at the ''lateral'' side if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), so it will be necessary the rod coming from below to be moved to counterweight’s upper/lateral side, besides the rod should be docked with electro motor’s axis as accurately as possible. How is it possible to realize such complex engineering operation? Here we can indicate one possible theoretical way: <br />
<br />
The rod will be parallel to Space Elevator’s cable when carried by cabin, but later the cabin’s mechanisms should rotate it so that the rod to be orthogonal to Space Elevator’s cable (this will not be necessary if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), exactly in this position the rod should be delivered to counterweight, besides the rod when moving along the cable should be shifted a bit upwards (relative to the Earth) than the cabin itself. Under such conditions we will easily achieve docking the rod to electro motor’s own axis which from its side should have some trapping device (magnetic for example) to “catch” the rod and thus guarantee docking the rod to electro motor and finishing assembling the Space Catapult as a whole. But if the rod’s plane of rotation is parallel to cable then assembling process will be much easier because the ascending rod may directly dock to electro motor’s own axis. See the image showing this process:<br />
<br />
[[File: Deliver - Copy.jpg]] <br />
<br />
We think that it would be useful if one Space Elevator is built specially for Space Catapult with its base station located on the land, not the ocean. This would be justified because transporting Space Catapult’s rod from its place of manufacture to Space Elevator’s base station should occur on the land by means of several transports simultaneously (due to rod’s great length), this will enable us to deliver the rod to its destination without any damage while this kind of operation is hardly possible on the water.<br />
<br />
=The technical aspects regarding the Space Catapult=<br />
<br />
As an example, we can try to calculate/ascertain all possible kinds of aspects regarding the rod with some certain mass and sizes, for example we can assume the Space Catapult has got 100 km length rod. <br />
<br />
The circumference of the circle that this rod’s end will draw in space will be equal to 2πr=628 km. As we have already mentioned payload’s abilities for withstanding the g-load is restricted, so if the electromotor rotates the rod so that payload’s speed is equal to 50 km/sec (this means that it will take 12.56 seconds for the rod to make one complete revolution), in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design the spacecraft that will withstand such acceleration, but what about the rod itself? Which material can be used for designing this rod, what will be its mass and how much energy and time will be needed for the rod to reach this velocity? <br />
<br />
For manufacturing the rod we should choose the material with very low density and highest value of strength. Currently, the ''Carbon nanotubes'' are the best candidates for this purpose. What will the mass of the rod made of this material? This depends on width also and it should be as less as possible (otherwise the rod will be too heavy and too wide for transporting from manufacture place to Space Elevator’s base station and for delivering it to space by means of Space Elevator) but from the other hand the ''applied load'' will not let us to design very narrow rod.<br />
<br />
Let’s assume that we intend to launch the payload with the mass of 10 000 kg (during calculation we will use ''SI system'' only). To clarify what kind of material will be able to withstand the acceleration we should calculate and then compare two values: the ''applied load'' and ''tensile strength''. For calculating the first one we should multiply g-load (which we already know-2 550 g) to its mass-10 000 kg, we will get 25 500 000. As for calculating tensile strength, we should take its values (for Carbon nanotubes it varies from 11 000 MPa to 63 000, we will take some medium value-40 000 MPa) and multiply it to cross-section’s area, in our case rod is cylinder with circular cross-section. If radius of cross-section is 1 meters then its area is 3.14 square meters, multiplying this value to value of tensile strength (40 GPa as said) we will get 125 600 000 000 and this is significantly more than value of applied load-25 500 000. Of course, we should also take into consideration ''factor of safety'' which is generally equal to 2 and this indicates us that for safety the payload’s actual mass should be twice less but in our case as we see the rod will be able to accelerate the payload to above-mentioned speed. By the way, note that if that g-load ''2 550 g'' is almost at the payload’s withstanding limit this is not serious problem for the rod itself (we have already seen that value of tensile strength is much more than value of applied load) and this is clear why: payload generally contains sophisticated equipments (electrical circuit, optics an etc.) that will not be able to withstand very high g-loads while the rod will be made of some continuous solid substance, Carbon nanotubes is this case and of course it will be able to withstand much higher g-loads.<br />
<br />
<br />
What will be the mass of such rod? Knowing its volume (for this purpose its cross-section’s area 3.14 square meters should be multiplied to rod’s length-100 000 meters, we get 314 000 cubic meters) and taking the value of density (this also varies for Carbon nanotubes from 0.037 to 1.34 g/cm<sup>3</sup>, let’s take 0.1 g/cm<sup>3</sup>) we get rod’s mass as 31 400 000 kilograms. This is too heavy for Space Elevator’s modern concepts and for improving this situation we should either use many cabins for raising the rod as single unit or use nuclear energy for feeding the cabins instead of laser/microwave beams or deliver the rod’s parts separately in space and then assemble them (see ''Assembling the Space Catapult''). But if some advanced substances are chosen for this purpose (for example ''Silica aerogel'' the density of which is about 1.9 mg/cm<sup>3</sup>, this is 50 times less than the density of the Carbon nanotubes taken above-0.1 g/cm<sup>3</sup>) than problem may be lightened in spite of the fact that their current tensile strength is quite low-16 kPa for the density of 0.1 g/cm<sup>3</sup> ['''7''']. So, we can conclude that we need the material with the density of ''Aerogels'' and tensile strength of Carbon nanotubes.<br />
<br />
How much energy and time will be needed for the rod to accelerate from zero to desired speed-50 km/sec? The amount of rotational energy of the rotating rod can be calculated by the following formula:<br />
Kinetic Energy<sub>rotational</sub>= (1/2)*I*ω2 <br />
<br />
Where:<br />
<br />
'''I'''=moment of inertia <br />
<br />
'''ω'''=angular velocity<br />
<br />
"I" depends on the shape of the mass under rotation. In the case of a uniform rod rotating from its end (axis of rotation is at the end of the rod) I = (m*L2)/3<br />
<br />
<br />
“ω” = V/R, where V = tangential velocity and R = radius<br />
<br />
In our case ''moment of inertia'' is equal to (31 400 000 kg*100 000 m2)/3=104 666 666 666 666 666<br />
ω is equal to (50 000 m/sec)/100 000 m=0.5<br />
<br />
So, Kinetic Energy<sub>rotational</sub>=(1/2)*104 666 666 666 666 666*(0.52)= 13 083 333 333 333 333.25 Joules<br />
<br />
Now, how much time and what amount of solar panels will be needed for accelerating this rod? The amount of Solar constant near the Earth is approximately equal to 1300 W/m2 [['''8'''], with assuming that ''coefficient of efficiency'' of solar panels is roughly 20 % we get 260 Watts per square meters and we can easily link amount energy (that we have already calculated) and power with the time needed. Particularly, ''Energy'' is equal to ''Power''’s multiplication to ''Time'':<br />
<br />
[[File: Formula - Copy.jpg]] <br />
<br />
So, Time is equal to 13 083 333 333 333 333.25 Joules/260 Watts=50320512820512.8 seconds, or 1 595 652 years. If we take much more area for solar panels, for example 10 millions square meters then 0.1595652 years or approximately 58 days will be needed and we think that this is acceptable time span.<br />
<br />
Actually, the time and energy will be needed a bit more for overcoming static friction in electro motor, for overcoming the rarified atmosphere’s resistance (we know that there no absolute vacuum in space), also we should take into consideration electric motors’ coefficient of efficiency that generally reaches 90-95 %, so some energy loss will occur here also. <br />
<br />
Now, what will be the total mass of solar panels producing the energy for Space Catapult? This depends on mass/power ratio, in near future it is expected that very lightweight designs could likely achieve 1 kg/kW [<sup>8</sup>] or 0.260 kg/ 260 W (per 1 square meter), so if for rotating the Space Catapult 10 millions square meters of solar panels are used then their total mass would be equal to 2 600 000 kg. We think that it is too heavy for Space Elevator the mass of which is expected to be equal around several hundred metric tons. If so, we will have to use fewer amounts of solar panels and therefore increase the time needed for accelerating the payload’s speed from zero to designed one. This will not make problems if the rod is accelerated only once and then keeps its constant rotation-for this purpose less energy will be needed and the payload will have to reach the rod’s end by first method as described earlier in this paper (see ''Rod’s plane of rotation towards the Earth'').<br />
<br />
We also need to take into consideration the value of deflection when the rod will be delivered to space by means of Space Elevator (see ''Assembling the Space Catapult''), in this case the thin and long rod will be bent due to its own weight and here we will try to calculate its value. This is quite complex problem that apparently cannot have an unambiguous solution because of many reasons, for example due to various temperatures in atmosphere’s different layers, various humidity and possible wind, but still we will try to calculate the value of ''Deflection'' that will occur in case when the rod’s one end is fastened to Space Elevator’s ascending cabin and the second end is fastened to the transport moving on the land, we discussed this option in above-mentioned section of our paper (see ''Assembling the Space Catapult''). The inclination angle for the rod will vary from 0º (rod is transported horizontally on the ground) to 90º (Space Elevator’s cabins are carrying the rod to space) and here we will discuss some medium case when the rod is semi-elevated in the air, when the angle between rod and ground/cable is equal to 45º. On the engineers’ ''eFunda'' web-site there is online calculator that enables to receive the value of ''Deflection'' (actually that site gives different term for this-''Displacement'') [10]:<br />
<br />
Here we need to enter the relevant values:<br />
<br />
''Length of beam'', ''L'': 100 000 meters<br />
<br />
''Line pressure load on beam'', p: In our case this is the weight per meter length. As we have already mentioned the radius of the rod’s cross-section is 1 meter, so the volume of rod’s 1 meter-length part will be 3.14 cubic meter. In case of using Carbon nanotubes with above-mentioned density-0.1 g/cm<sup>3</sup> the weight will be equal to 314 kg or 3 079 Newton. Since we have got the inclination of 45º we should multiply this value to cos45º- 0.707, so we get 2176 N/m.<br />
<br />
''Young's Modulus'', ''E'': This is equal to 1 000 GPa for Carbon nanotubes [11] <br />
<br />
''Distance from neutral axis to extreme fibers'', ''c'': In our case it is equal to the radius of the rod-1 meter<br />
<br />
''Moment of Inertia'', ''I'': It is equal to (pi*r<sup>4</sup>)/4, so it is equal to 0.785<br />
<br />
According to these initial data the calculator returns extremely high value of Deflection, much higher than the length of the rod itself: -3.61 × 10<sup>9</sup> meters. This result shows us that with the current materials (Carbon nanotubes in our case) it is impossible to raise the rod as ''one single unit'' to space by means of Space Elevator and we need other materials with less density and more ''Young's Modulus'' (or the rod should be much thicker but this will lead to increasing its mass). Therefore, we have got two options: either we should deliver the parts of that rod and then assemble them in space (we have already discussed this option) or completely different technologies for manufacturing the rod should be developed. Particularly, it would be very good if it was possible to manufacture the rod ''in continuous mode'' in vertical position and then uninterruptedly directly to carry it to space by means of Space Elevator’s cabins. Under such approach there will be no ''Deflection'' and several cabins will be able to deliver the rod in space. <br />
<br />
One note about transporting the rod from its place of manufacture to Space Elevator’s base station. We think that this process should be executed by many transports, in other words we are convinced that if the rod is carried by two trains only (or any other kind of transport) then the rod will continuously touch the ground since the ''Deflection'' occurs in any position-horizontal, inclined or vertical and this circumstance will lead to its damage, that’s why several transports will be needed to hold the rod at as many places as possible.<br />
<br />
=Stabilizing the counterweight=<br />
Stabilizing the Space Elevator’s counterweight is very important question during Space Catapult’s performance. Indeed, when the rod rotates it makes the imaginary circles in space and due to rod’s and payload’s masses the Space Catapult’s ''center of mass'' will be continuously shifted and if the counterweight is not somehow stabilized then it will make problems for accurate aiming to certain point at the celestial sphere. Also, if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable then there will be the danger that the rod may actually hit the cable and cut it. To avoid these problems we need to apply to serious measurements. <br />
<br />
First of all, the electro motor’s own axis can be quite long and this will diminish the chance to failure of the whole system. Actually, we are convinced that counterweight’s (where the electric motor will be placed) size will be quite large, mainly due to solar panels’ sizes and amount (this issue was discussed above), also the electromotor should be quite large and powerful to rotate the rod, and hence there will be enough distance between the rod and Space Elevator’s cable. <br />
<br />
The second serious problem is that the center of gravity of the system is not at the center of rotation, therefore it will be necessary to balance the rotating system when the payload is attached and when it is released.<br />
<br />
We think that the Space Catapult’s rod should not be deployed/directed to one side only but some counterweight of it should also exist. This is necessary since the unilaterally loaded (we mean the rod itself plus payload) rod will cause the counterweight to somersault. In other words, the rod should extend to other side and the ''moments of inertia'' of both sides should be the same as during rotating the rod as after releasing the payload when the rod still rotates. This is easily achievable if some additional, second payload is placed on the rod’s second end. Therefore, the Space Catapult will launch two payloads at the same time to the ''opposite'' directions but at various speeds if the second part/side of the rod is shorter.<br />
<br />
How the second payload should be placed on the rod and should we really send two payloads? Until we have got balanced rod this problem does not arise but as soon as the Space Catapult releases the payload this balance will be violated, how it can be restored? There are two theoretical ways for achieving this: reducing the ''mass'' or reducing the ''length''-with diminishing either one of them the ''moment of inertia'' will be decreased. We think that reducing the mass will be less practicable since this would require placing the second payload (spacecraft or anything else) on the rod’s second part and this cannot be done from the Space Elevator’s cabin-this is the easiest way for delivering the payload from Earth to Space Catapult’s rod; so we would have to (see ''Rod’s plane of rotation towards the Earth'') put the second payload on the electro motor and then send it rod’s second part’s end. This is quite complicated task; therefore we can apply to second approach-put some sliding object that will immediately move to electromotor as soon as the spacecraft is released.<br />
<br />
[[File: MOI.jpg]] <br />
<br />
The next problem that may occur is that when the electro motor rotates the rod this motion will make the Space Elevator to rotate to the opposite direction. The same problem arises when helicopter’s primary blade’s rotation forces the helicopter to rotate to opposite direction and this possible rotation is annulled by ''tail rotor''. We think that for balancing the counterweight the additional motor and rod should be installed and this rod should rotate to opposite direction and if their ''angular momentums'' are equal to each other, then their rotations will cancel each other. More precisely, the following equation should be fulfilled:<br />
<br />
[[File: Angular momentum.png]] <br />
<br />
Where ''m'' is mass of the rod, ''v'' is angular speed and ''L'' is rod’s length, the numbers ''1'' and ''2'' refer to first and second rods correspondingly. For balancing both rods’ rotation the multiplication at both sides of the counterweight should be equal, by the way this circumstance enables us to use the second rod with shorter length and even with less mass but rotating at more angular velocity.<br />
<br />
Such approach will effectively deal with other problem which will arise when the Space Catapult releases the payload(s), at this moment the second motor should instantly diminish its angular velocity to some certain level (an ordinary mechanical brakes could be used for this purpose), in this case ''angular momentums'' for both motors/rods will be equal again and Space Elevator’s counterweight will maintain its attitude in space. See the image below depicting the Space Catapult with two electro motors and rods:<br />
<br />
[[File: Two-rods.jpg]] <br />
<br />
Such approach will justify itself if rod’s plane of rotation is parallel to Space Elevator’s cable, but if this plane is orthogonal to cable (see ''Rod’s plane of rotation towards the Earth'') then the second/balancing electromotor cannot be placed under the counterweight because the cable will be cut when rod touches it. Therefore a bit different approach should used and we need to install two/four/eight electro motors with their own relatively shorter rods rotating to opposite direction. They should be placed at the counterweight’s lower side and on its edge (as we suppose the counterweight should be disc) so that their rods not to touch and cut Space Elevator’s cable. Also, total a''ngular momentums'' from these motors should be equal to the ''angular momentum'' from upper motor and thus the counterweight will not rotate and the Space Elevator’s cable will not be twisted. This situation is presented below:<br />
<br />
[[File: Modified-2.jpg]] <br />
<br />
We think that the array of gyroscopes would be also very useful to be installed at the counterweight since they can maintain the attitude of the whole system and this is important for precise aiming to certain point at the celestial sphere. As for the energy required for gyroscopes’ performance it could be received from the array of solar panels which as a result will generally serve Space Catapult’s precise performance.<br />
<br />
=Space Catapult placed at Lagrangian points-the way for gaining subluminal speeds=<br />
<br />
In our paper we discussed the Space Catapult based on the Space Elevator’s counterweight and concluded that this would be convenient when we intend to deliver the payload to space from the Earth. However, such Space Catapult cannot gain very high speeds and therefore we need to choose other way. It is obvious that we need to keep rod’s plane of rotation orthogonally relative to the ''Earth-Sun connecting line'' and hence we should place the rod on the celestial body which will be in synchronous rotation with the Sun but since there is no such body in the solar system we conclude that the Space Catapult for subluminal speeds (the speeds close to speed of light are in mind) should be placed at such point near the Earth where it will be easy to reach it from our planet and where the rotating rod will not hit the Earth and will be always at the same distance from the Sun to avoid the influence of its tidal forces. The examples of such places are '''Lagrangian''' L<sub>1</sub> and/or L<sub>2</sub> points at 1.5 million km away from the Earth. If the Space Catapult is placed at one of these points then its rod can be always orthogonal to the Sun in principle, at the same time it will never collide with the Earth and also it will be quite close to the Earth since 1.5 million km distance is very negligible in space.<br />
<br />
We have got several notes regarding such approach. First, when we mentioned that the rod’s various parts can be at the same distance from the Sun this strictly speaking is not very true because the Sun can be referred as little point where its gravity “comes out” from while the rod is quite long and its initial part (placed at one of the Lagrangian points) will be attracted stronger than the utmost one (for equal attracting the rod should the arc ''with the same curviness as Sun’s surface'' and not straight line); but still this is better than to direct the rod exactly towards the Sun where the tidal forces will try to tear the rod. Second, the Space Catapult should be placed at Lagrangian L1 point which is closer to the Sun than L2 one and therefore receives by 4 % more energy per area from the Sun. Third, the rod should be in constant rotation, this requires much less energy than accelerating it from zero, then stopping it and accelerating it again. Fourth, the existence of the asteroid belt in the solar system between Mars and Jupiter will somehow restrict the actual length of the rod. Indeed, the Space Catapult should be placed at one of the Lagrangian points at 1 AU distance from the Sun while asteroid belt approximately lays at 2.7 AU, from the simple geometry it is obvious that the length of the rod ''almost reaching'' the asteroid belt can be approximately equal to 390 million km, and if the rod is longer then it may simply hit any asteroid within that belt. For 390 million km length rod and for 100 000 m/sec2 acceleration at rod’s end (where the payload will be attached) the maximal speed that the spacecraft can gain will be approximately equal to 200 000 km/sec (two thirds of the speed of light) and this can be considered as enough for practical interstellar spaceflight. Fifth, the spacecraft should be directly put on the rotating rod’s initial end (near electromotor) and then slide towards the other end with its own rocket engines. To achieve this, the spacecraft will have to cover relatively less distance on the rod and then rod’s circular motion will accelerate the spacecraft further-we have already mentioned this in this paper when speaking about deploying the Lunar Space Catapult. This action-putting the spacecraft on the rod will not be difficult since rod’s angular velocity will be quite low due to rod’s huge length, particularly for 400 million km length rod and for 200 000 km/sec linear speed the rod’s angular velocity will be 0.0000796 revolutions/sec.<br />
<br />
[[File: Lagrangian-point.jpg]] <br />
<br />
We have already mentioned that to avoid the destructive influence of the Sun’s tidal forces the rod’s plane of rotation should be orthogonal to the Earth-Sun connecting line. By the way, note that under such approach we may have to wait one year until the Lagrangian Space Catapult occupies the relevant position towards the certain point at the celestial sphere where the spacecraft should be sent to. But from the other hand it would be useful if it is feasible to rotate this whole structure around the imaginary axis directed towards the ''ecliptic poles'' (depicted as faint green dash line on the image above), the reason if this is the possible danger when the rotating rod may hit Mars or asteroids that orbit around the Sun closer than 2.7 AU distance (for example ''433 Eros'' or ''1036 Ganymed''), hence for avoiding such undesired collision the Lagrangian Space Catapult should be slightly rotated by several degrees clockwise/counterclockwise so that the rod not to collide with any celestial object. We are convinced that rotation by several degrees will be absolutely enough measurement due to rod’s gigantic length and relatively less sizes of the celestial objects in the solar system.<br />
<br />
The next issue that we should discuss refers to stability of the Lagrangian Space Catapult placed at L<sub>1</sub> point. As we see this structure will have enormously gigantic size while the Lagrangian point is relatively little mathematical one in space, so what can be done to be convinced that this structure will remain at that point and do not shift aside? The body placed at one of the Lagrangian points is affected by other celestial objects’ gravity and therefore for achieving the balance the rod needs to have the counterweight with more mass if it (counterweight) is shorter. As we clearly see the rod needs the counterweight for two reasons: not to let the Space Catapult somersault and for maintaining it at the L1 point. We think that it would be very useful if the arrays of solar panels act as counterweight since exactly they can give us energy for rotating the rod. Also, we need the second, shorter, perhaps less massive but faster-rotating rod (again-solar panel arrays) the opposite rotation of which would cancel first rod’s rotation, this issue was discussed in this paper. These arrays of solar panels are depicted on the image shown above. <br />
<br />
How such a gigantic structure as Lagrangian Space Catapult can be assembled in space? In our paper we discussed the possible ways for delivering the rod from the Earth to the Space Elevator’s counterweight, now we will try to show that it is possible ''in principle'' to assemble the extra-long rod in space. <br />
<br />
If it is possible from the technical point of view to manufacture extra-long rod then we can use this approach and make 1.5 million km length rod (this is the distance between the Earth and Lagrangian L<sub>1</sub>/L<sub>2</sub> point) that will be mechanically directed to the base station at L<sub>1</sub> point. The capturing devices there will catch the rod and attach it to the electro motor’s shaft after which the rod should be spun by 90º so that it to be orthogonal to Earth-Sun connecting line (for this purpose the additional mechanisms will be needed), this spin is necessary because L<sub>1</sub> point is located on the Earth-Sun connecting line (that is towards the Sun if we look from the Earth) and when directing the rod from the Moon it will lay ''along'' this line while we need across. After this the rod should be slid to another side and then the next rod should be directed to the Lagrangian Space Catapult where it will be attached to the previous rod and etc. In other words, the extra-long rod will be assembled from one side and its length will “grow” from this side to other one, this is necessary because the distance between Moon (the rod should be manufactured exactly there and not on the Earth due to our planet’s relatively more gravity, atmosphere and problematic space debris belt around it) and L<sub>1</sub> point is constant and rod’s parts cannot be more. Due to whole rod’s and its parts’ lengths (400 million and 1.5 million km correspondingly) we think that about 260-270 such operations will be needed to finish assembling the rod (400/1.5). The process of assembling the Lagrangian Space Catapult is shown on the image below:<br />
<br />
[[File: Lagrangian-point-assemble.jpg]]<br />
<br />
=Conclusion=<br />
<br />
As we have seen, for leaving the Solar system and reaching the remote celestial bodies (stars, nebulas) there is no need to develop advanced and complicated technologies that mostly are not capable for gaining extra high velocities nevertheless. In any case, until the Space Elevator is really built (scheduled for construction by 2031) we have got much time for developing the idea of Space Catapult in technical aspect, like finding appropriate materials for the rod, perfect the ways how the Space Catapult can be assembled in space and etc. The concept of Space Catapult itself is the easiest one, does not need developing neither complex and sophisticated technologies, nor some exotic methods (such as ''Gravitoelectromagnetic toroidal launchers'', ''Antimatter rocket'' and etc.) and can be easily implemented in near future; in other words the Space Catapult is not some sophisticated structure that would need profound science research and the fact that it will enable us to gain whatever high speed will justify its developing and building by the humankind. As for other technologies like Ion Drive, they could be used by the spacecraft during flight for other purposes, for example for correcting/changing the flight direction.<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Space_Elevator<br />
<br />
2. http://www.isec.info/index.php?option=com_content&view=article&id=14&Itemid=9<br />
<br />
3. http://www.space-track.org/perl/geo_report.pl (provided data updates regularly, registering is needed) <br />
<br />
4. http://www.oosa.unvienna.org/pdf/reports/ac105/AC105_720E.pdf page 24 (data as at 21 August, 1997) <br />
<br />
5. http://www.amostech.com/ssw/presentations/Session7/S7-1Molotov.pdf page 16<br />
<br />
6. http://www.esa.int/SPECIALS/ESOC/SEMN2VM5NDF_mg_1_s_b.html <br />
<br />
7. http://eetd.lbl.gov/ecs/aerogels/sa-physical.html<br />
<br />
8. http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant<br />
<br />
9. http://www.you.com.au/news/2005.htm, http://www.spacedaily.com/news/ssp-03b.html<br />
<br />
10. http://www.efunda.com/formulae/solid_mechanics/beams/casestudy_display.cfm?case=simple_uniformload<br />
<br />
11. http://en.wikipedia.org/wiki/Young%27s_modulus<br />
<br />
<br />
'''Appendix''': <br />
<br />
Animation illustrating the payload’s departure from the Lagrangian Space Catapult:<br />
[[File: Lagrangian-point-animation.gif]]</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_5&diff=3671OpenSpace 52013-09-21T13:03:30Z<p>Eagle9: /* Rod’s plane of rotation towards the Earth */</p>
<hr />
<div>== '''Space Catapult''' ==<br />
<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
=INTRODUCTION=<br />
<br />
<br />
The new method for sending the spacecrafts in deep space is presented here. The paper describes the long rod rotated by electro motor placed at the Space Elevator’s counterweight and at Lagrangian points. This simple structure will enable the rod to gain high velocity and carry the payload with it. After reaching the desired speed the rod will release the payload that will fly in space along the imaginary circle’s tangent. This structure we called Space Catapult and it should work with the assist of Space Elevator. This latter should be used for carrying the payload from the Earth to Space Catapult’s rod.<br />
<br />
For exploring the outer space the humankind generally uses the rocket engines, mostly chemical-propelled ones. They enable us the explore near-Earth celestial bodies and other planets in the solar system. They even enabled us to send several deep space missions beyond the solar system such as '''Pioneer-10''', '''Pioneer-11''', '''Voyager-1''', '''Voyager-2''', however by means of this technology the flight lasts undesirably long and it seems to be impossible to reach remote celestial bodies in space such as stars, so new technologies are necessary for this purpose. However new technologies do not necessary imply new kind of rocket engines, such as ''Ion Drives'' because they are capable for gaining several ten times higher speeds only, but for remote celestial bodies even they are not suitable. Besides, they need a huge amount of energy to be stored onboard the spacecraft and this will make additional problems. So, high speed should be achieved with absolutely different approach. How this can be done?<br />
<br />
High speed can be easily achieved by means of fast-rotating rod around the electric motor. The motor’s rotational speed can be very high; the rod also can be quite long, hence the rod’s end’s linear speed can be extremely high, absolutely unachievable for any other technologies nowadays. The payload should be fastened at the rod’s end where the linear speed generally reaches maximal value. After reaching the necessary speed the rod will release the payload that will fly along the tangent from the current position. Thus the electric energy can be turned into payload’s speed and its velocity could be as high as we wish (except the ''speed of light'' of course). In principle the '''Space Catapult''' (thus we call this structure) would be the simplest, the most convenient and direct way for converting the energy/electricity into speed and conveying it to payload. <br />
<br />
As we see the Space Catapult is quite uncomplicated structure, however if we wish to gain high speeds we should deploy it in space, not on the Earth. Indeed, our planet is surrounded with dense atmosphere that impedes any quick motion, so if we rotate the rod quickly the atmospheric drag and generated heat would burn it very soon, therefore the Space Catapult should be built and deployed in space only, and as we suppose-at the Space Elevator’s counterweight. In other words, the Space Elevator’s counterweight will operate as Space Catapult. See image below:<br />
[[File:Space-catapult.jpg]]<br />
Generally, what is the Space Elevator ['''1''']['''2''']? According to modern concepts it will be the tall vertical structure built on equator and will have height of several ten thousand kilometers with its thin cable fastened to the base station on the Earth and with counterweight placed higher geostationary orbit. Because of balance between centrifugal force and gravity this structure will be stretched and the cabin will move along its cable carrying the goods into high orbit. After delivering the payload, the cabin will descend and carry the next one.<br />
In Space Elevator’s concepts several solutions have been proposed to act as a counterweight: <br />
<br />
1. Heavy, captured asteroid <br />
<br />
2. Space dock, space station or spaceport positioned past geostationary orbit <br />
<br />
3. Extension of the cable itself far beyond geostationary orbit. <br />
<br />
The third idea has gained more support in recent years due to the relative simplicity of the task and the fact that a payload that went to the end of the counterweight-cable would acquire considerable velocity relative to the Earth, allowing it to be launched into interplanetary space. However this idea cannot be completely shared by us due to following reason: <br />
<br />
It is well-known that the values of both '''Orbital''' and '''Escape Velocities''' decreases with increasing the altitude while the '''tangential velocity''' of Space Elevator’s cable increases. We can see the differences between them from the chart presented below:<br />
[[Image: Cxrili.gif]]<br />
<br />
As we see from this chart the ''tangential velocity'' of the Space Elevator even at its end (144 000 or 200 000 km altitude) is not very high to decrease the necessary time for covering the distance from the Earth to remote celestial bodies significantly. To achieve this, even the longer Space Elevator would be needed (its ''tangential velocity'' is directly proportional to its length) and this circumstance would complicate the technical task for building such Space Elevator. Because of this, there is no necessity to extend the cable itself far beyond geostationary orbit as proposed in the third variant. In any case, we have already seen that by means of Space Catapult it is possible to gain such huge velocities that are absolutely unachievable with other technologies, for example with Space Elevator. Therefore, using the counterweight and placing the Space Catapult there definitely has got some technical sense. <br />
<br />
However, we think that the question where the Space Catapult should be placed needs further discussion. Theoretically, the Space Catapult with its payload and nuclear reactor/solar panel needed for rotating the rod may be mounted not only at the counterweight, but on the Space Elevator’s cabin also that can carry all these goods to space in a usual way, as it should do it according to Space Elevator’s modern concepts. This option is quite possible, however for realizing this we need to know the mass of the payload, nuclear reactor/solar panels’ mass plus Space Catapult’s mass from one hand and Space Elevator’s lifting capacity (this ''must'' be more) from other hand, but these data are not available nowadays, therefore we think that the Space Catapult should be still mounted at the Space Elevator’s counterweight where it will be possible to send the payloads into deep space in ''continuous mode'' at high velocities.<br />
<br />
As we saw the Space Catapult is capable to gain very high velocities; however there is being developed other technologies and they in future will enable the spacecraft to fly at high speeds in space. These are Ion Drive systems, more precisely the most perspective one-''Variable Specific Impulse Magnetoplasma Rocket'' (VASIMR) which still under development can be used in future for deep space missions. Can these engines and Space Catapult be the rivals in space? Since none of them have been built and used in space yet we cannot give a persuasive answer to this question; however still it is possible to underline Space Catapult’s one significant advantage: if the future spacecraft uses the VASIMR (or any other kind of Ion Drive) engine it will definitely need to be equipped with nuclear reactor, otherwise the spacecraft will not be able to gain high speeds, also it will need to carry fuel tanks for this purpose. As for the Space Catapult, it can give much higher speed to spacecraft, besides it will have ''stationery'' power plant (see ''Energy source placed on the Space Elevator’s counterweight'') at the Space Elevator’s counterweight, so the payload will ''not'' have to carry the nuclear reactor onboard and this circumstance will lighten the work for deep space spacecraft. Besides, we should not forget that unlike the spacecrafts equipped with ion drive engines the Space Catapult will need no fuel for gaining high velocities. <br />
<br />
Briefly, Space Catapult’s advantages over any kind of propulsion systems are: <br />
<br />
1. Ability to gain any speed that is absolutely unachievable by means of other kinds of engines. <br />
<br />
2. No need by spacecraft to carry energy source that would make it too heavy and impracticable.<br />
<br />
=The Space Catapult needs long rod=<br />
<br />
When building the Space Catapult at Space Elevator’s counterweight we should install quite long rod there, the shorter the rod is, the easier would be installing it, however we should note that rod cannot be extremely short, let’s say 1 km length or so due to following reason:<br />
<br />
When we are going to send some payload into space, we need not only high velocity, but one certain direction also. The little inaccuracy in direction, inclination in several arcminutes is actually acceptable since the spacecraft would easily balance it with its engines; however great inclination from the initial direction would send the spacecraft into the completely different direction and in such case the whole mission will fail.<br />
<br />
If two Space Catapult’s rods have the length of let’s say 1 kilometer and 10 kilometers, then for giving to payload some certain linear speed (for instance 100 km/sec) these rods should rotate at different angular velocity. It is easy to ascertain that the shorter rod should rotate 10 times faster to gain the same linear speed than the rod with more length. But the faster the rod rotates, the more difficult will be to “catch” the needed moment for releasing the payload from the rod for sending it towards some certain direction. If the rod is too short, then it has to rotate very quickly for gaining some certain linear speed and therefore it will be extremely difficult catching the needed moment for releasing the payload. Hence, too short rod can make problem for sending the payload to some certain direction in space especially at high velocities. So, based on payload’s needed velocity we should find rod’s desired, minimal length that will enable us to send the payload in space to necessary direction without fear that it may yaw from the course. <br />
<br />
However, rod’s length will be crucial for payload’s abilities for withstanding the acceleration also. As an example, we can try to calculate its value which the payload will have to withstand during rod’s rotation. The acceleration of the body rotating at the circle with some constant velocity is calculated by the following formula:<br />
<br />
[[File: Acceleration - Copy.jpg]] <br />
<br />
Where a is acceleration in ''m/sec''<sup>2</sup>, ''v'' is payload’s linear velocity on the circle in ''m/sec'' and ''r'' is radius of the circle in ''meters'', in our case it is equal to rod’s length. Let’s assume that the rod is 100 km length and the electromotor rotates it so that payload’s speed is equal to 50 km/sec, in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design and manufacture the spacecraft’s subsystems (avionic and etc.) capable to withstand such acceleration. This circumstance somehow restricts the speeds that we can achieve, in any case their values actually depends on spacecrafts’ abilities for withstanding g-loads. But what can we do if much higher speeds are needed? The answer directly derives from that formula: the radius should be more; by the way note that this is additional reason why the longer rod is more useful. If we are able to make the extra long rod, then this will enable us to gain much higher velocities. <br />
<br />
What material should be used for manufacturing the rod? It is obvious that if very high speeds are needed the rod should be long and even in this case the acceleration at its end will be quite high, therefore ''sufficiently strong and light materials'' are needed for this purpose and making them is as similar challenge as in case of Space Elevator where the same requirements arises for the cable’s material. The lightness is needed because in case of heavy rod a lot of energy will be needed to rotate it; the strength is needed because in case of lack this property the rod will be destroyed due to great acceleration.<br />
<br />
=The mechanism for holding and releasing the payload=<br />
<br />
How the payload can be held by Space Catapult’s rod during rotation and how it can be released from the rod? We think that using ''electromagnet plus mechanical holding devices'' would be a good solution. More precisely, after the payload is attached to the rod it must be held by means of both methods until the rod accelerates and reaches necessary velocity (it may take even several days), but with approaching the desired speed the mechanical device should release the payload however the electromagnet(s) should still hold it. The explanation of such approach is following: generally the mechanical devices are much slower/sluggish in performance than electronic ones. We have already said that when releasing the payload the extreme accuracy is needed and mechanical devices cannot guarantee ''the exact time of releasing'' the payload unlike electronic ones. That is, it’s unlikely that mechanical devices can release the payload at some certain moment when needed while in case of electromagnet it would be enough to cease electric current there, it would lead to immediate vanishing of the magnetic field and sending the payload along the tangent from the point where the payload would be at the current moment. <br />
<br />
<br />
We think that the ''fastest control system'' would enable to release the payload to certain direction. This system (extremely fast-operating computer plus measuring equipments) should know the current position of the rod’s end, the current speed, the needed direction and be capable for computing the necessary moment for giving the order for diminishing the voltage for electromagnets and hence releasing the payload to desired direction and velocity.<br />
<br />
=Rod’s plane of rotation towards the Earth=<br />
<br />
The Space Catapult’s rod when rotating makes the circular plane/flatness in space and this plane may be horizontal/parallel to Earth surface, that is making the right angle to Space Elevator’s cable or it may be placed along the cable; see the both possible situations here:<br />
<br />
[[File: Planes-of-rotation - Copy.jpg]] <br />
<br />
Both approaches have got their advantages/disadvantages and here we will discuss this question, first of all from the point of view of safety.<br />
<br />
For gaining extremely high velocities quite long rod would be needed, maybe with the length of several thousand kilometers or even more. If such rod is placed ''along'' the Space Elevator’s cable then the rod during rotation will cross many orbits from the ''Medium Earth Orbit'' to ''High'' ones. When rotating, the rod may actually hit any satellite and/or space debris object and such collision can lead to rod’s complete destruction; therefore we should choose such plane which would be much more free from any artificial objects; hence if the rod rotates ''horizontally/parallel'' to Earth’s surface at high enough altitude where the satellites’ population is relatively low then this measurement would justify itself because under such circumstance the rod will not cross satellites’ orbits (rod’s plane of rotation will simply coincide to ''one'' orbit’s path). However, we should also note that this altitude actually depends on the Space Elevator’s proposed length. Indeed, the Space Catapult’s rod should be mounted at the Space Elevator’s counterweight; this counterweight from its side should be placed at the end of the Space Elevator at such altitude where the satellites’ population is as low as possible. This means that Space Elevator’s proposed height should be agreed with mounting Space Catapult on its counterweight. According to various databases the number of man-made objects at high orbits, more precisely beyond geostationary orbit is much less than on the lower orbits ['''3''']['''4''']['''5''']['''6'''], therefore the Space Catapult with its rod should be located at the altitude of 50 000-60 000 km above the sea level. At such altitude the space is almost free and nothing will impede rod’s rapid rotation. Besides, the satellites at high orbits are orbiting around the Earth slower than on the lower orbits (as known any satellite orbits around its primary body slower in apogee than in perigee), therefore if some tracking system is mounted at Space Elevator’s counterweight then it will enable the Space Catapult to avoid undesired collision with satellites during Space Catapult’s performance. In other words, the Space Catapult should operate only when the there are no satellites near its vicinities.<br />
<br />
Now we will try to discuss this question from other side.<br />
<br />
How the payload can be transferred from the Space Elevator’s cabin to the Space Catapult’s rod? One way is following: cabin reaches the counterweight where the payload will be released, then payload will be mechanically conveyed to rod, continues its way ''on the rod'' (like the train rides on the rails) and after reaching rod’s end it stops, the rod begins rotating and after gaining necessary linear speed it releases the payload to needed direction. This method is generally realizable; however it seems to be too complicated and unpromising compare to the second one: the Space Catapult’s rod is stopped in space so that it to be directed downwards to the Earth and be parallel to Space Elevator’s cable. The Space Elevator’s cabin moving along the cable with payload stops at the cable ''near'' the end of the Space Catapult’s rod and releases the payload that will fly to the rod, attaches itself to the rod’s end (here the electromagnets would be useful), the rod begins rotating and after gaining needed linear speed will release the payload to necessary direction.<br />
<br />
This second way seems to be more promising because the first one is much more complicated as we have already said: first of all there would be needed some mechanical devices for transferring the payload from the Space Elevator’s cabin to counterweight, the counterweight should have the hole for the payload to move through it from below (we should not forget that the Space Catapult should be mounted ''at'' the counterweight, not ''beneath'' it), besides the rod should be made so that it to have some conveying surface (rails for instance) the payload to move on it. As we see it would be much more convenient if it is possible to convey the payload from the cabin to the rod directly and this would be feasible under the second method which is depicted below:<br />
<br />
[[File: Convey.jpg]] <br />
<br />
One more aspect regarding Space Catapult’s position. This structure, its rod, its electro motor and etc should be mounted at Space Elevator’s counterweight so that the rod to be placed westwards from the cable. The reason of it is following: when the Space Elevator’s cabin stops and releases the payload (which should fly to Space Catapult’s rod) the current speed of which will/should be more than the value of the ''Orbital/Escape Velocity'' at the current altitude. After releasing the payload will fly westwards and upwards because its orbit will be ellipse, under ellipse the payload will fly higher to apogee and at the speed less than Space Elevator’s current speed at the given altitude, in other words the released payload will “lag behind” the Space Elevator’s cable; therefore payloads’ ''stopping points'' at the cable and Space Catapult’s rod’s length should be calculated and chosen so that the payload to fly directly towards rod’s end. This process would be feasible in both cases-if the rod’s plane of rotation is parallel to Earth’s surface and if it is placed along the cable-but still this would be easier for the payload to achieve the rod’s end if the rod is placed along the cable because at least the distance that the payload should cover in space will be less.<br />
<br />
The length of the Space Catapult’s rod placed at the Space Elevator’s counterweight might vary since for various spaceflight purposes different initial speed will be needed and relatively low speed could be achieved by means of shorter rod. Because of this reason it might be necessary to change Space Catapult’s rod’s length, therefore it would be useful if the rod consists of two parts where the first part would be perpetually attached to electro motor and the second one will be attached to the first part if necessary. For this operation Space Catapult’s rod should be placed along the cable since the relative nearness would make this operation quite easy and it could be accomplished by the crew directly from the Space Elevator’s cabin stopped at the needed altitude. <br />
<br />
For deciding the question how the Space Catapult’s rod should be placed towards the Space Elevator’s cable we should take into consideration one substantial circumstance-to which direction do we plan to send the payload in space by means of Space Catapult? This circumstance will influence deciding this problem due to following reason:<br />
<br />
In case ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and if rod’s plane of rotation is parallel to Earth equator, then this plane will be orthogonal to Earth’s rotation axis. This axis from its side is tilted to ''ecliptic plane'' by 66° 34'. This means that Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 23°26'. Here follows very important consequence: under above-mentioned conditions the rod when rotating will be capable for covering only the part of the ''celestial sphere'' from 0° to 23°26' (counted from ''ecliptic plane'' northwards and southwards to ''Ecliptic poles''). This is about one fourth of the ''celestial sphere'' (23°/90°), this will not make problems if we intend to use the Space Catapult for exploring the solar system’s planets because their orbits’ tilts towards ''ecliptic plane'' do not exceed 7° (for planet Mercury, for other planets this tilt is even less); however we will not be able to send the payload for example to the nearest star ''Alpha Centaurs'' because this star is located at -42 degree according to ''ecliptic coordinate system'' in the celestial sphere.<br />
<br />
The situation will drastically change ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and ''if'' rod’s plane of rotation is orthogonal to Earth’s equator and therefore parallel to Earth’s axis of rotation. We have already discussed this option when we mentioned that the rod should be placed westwards from the cable and explained why it would be useful-for delivering the payload from Space Elevator’s cabin to Space Catapult’s rod. Under such conditions the Space Catapult will be capable to aim to any point on the ''celestial sphere''. Indeed, the Earth with the Space Elevator rotates around its axis and Space Elevator’s counterweight draws an imaginary circle in space. This circle is tilted to ''ecliptic plane'' at 23°26' and crosses this plane in two point called ''ascending'' and ''descending nodes''. The other points that are 90° away from these nodes we call point(s) of ''maximum elevation/depression'' (relative to ''ecliptic plane''). When the Space Elevator is at a''scending/descending node'' its rod and hence the payload can be directed to any point from 0º to 66º on the celestial sphere northwards and southwards from ecliptic plane. This makes about 75 % of celestial sphere. See the image depicting this situation:<br />
<br />
[[File: Node.jpg]]<br />
<br />
But when the space Elevator reaches the points of ''maximum elevation/depression'' then its rod during rapid rotation may be directed to any point from southern ''Ecliptic pole'' to ''Northern pole'' at the celestial sphere because at these points rod’s ''plane of rotation'' is orthogonal to ''ecliptic plane'' and thus the rotating rod can aim to ecliptic poles as well as other points. See this situation below:<br />
<br />
[[File: Elevation.jpg]] <br />
<br />
The situation will be similar if the Space Catapult’s rod is orthogonally placed towards cable. Under such approach Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 66° 34' and the Space Catapult will be capable to cover ''three fourths'' (66°/90°) of the ''celestial'' ''sphere'' when the Space Elevator is at the points of ''maximum elevation/depression'' and the whole celestial sphere when the Space Elevator is at ascending/descending nodes. For aiming the needed point on the celestial sphere the Earth should occupy the appropriate attitude towards the stars during the revolution around its axis, the same thing should be done under previous case described in the paragraph above. <br />
<br />
In conclusion, thinking about rod’s plane of rotation towards the Earth, we should note one important difference between above-mentioned approaches: if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, then in case of emergency during Space Catapult’s performance (for example if the Space Catapult’s rod is cut by sudden meteorite bombardment) the rod’s part with the payload may simply crash to the Earth at huge velocity if the rod at this moment is directed to the Earth. This cannot happen if Space Catapult’s rod’s plane of rotation is orthogonal to Space Elevator’s cable because payload’s rotational path will not be directed towards the Earth and hence its flying trajectory will never cross the Earth.<br />
<br />
=Braking the Space Catapult’s rod=<br />
<br />
After releasing the payload at necessary speed and direction, the Space Catapult’s rod will have a huge angular velocity that needs to be decreased to zero in order the Space Catapult’s rod to get another payload in motionless position and then to send it to space. <br />
What methods can we use to reduce Space Catapult’s rod’s rotation to zero? There are several possible ways: <br />
<br />
1. The electromotor designed for accelerating the rod may actually play a role of brakes, more precisely after releasing the payload to space the electromotor should operate/rotate in the opposite direction, hence rod’s rotational speed will be diminished to zero after that electromotor will stop operating. Under such method a bit less energy will be spent for decelerating the rod than in case of accelerating because when decelerating the rod is free from payload. <br />
<br />
2. An ordinary mechanical brakes, however due to electro motor’s and rod’s sizes a huge brake(s) would be needed to be installed on the Space Elevator’s counterweight and this circumstance would make additional problems from the engineering point of view. Nevertheless, we should admit that under such method we would not need as much energy as during accelerating; on the contrary, in this process the heat will be emitted as it generally happens during braking. <br />
<br />
3. For decelerating the rod we can use the well-known phenomenon in physics-''electromagnetic induction'': when the c''onductor/ closed circuit'' moves into the magnetic field the electric current is generated there. In case of Space Catapult we can use this phenomenon in the following manner: the conductor should be wrapped around the whole length of the rod like a helix and there should be possibility that this conductor to be turned into the ''closed circuit'' by means of mechanically connecting its ends (see the image below). After releasing the payload at necessary speed and direction this circuit should be closed, then according to ''electromagnetic induction'' the electric current will be generated in the conductor and the energy of this electric current will come from rod’s kinetic energy. Therefore, inducted electric current in the enclosed circuit will force this circuit and rod to lose kinetic energy and speed. The part of the generated electric current will be spent in prevailing conductor’s electric resistance:<br />
<br />
[[File: Helix.jpg]] <br />
<br />
The advantage of this method is that for decelerating the rod no energy will be required, as for drawback-much time will be required for this purpose because at the altitude of several ten thousand kilometers the Earth’s magnetic field is quite weak and the effect described in the paragraph above will need much time to operate and give necessary result. <br />
<br />
4. The above-described third method could be realized in a bit different way: if the conductor wrapped around the rod is a closed circuit and if we conduct the electricity there then the electric current will generate its own magnetic field that will counteract with Earth’s one. More precisely, according to ''Lenz's law'' induced current’s magnetic field will be in such a direction as to oppose the motion or change causing it, in other words induced current’s magnetic field will counteract outer magnetic field’s any change and this will cause decelerating rod’s rotation and finally its stopping. <br />
<br />
5. The obvious disadvantage of the third and fourth method described above is weakness of the Earth’s magnetic field because of which decelerating the rod may be delayed in time. For solving this problem we can create artificial magnetic field by means of electromagnets. Particularly, one electromagnet should be placed at the Space Elevator’s counterweight, very close to Space Catapult’s rod. The second electromagnet should be placed directly on the Space Catapult’s rod close to first electromagnet (actually, instead of this second electromagnet there could be used the conductor wrapped around the rod as we described above in previous methods). The reason of this nearness is that magnetic field generally weakens directly proportional to distance’s third power and much time will be needed for decelerating Space Catapult’s rod if two electromagnets are far from each other.<br />
<br />
This method probably will consume the most amount of energy but at the same time it will be the most effective because it does not depend on outer factors such as Earth’s magnetic field which is quite weak at the altitude of several ten thousand kilometers above the sea level. <br />
<br />
Eventually, which methods for decelerating the Space Catapult’s rod would be the best? As we see each one of them have got their advantages and disadvantages. We can state that we should choose one of them according to spaceflight’s profile and goal. Particularly, if we decide to send the spacecraft into the deep space mission where especially high speed is necessary then in this case ''longer/more massive'' rod would be needed rotating at very high speed. Under such circumstance much energy will be needed for accelerating/decelerating the rod. We should also take into consideration the fact how frequently the Space Catapult will operate, in other words how mane payloads it will have to send into space per some certain amount of time, week/month and etc. If time interval between two following missions is relatively high then we should choose the method that will consume less energy and more time for decelerating the rod. On the contrary, if the Space Catapult has to send payloads very often then we should choose the method that will consume more energy and enable the rod to decelerate faster. In other words, we should find ''golden mean'' between consuming time and energy. We should also take into account how much energy supply will be produced at the Space Elevator’s counterweight (see ''Energy source placed on the Space Elevator’s counterweight'') and what part of this energy can we spend for accelerating/decelerating the rod.<br />
<br />
The rod’s rotations can be decelerated much faster than accelerated; the reason of it is that when accelerating the rod has got some sophisticated device as payload and generally unmanned spacecrafts are capable to high g-loads, but still for them some restrictions exist. After the payload is released at needed direction and speed, the rod can decelerate much faster because the rod itself is quite simple device without any complex and sophisticated details. <br />
<br />
We can actually use several methods, such as the third one and then the first/fifth ones. This would be justified because of following reason: as we have already said when decelerating with the third/forth method the problem of weakness of the Earth’s magnetic field would occur, therefore much time would be necessary for described method(s) to perform and give us result. However, we should note that in the beginning when the rod rotates very quickly this method would still operate strong enough. This derives from Faraday's law of induction stating that “the electromotive force generated is proportional ''to the rate of change of the magnetic flux''”. Therefore, in the beginning when the rod is rotating very quickly we can use the third/forth method(s) and when the rod significantly brakes we can apply to the first/fifth ones-they do not depend on Earth magnetic field. In other words, such approach would greatly help us in finding the golden mean between spending energy and time necessary for decelerating the rod. <br />
<br />
And finally: after releasing the payload the Space Catapult’s rod can actually give us energy. More precisely, the electro motor itself can serve as electric generator also since we know that the same machine can operate as electric motor if it is fed with electricity and as generator for electricity if its rotor is rotated by other machines. Therefore after releasing the payload when the electro motor’s rotor is rotating very quickly it can give us energy, in result of which the rod will lose its kinetic energy and speed, as for generated energy it can be sent downwards to the Earth for our terrestrial needs (see the next section in this paper) or stored onboard the Space Elevator’s counterweight. This approach has got one substantial advantage: it does not imply additional mass (wrapped wire) that will cause problems because rotating heavier rod would consume more energy.<br />
<br />
=Energy source placed on the Space Elevator’s counterweight=<br />
<br />
As well-known, the Space Elevator’s cabin needs energy when moving along the cable and it can get it from the Earth by means of various ways, such as: laser beam, microwaves, through the cable itself and etc. On the other hand, Space Catapult also needs much energy for rotating the rod and for this purpose some energy source should be placed on the Space Elevator’s counterweight, presumably solar panels array. Doing this would demand additional funding and engineering work and this undertaking should be justified, so how can we prove that placing energy source on the counterweight would be necessary and useful? We should not forget that the energy generally could be simply transmitted from the Earth without carrying any material for energy source on counterweight; so we can justify this undertaking if we declare/prove that: <br />
<br />
1. Energy source should be designed for ''both'' Space Elevator’s cabin and Space Catapult’s rod. We can imagine it as array of numerous solar panels producing enough energy for both above-mentioned constructions. For this purpose solar panels would be better solution than nuclear reactor because they do not need nuclear fuel to be carried from the Earth to counterweight, also they are capable for producing energy in a continuous mode. By the way this circumstance will enable us to send the payload to space by Space Catapult whenever we want without depending existence nuclear fuel at the counterweight. <br />
<br />
2. Transmitting energy from the counterweight (“from above”) is better and advantageous than doing the same thing from Earth (“from below”). Indeed, when we try to transmit energy (laser or microwave beam) from the Earth to ascending cabin, the part of energy is inevitably lost and dispersed in the Earth’s atmosphere and (this is point of the question) this continues during the whole process of ascent. On the contrary, when transmitting the energy from counterweight to cabin the energy will be lost only on the little part of this voyage, more specifically until the cabin leaves the atmosphere (100 km in height) and when cabin leaves it the energy will be transmitted in vacuum without loss. <br />
<br />
3. For receiving the energy from the Earth the huge solar panels (in case of laser beam) or antennas (in case of microwaves) will be needed to be mounted on the counterweight and this is additional mass and additional engineering work.<br />
<br />
We think that these arguments given above are enough for shoving that placing energy source on the Space Elevator’s counterweight have advantages over transmitting energy from the Earth and as conclusion we can state that energy source on counterweight would serve both space transportation systems-Space Elevator and Space catapult. <br />
<br />
As addition, we could use the energy produced on the counterweight for terrestrial needs also. Indeed, there have been developed numerous projects for receiving energy from space since 60-ies implying producing it by means of solar panels and then transmitting to the Earth. Combining all these three goals we can conclude that placing solar power plant on the Space Elevator’s counterweight would be triply useful and advantageous. In other words, when the Space Catapult and Space Elevator do not function, the energy produced on the counterweight should be directly transmitted to the Earth for our terrestrial needs and thus the idea of Space Elevator, Space Catapult and space power plant will be combined in one project.<br />
<br />
=Assembling the Space Catapult=<br />
<br />
Assembling in space such a huge structure as Space Catapult will not be an easy task from the technical point of view and definitely needs special engineering approach. Besides, we think that Space Catapult’s rod should be mounted at the Space Elevator’s counterweight separately from every other parts of the Space Catapult (e.g. electro motor and etc.); this circumstance is caused by rod’s gigantic sizes. More precisely, electric motor and plus any other equipments necessary for Space Catapult’s performance should be delivered to space by means of Space Elevator in a usual way; as for Space Catapult’s rod, it is a different matter and it should be delivered and mounted separately in the end. <br />
<br />
Eventually, Space Catapult’s rod will be quite long, perhaps much more than 100 kilometers. It is obvious that delivering such a long rod as ''one single unit'' would be quite difficult task; also it is possible that due to its total mass the Space Elevator’s cabin will not be able to deliver such rod at all, but we have already mentioned that the Space Catapult may have the rod with various length; more precisely the rod may consist of two/more parts. In such case these parts should be delivered towards the counterweight separately and then assembled. <br />
<br />
But the Space Elevator’s cabin can actually deliver the Space Catapult’s rod as ''one single unit'' in space. We think that this would depend only on rod’s mass. The Space Elevator’s lifting capacity is not well-known yet; however apparently it will not exceed one hundred metric tons and if Space Catapult’s rod is made of extra light material then cabin will be able to deliver it in space and in such case the following question will arise: how the cabin will deliver such a huge object in space without any damage?<br />
<br />
This can be done by means of two cabins. Generally, Space Elevator’s conception implies only one cabin moving along the cable, but for some special purpose (like delivering Space Catapult’s rod in space) we can use the second cabin also that will descend downwards after finishing its job and will not participate in Space Elevator’s further performance. As for the process of delivering the rod, we can imagine it in a following manner: at first the rod will be placed horizontally on the Earth (thus it must be manufactured and then transported to the Space Elevator’s base station), then the Space Elevator’s first cabin will carry rod’s one end along the cable while the rod’s second end will be moved on the Earth so that the rod to take more and more vertical position. When the rod is in vertical position the second cabin will capture rod’s second end and will carry it in space. We think that without the second cabin it would be quite difficult for one cabin only to carry long/heavy rod because the rod may actually shake and crash to the Space Elevator’s cable and this is absolutely undesirable. <br />
<br />
So, as we see in principle it looks to be quite easy, however the assembling may complicate due to rod’s length. In this case it would be better to carry not the rod as ''one single unit'' but its parts and then to assemble them in space in the following manner: ''two'' cabins will carry the first part as described above, when this part is delivered to space and temporarily hung at the cable the next two cabins will carry the second part that will be attached to the first one from below; the other parts will be delivered to space and assembled into the rod in the same way. <br />
<br />
The obvious disadvantage of the above-described method is that each part needs two cabins on the Space Elevator’s cable, besides the humans will be needed for assembling the rod from these parts in the atmosphere’s upper layers; therefore we think that the first way-delivering the rod into space as one single unit still would be easier and more realistic; besides we should take into consideration the fact that if the rod is assembled the additional devices will be needed ''on the rod itself'' for joining these parts and this circumstance would lead to increasing the rod’s total mass and this is undesirable. See the image showing assembling process:<br />
<br />
[[File: Assembling.jpg]] <br />
<br />
Whatever design/structure the rod has-assembled from several parts or as one single unit, it must be delivered to its destination-Space Elevator’s counterweight and must be fastened to electro motor’s own axis. But the problem is that the rod will be quite long and also the fact that Space Catapult’s electro motor will be placed at counterweight’s upper side (or at the ''lateral'' side if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), so it will be necessary the rod coming from below to be moved to counterweight’s upper/lateral side, besides the rod should be docked with electro motor’s axis as accurately as possible. How is it possible to realize such complex engineering operation? Here we can indicate one possible theoretical way: <br />
<br />
The rod will be parallel to Space Elevator’s cable when carried by cabin, but later the cabin’s mechanisms should rotate it so that the rod to be orthogonal to Space Elevator’s cable (this will not be necessary if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), exactly in this position the rod should be delivered to counterweight, besides the rod when moving along the cable should be shifted a bit upwards (relative to the Earth) than the cabin itself. Under such conditions we will easily achieve docking the rod to electro motor’s own axis which from its side should have some trapping device (magnetic for example) to “catch” the rod and thus guarantee docking the rod to electro motor and finishing assembling the Space Catapult as a whole. But if the rod’s plane of rotation is parallel to cable then assembling process will be much easier because the ascending rod may directly dock to electro motor’s own axis. See the image showing this process:<br />
<br />
[[File: Deliver - Copy.jpg]] <br />
<br />
We think that it would be useful if one Space Elevator is built specially for Space Catapult with its base station located on the land, not the ocean. This would be justified because transporting Space Catapult’s rod from its place of manufacture to Space Elevator’s base station should occur on the land by means of several transports simultaneously (due to rod’s great length), this will enable us to deliver the rod to its destination without any damage while this kind of operation is hardly possible on the water.<br />
<br />
=The technical aspects regarding the Space Catapult=<br />
<br />
As an example, we can try to calculate/ascertain all possible kinds of aspects regarding the rod with some certain mass and sizes, for example we can assume the Space Catapult has got 100 km length rod. <br />
<br />
The circumference of the circle that this rod’s end will draw in space will be equal to 2πr=628 km. As we have already mentioned payload’s abilities for withstanding the g-load is restricted, so if the electromotor rotates the rod so that payload’s speed is equal to 50 km/sec (this means that it will take 12.56 seconds for the rod to make one complete revolution), in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design the spacecraft that will withstand such acceleration, but what about the rod itself? Which material can be used for designing this rod, what will be its mass and how much energy and time will be needed for the rod to reach this velocity? <br />
<br />
For manufacturing the rod we should choose the material with very low density and highest value of strength. Currently, the ''Carbon nanotubes'' are the best candidates for this purpose. What will the mass of the rod made of this material? This depends on width also and it should be as less as possible (otherwise the rod will be too heavy and too wide for transporting from manufacture place to Space Elevator’s base station and for delivering it to space by means of Space Elevator) but from the other hand the ''applied load'' will not let us to design very narrow rod.<br />
<br />
Let’s assume that we intend to launch the payload with the mass of 10 000 kg (during calculation we will use ''SI system'' only). To clarify what kind of material will be able to withstand the acceleration we should calculate and then compare two values: the ''applied load'' and ''tensile strength''. For calculating the first one we should multiply g-load (which we already know-2 550 g) to its mass-10 000 kg, we will get 25 500 000. As for calculating tensile strength, we should take its values (for Carbon nanotubes it varies from 11 000 MPa to 63 000, we will take some medium value-40 000 MPa) and multiply it to cross-section’s area, in our case rod is cylinder with circular cross-section. If radius of cross-section is 1 meters then its area is 3.14 square meters, multiplying this value to value of tensile strength (40 GPa as said) we will get 125 600 000 000 and this is significantly more than value of applied load-25 500 000. Of course, we should also take into consideration ''factor of safety'' which is generally equal to 2 and this indicates us that for safety the payload’s actual mass should be twice less but in our case as we see the rod will be able to accelerate the payload to above-mentioned speed. By the way, note that if that g-load ''2 550 g'' is almost at the payload’s withstanding limit this is not serious problem for the rod itself (we have already seen that value of tensile strength is much more than value of applied load) and this is clear why: payload generally contains sophisticated equipments (electrical circuit, optics an etc.) that will not be able to withstand very high g-loads while the rod will be made of some continuous solid substance, Carbon nanotubes is this case and of course it will be able to withstand much higher g-loads.<br />
<br />
<br />
What will be the mass of such rod? Knowing its volume (for this purpose its cross-section’s area 3.14 square meters should be multiplied to rod’s length-100 000 meters, we get 314 000 cubic meters) and taking the value of density (this also varies for Carbon nanotubes from 0.037 to 1.34 g/cm<sup>3</sup>, let’s take 0.1 g/cm<sup>3</sup>) we get rod’s mass as 31 400 000 kilograms. This is too heavy for Space Elevator’s modern concepts and for improving this situation we should either use many cabins for raising the rod as single unit or use nuclear energy for feeding the cabins instead of laser/microwave beams or deliver the rod’s parts separately in space and then assemble them (see ''Assembling the Space Catapult''). But if some advanced substances are chosen for this purpose (for example ''Silica aerogel'' the density of which is about 1.9 mg/cm<sup>3</sup>, this is 50 times less than the density of the Carbon nanotubes taken above-0.1 g/cm<sup>3</sup>) than problem may be lightened in spite of the fact that their current tensile strength is quite low-16 kPa for the density of 0.1 g/cm<sup>3</sup> <sup>7</sup>. So, we can conclude that we need the material with the density of ''Aerogels'' and tensile strength of Carbon nanotubes.<br />
<br />
How much energy and time will be needed for the rod to accelerate from zero to desired speed-50 km/sec? The amount of rotational energy of the rotating rod can be calculated by the following formula:<br />
Kinetic Energy<sub>rotational</sub>= (1/2)*I*ω2 <br />
<br />
Where:<br />
<br />
'''I'''=moment of inertia <br />
<br />
'''ω'''=angular velocity<br />
<br />
"I" depends on the shape of the mass under rotation. In the case of a uniform rod rotating from its end (axis of rotation is at the end of the rod) I = (m*L2)/3<br />
<br />
<br />
“ω” = V/R, where V = tangential velocity and R = radius<br />
<br />
In our case ''moment of inertia'' is equal to (31 400 000 kg*100 000 m2)/3=104 666 666 666 666 666<br />
ω is equal to (50 000 m/sec)/100 000 m=0.5<br />
<br />
So, Kinetic Energy<sub>rotational</sub>=(1/2)*104 666 666 666 666 666*(0.52)= 13 083 333 333 333 333.25 Joules<br />
<br />
Now, how much time and what amount of solar panels will be needed for accelerating this rod? The amount of Solar constant near the Earth is approximately equal to 1300 W/m2 [<sup>8</sup>], with assuming that ''coefficient of efficiency'' of solar panels is roughly 20 % we get 260 Watts per square meters and we can easily link amount energy (that we have already calculated) and power with the time needed. Particularly, ''Energy'' is equal to ''Power''’s multiplication to ''Time'':<br />
<br />
[[File: Formula - Copy.jpg]] <br />
<br />
So, Time is equal to 13 083 333 333 333 333.25 Joules/260 Watts=50320512820512.8 seconds, or 1 595 652 years. If we take much more area for solar panels, for example 10 millions square meters then 0.1595652 years or approximately 58 days will be needed and we think that this is acceptable time span.<br />
<br />
Actually, the time and energy will be needed a bit more for overcoming static friction in electro motor, for overcoming the rarified atmosphere’s resistance (we know that there no absolute vacuum in space), also we should take into consideration electric motors’ coefficient of efficiency that generally reaches 90-95 %, so some energy loss will occur here also. <br />
<br />
Now, what will be the total mass of solar panels producing the energy for Space Catapult? This depends on mass/power ratio, in near future it is expected that very lightweight designs could likely achieve 1 kg/kW [<sup>8</sup>] or 0.260 kg/ 260 W (per 1 square meter), so if for rotating the Space Catapult 10 millions square meters of solar panels are used then their total mass would be equal to 2 600 000 kg. We think that it is too heavy for Space Elevator the mass of which is expected to be equal around several hundred metric tons. If so, we will have to use fewer amounts of solar panels and therefore increase the time needed for accelerating the payload’s speed from zero to designed one. This will not make problems if the rod is accelerated only once and then keeps its constant rotation-for this purpose less energy will be needed and the payload will have to reach the rod’s end by first method as described earlier in this paper (see ''Rod’s plane of rotation towards the Earth'').<br />
<br />
We also need to take into consideration the value of deflection when the rod will be delivered to space by means of Space Elevator (see ''Assembling the Space Catapult''), in this case the thin and long rod will be bent due to its own weight and here we will try to calculate its value. This is quite complex problem that apparently cannot have an unambiguous solution because of many reasons, for example due to various temperatures in atmosphere’s different layers, various humidity and possible wind, but still we will try to calculate the value of ''Deflection'' that will occur in case when the rod’s one end is fastened to Space Elevator’s ascending cabin and the second end is fastened to the transport moving on the land, we discussed this option in above-mentioned section of our paper (see ''Assembling the Space Catapult''). The inclination angle for the rod will vary from 0º (rod is transported horizontally on the ground) to 90º (Space Elevator’s cabins are carrying the rod to space) and here we will discuss some medium case when the rod is semi-elevated in the air, when the angle between rod and ground/cable is equal to 45º. On the engineers’ ''eFunda'' web-site there is online calculator that enables to receive the value of ''Deflection'' (actually that site gives different term for this-''Displacement'') [10]:<br />
<br />
Here we need to enter the relevant values:<br />
<br />
''Length of beam'', ''L'': 100 000 meters<br />
<br />
''Line pressure load on beam'', p: In our case this is the weight per meter length. As we have already mentioned the radius of the rod’s cross-section is 1 meter, so the volume of rod’s 1 meter-length part will be 3.14 cubic meter. In case of using Carbon nanotubes with above-mentioned density-0.1 g/cm<sup>3</sup> the weight will be equal to 314 kg or 3 079 Newton. Since we have got the inclination of 45º we should multiply this value to cos45º- 0.707, so we get 2176 N/m.<br />
<br />
''Young's Modulus'', ''E'': This is equal to 1 000 GPa for Carbon nanotubes [11] <br />
<br />
''Distance from neutral axis to extreme fibers'', ''c'': In our case it is equal to the radius of the rod-1 meter<br />
<br />
''Moment of Inertia'', ''I'': It is equal to (pi*r<sup>4</sup>)/4, so it is equal to 0.785<br />
<br />
According to these initial data the calculator returns extremely high value of Deflection, much higher than the length of the rod itself: -3.61 × 10<sup>9</sup> meters. This result shows us that with the current materials (Carbon nanotubes in our case) it is impossible to raise the rod as ''one single unit'' to space by means of Space Elevator and we need other materials with less density and more ''Young's Modulus'' (or the rod should be much thicker but this will lead to increasing its mass). Therefore, we have got two options: either we should deliver the parts of that rod and then assemble them in space (we have already discussed this option) or completely different technologies for manufacturing the rod should be developed. Particularly, it would be very good if it was possible to manufacture the rod ''in continuous mode'' in vertical position and then uninterruptedly directly to carry it to space by means of Space Elevator’s cabins. Under such approach there will be no ''Deflection'' and several cabins will be able to deliver the rod in space. <br />
<br />
One note about transporting the rod from its place of manufacture to Space Elevator’s base station. We think that this process should be executed by many transports, in other words we are convinced that if the rod is carried by two trains only (or any other kind of transport) then the rod will continuously touch the ground since the ''Deflection'' occurs in any position-horizontal, inclined or vertical and this circumstance will lead to its damage, that’s why several transports will be needed to hold the rod at as many places as possible.<br />
<br />
=Stabilizing the counterweight=<br />
Stabilizing the Space Elevator’s counterweight is very important question during Space Catapult’s performance. Indeed, when the rod rotates it makes the imaginary circles in space and due to rod’s and payload’s masses the Space Catapult’s ''center of mass'' will be continuously shifted and if the counterweight is not somehow stabilized then it will make problems for accurate aiming to certain point at the celestial sphere. Also, if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable then there will be the danger that the rod may actually hit the cable and cut it. To avoid these problems we need to apply to serious measurements. <br />
<br />
First of all, the electro motor’s own axis can be quite long and this will diminish the chance to failure of the whole system. Actually, we are convinced that counterweight’s (where the electric motor will be placed) size will be quite large, mainly due to solar panels’ sizes and amount (this issue was discussed above), also the electromotor should be quite large and powerful to rotate the rod, and hence there will be enough distance between the rod and Space Elevator’s cable. <br />
<br />
The second serious problem is that the center of gravity of the system is not at the center of rotation, therefore it will be necessary to balance the rotating system when the payload is attached and when it is released.<br />
<br />
We think that the Space Catapult’s rod should not be deployed/directed to one side only but some counterweight of it should also exist. This is necessary since the unilaterally loaded (we mean the rod itself plus payload) rod will cause the counterweight to somersault. In other words, the rod should extend to other side and the ''moments of inertia'' of both sides should be the same as during rotating the rod as after releasing the payload when the rod still rotates. This is easily achievable if some additional, second payload is placed on the rod’s second end. Therefore, the Space Catapult will launch two payloads at the same time to the ''opposite'' directions but at various speeds if the second part/side of the rod is shorter.<br />
<br />
How the second payload should be placed on the rod and should we really send two payloads? Until we have got balanced rod this problem does not arise but as soon as the Space Catapult releases the payload this balance will be violated, how it can be restored? There are two theoretical ways for achieving this: reducing the ''mass'' or reducing the ''length''-with diminishing either one of them the ''moment of inertia'' will be decreased. We think that reducing the mass will be less practicable since this would require placing the second payload (spacecraft or anything else) on the rod’s second part and this cannot be done from the Space Elevator’s cabin-this is the easiest way for delivering the payload from Earth to Space Catapult’s rod; so we would have to (see ''Rod’s plane of rotation towards the Earth'') put the second payload on the electro motor and then send it rod’s second part’s end. This is quite complicated task; therefore we can apply to second approach-put some sliding object that will immediately move to electromotor as soon as the spacecraft is released.<br />
<br />
[[File: MOI.jpg]] <br />
<br />
The next problem that may occur is that when the electro motor rotates the rod this motion will make the Space Elevator to rotate to the opposite direction. The same problem arises when helicopter’s primary blade’s rotation forces the helicopter to rotate to opposite direction and this possible rotation is annulled by ''tail rotor''. We think that for balancing the counterweight the additional motor and rod should be installed and this rod should rotate to opposite direction and if their ''angular momentums'' are equal to each other, then their rotations will cancel each other. More precisely, the following equation should be fulfilled:<br />
<br />
[[File: Angular momentum.png]] <br />
<br />
Where ''m'' is mass of the rod, ''v'' is angular speed and ''L'' is rod’s length, the numbers ''1'' and ''2'' refer to first and second rods correspondingly. For balancing both rods’ rotation the multiplication at both sides of the counterweight should be equal, by the way this circumstance enables us to use the second rod with shorter length and even with less mass but rotating at more angular velocity.<br />
<br />
Such approach will effectively deal with other problem which will arise when the Space Catapult releases the payload(s), at this moment the second motor should instantly diminish its angular velocity to some certain level (an ordinary mechanical brakes could be used for this purpose), in this case ''angular momentums'' for both motors/rods will be equal again and Space Elevator’s counterweight will maintain its attitude in space. See the image below depicting the Space Catapult with two electro motors and rods:<br />
<br />
[[File: Two-rods.jpg]] <br />
<br />
Such approach will justify itself if rod’s plane of rotation is parallel to Space Elevator’s cable, but if this plane is orthogonal to cable (see ''Rod’s plane of rotation towards the Earth'') then the second/balancing electromotor cannot be placed under the counterweight because the cable will be cut when rod touches it. Therefore a bit different approach should used and we need to install two/four/eight electro motors with their own relatively shorter rods rotating to opposite direction. They should be placed at the counterweight’s lower side and on its edge (as we suppose the counterweight should be disc) so that their rods not to touch and cut Space Elevator’s cable. Also, total a''ngular momentums'' from these motors should be equal to the ''angular momentum'' from upper motor and thus the counterweight will not rotate and the Space Elevator’s cable will not be twisted. This situation is presented below:<br />
<br />
[[File: Modified-2.jpg]] <br />
<br />
We think that the array of gyroscopes would be also very useful to be installed at the counterweight since they can maintain the attitude of the whole system and this is important for precise aiming to certain point at the celestial sphere. As for the energy required for gyroscopes’ performance it could be received from the array of solar panels which as a result will generally serve Space Catapult’s precise performance.<br />
<br />
=Space Catapult placed at Lagrangian points-the way for gaining subluminal speeds=<br />
<br />
In our paper we discussed the Space Catapult based on the Space Elevator’s counterweight and concluded that this would be convenient when we intend to deliver the payload to space from the Earth. However, such Space Catapult cannot gain very high speeds and therefore we need to choose other way. It is obvious that we need to keep rod’s plane of rotation orthogonally relative to the ''Earth-Sun connecting line'' and hence we should place the rod on the celestial body which will be in synchronous rotation with the Sun but since there is no such body in the solar system we conclude that the Space Catapult for subluminal speeds (the speeds close to speed of light are in mind) should be placed at such point near the Earth where it will be easy to reach it from our planet and where the rotating rod will not hit the Earth and will be always at the same distance from the Sun to avoid the influence of its tidal forces. The examples of such places are '''Lagrangian''' L<sub>1</sub> and/or L<sub>2</sub> points at 1.5 million km away from the Earth. If the Space Catapult is placed at one of these points then its rod can be always orthogonal to the Sun in principle, at the same time it will never collide with the Earth and also it will be quite close to the Earth since 1.5 million km distance is very negligible in space.<br />
<br />
We have got several notes regarding such approach. First, when we mentioned that the rod’s various parts can be at the same distance from the Sun this strictly speaking is not very true because the Sun can be referred as little point where its gravity “comes out” from while the rod is quite long and its initial part (placed at one of the Lagrangian points) will be attracted stronger than the utmost one (for equal attracting the rod should the arc ''with the same curviness as Sun’s surface'' and not straight line); but still this is better than to direct the rod exactly towards the Sun where the tidal forces will try to tear the rod. Second, the Space Catapult should be placed at Lagrangian L1 point which is closer to the Sun than L2 one and therefore receives by 4 % more energy per area from the Sun. Third, the rod should be in constant rotation, this requires much less energy than accelerating it from zero, then stopping it and accelerating it again. Fourth, the existence of the asteroid belt in the solar system between Mars and Jupiter will somehow restrict the actual length of the rod. Indeed, the Space Catapult should be placed at one of the Lagrangian points at 1 AU distance from the Sun while asteroid belt approximately lays at 2.7 AU, from the simple geometry it is obvious that the length of the rod ''almost reaching'' the asteroid belt can be approximately equal to 390 million km, and if the rod is longer then it may simply hit any asteroid within that belt. For 390 million km length rod and for 100 000 m/sec2 acceleration at rod’s end (where the payload will be attached) the maximal speed that the spacecraft can gain will be approximately equal to 200 000 km/sec (two thirds of the speed of light) and this can be considered as enough for practical interstellar spaceflight. Fifth, the spacecraft should be directly put on the rotating rod’s initial end (near electromotor) and then slide towards the other end with its own rocket engines. To achieve this, the spacecraft will have to cover relatively less distance on the rod and then rod’s circular motion will accelerate the spacecraft further-we have already mentioned this in this paper when speaking about deploying the Lunar Space Catapult. This action-putting the spacecraft on the rod will not be difficult since rod’s angular velocity will be quite low due to rod’s huge length, particularly for 400 million km length rod and for 200 000 km/sec linear speed the rod’s angular velocity will be 0.0000796 revolutions/sec.<br />
<br />
[[File: Lagrangian-point.jpg]] <br />
<br />
We have already mentioned that to avoid the destructive influence of the Sun’s tidal forces the rod’s plane of rotation should be orthogonal to the Earth-Sun connecting line. By the way, note that under such approach we may have to wait one year until the Lagrangian Space Catapult occupies the relevant position towards the certain point at the celestial sphere where the spacecraft should be sent to. But from the other hand it would be useful if it is feasible to rotate this whole structure around the imaginary axis directed towards the ''ecliptic poles'' (depicted as faint green dash line on the image above), the reason if this is the possible danger when the rotating rod may hit Mars or asteroids that orbit around the Sun closer than 2.7 AU distance (for example ''433 Eros'' or ''1036 Ganymed''), hence for avoiding such undesired collision the Lagrangian Space Catapult should be slightly rotated by several degrees clockwise/counterclockwise so that the rod not to collide with any celestial object. We are convinced that rotation by several degrees will be absolutely enough measurement due to rod’s gigantic length and relatively less sizes of the celestial objects in the solar system.<br />
<br />
The next issue that we should discuss refers to stability of the Lagrangian Space Catapult placed at L<sub>1</sub> point. As we see this structure will have enormously gigantic size while the Lagrangian point is relatively little mathematical one in space, so what can be done to be convinced that this structure will remain at that point and do not shift aside? The body placed at one of the Lagrangian points is affected by other celestial objects’ gravity and therefore for achieving the balance the rod needs to have the counterweight with more mass if it (counterweight) is shorter. As we clearly see the rod needs the counterweight for two reasons: not to let the Space Catapult somersault and for maintaining it at the L1 point. We think that it would be very useful if the arrays of solar panels act as counterweight since exactly they can give us energy for rotating the rod. Also, we need the second, shorter, perhaps less massive but faster-rotating rod (again-solar panel arrays) the opposite rotation of which would cancel first rod’s rotation, this issue was discussed in this paper. These arrays of solar panels are depicted on the image shown above. <br />
<br />
How such a gigantic structure as Lagrangian Space Catapult can be assembled in space? In our paper we discussed the possible ways for delivering the rod from the Earth to the Space Elevator’s counterweight, now we will try to show that it is possible ''in principle'' to assemble the extra-long rod in space. <br />
<br />
If it is possible from the technical point of view to manufacture extra-long rod then we can use this approach and make 1.5 million km length rod (this is the distance between the Earth and Lagrangian L<sub>1</sub>/L<sub>2</sub> point) that will be mechanically directed to the base station at L<sub>1</sub> point. The capturing devices there will catch the rod and attach it to the electro motor’s shaft after which the rod should be spun by 90º so that it to be orthogonal to Earth-Sun connecting line (for this purpose the additional mechanisms will be needed), this spin is necessary because L<sub>1</sub> point is located on the Earth-Sun connecting line (that is towards the Sun if we look from the Earth) and when directing the rod from the Moon it will lay ''along'' this line while we need across. After this the rod should be slid to another side and then the next rod should be directed to the Lagrangian Space Catapult where it will be attached to the previous rod and etc. In other words, the extra-long rod will be assembled from one side and its length will “grow” from this side to other one, this is necessary because the distance between Moon (the rod should be manufactured exactly there and not on the Earth due to our planet’s relatively more gravity, atmosphere and problematic space debris belt around it) and L<sub>1</sub> point is constant and rod’s parts cannot be more. Due to whole rod’s and its parts’ lengths (400 million and 1.5 million km correspondingly) we think that about 260-270 such operations will be needed to finish assembling the rod (400/1.5). The process of assembling the Lagrangian Space Catapult is shown on the image below:<br />
<br />
[[File: Lagrangian-point-assemble.jpg]]<br />
<br />
=Conclusion=<br />
<br />
As we have seen, for leaving the Solar system and reaching the remote celestial bodies (stars, nebulas) there is no need to develop advanced and complicated technologies that mostly are not capable for gaining extra high velocities nevertheless. In any case, until the Space Elevator is really built (scheduled for construction by 2031) we have got much time for developing the idea of Space Catapult in technical aspect, like finding appropriate materials for the rod, perfect the ways how the Space Catapult can be assembled in space and etc. The concept of Space Catapult itself is the easiest one, does not need developing neither complex and sophisticated technologies, nor some exotic methods (such as ''Gravitoelectromagnetic toroidal launchers'', ''Antimatter rocket'' and etc.) and can be easily implemented in near future; in other words the Space Catapult is not some sophisticated structure that would need profound science research and the fact that it will enable us to gain whatever high speed will justify its developing and building by the humankind. As for other technologies like Ion Drive, they could be used by the spacecraft during flight for other purposes, for example for correcting/changing the flight direction.<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Space_Elevator<br />
<br />
2. http://www.isec.info/index.php?option=com_content&view=article&id=14&Itemid=9<br />
<br />
3. http://www.space-track.org/perl/geo_report.pl (provided data updates regularly, registering is needed) <br />
<br />
4. http://www.oosa.unvienna.org/pdf/reports/ac105/AC105_720E.pdf page 24 (data as at 21 August, 1997) <br />
<br />
5. http://www.amostech.com/ssw/presentations/Session7/S7-1Molotov.pdf page 16<br />
<br />
6. http://www.esa.int/SPECIALS/ESOC/SEMN2VM5NDF_mg_1_s_b.html <br />
<br />
7. http://eetd.lbl.gov/ecs/aerogels/sa-physical.html<br />
<br />
8. http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant<br />
<br />
9. http://www.you.com.au/news/2005.htm, http://www.spacedaily.com/news/ssp-03b.html<br />
<br />
10. http://www.efunda.com/formulae/solid_mechanics/beams/casestudy_display.cfm?case=simple_uniformload<br />
<br />
11. http://en.wikipedia.org/wiki/Young%27s_modulus<br />
<br />
<br />
'''Appendix''': <br />
<br />
Animation illustrating the payload’s departure from the Lagrangian Space Catapult:<br />
[[File: Lagrangian-point-animation.gif]]</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_5&diff=3670OpenSpace 52013-09-21T13:02:39Z<p>Eagle9: </p>
<hr />
<div>== '''Space Catapult''' ==<br />
<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
=INTRODUCTION=<br />
<br />
<br />
The new method for sending the spacecrafts in deep space is presented here. The paper describes the long rod rotated by electro motor placed at the Space Elevator’s counterweight and at Lagrangian points. This simple structure will enable the rod to gain high velocity and carry the payload with it. After reaching the desired speed the rod will release the payload that will fly in space along the imaginary circle’s tangent. This structure we called Space Catapult and it should work with the assist of Space Elevator. This latter should be used for carrying the payload from the Earth to Space Catapult’s rod.<br />
<br />
For exploring the outer space the humankind generally uses the rocket engines, mostly chemical-propelled ones. They enable us the explore near-Earth celestial bodies and other planets in the solar system. They even enabled us to send several deep space missions beyond the solar system such as '''Pioneer-10''', '''Pioneer-11''', '''Voyager-1''', '''Voyager-2''', however by means of this technology the flight lasts undesirably long and it seems to be impossible to reach remote celestial bodies in space such as stars, so new technologies are necessary for this purpose. However new technologies do not necessary imply new kind of rocket engines, such as ''Ion Drives'' because they are capable for gaining several ten times higher speeds only, but for remote celestial bodies even they are not suitable. Besides, they need a huge amount of energy to be stored onboard the spacecraft and this will make additional problems. So, high speed should be achieved with absolutely different approach. How this can be done?<br />
<br />
High speed can be easily achieved by means of fast-rotating rod around the electric motor. The motor’s rotational speed can be very high; the rod also can be quite long, hence the rod’s end’s linear speed can be extremely high, absolutely unachievable for any other technologies nowadays. The payload should be fastened at the rod’s end where the linear speed generally reaches maximal value. After reaching the necessary speed the rod will release the payload that will fly along the tangent from the current position. Thus the electric energy can be turned into payload’s speed and its velocity could be as high as we wish (except the ''speed of light'' of course). In principle the '''Space Catapult''' (thus we call this structure) would be the simplest, the most convenient and direct way for converting the energy/electricity into speed and conveying it to payload. <br />
<br />
As we see the Space Catapult is quite uncomplicated structure, however if we wish to gain high speeds we should deploy it in space, not on the Earth. Indeed, our planet is surrounded with dense atmosphere that impedes any quick motion, so if we rotate the rod quickly the atmospheric drag and generated heat would burn it very soon, therefore the Space Catapult should be built and deployed in space only, and as we suppose-at the Space Elevator’s counterweight. In other words, the Space Elevator’s counterweight will operate as Space Catapult. See image below:<br />
[[File:Space-catapult.jpg]]<br />
Generally, what is the Space Elevator ['''1''']['''2''']? According to modern concepts it will be the tall vertical structure built on equator and will have height of several ten thousand kilometers with its thin cable fastened to the base station on the Earth and with counterweight placed higher geostationary orbit. Because of balance between centrifugal force and gravity this structure will be stretched and the cabin will move along its cable carrying the goods into high orbit. After delivering the payload, the cabin will descend and carry the next one.<br />
In Space Elevator’s concepts several solutions have been proposed to act as a counterweight: <br />
<br />
1. Heavy, captured asteroid <br />
<br />
2. Space dock, space station or spaceport positioned past geostationary orbit <br />
<br />
3. Extension of the cable itself far beyond geostationary orbit. <br />
<br />
The third idea has gained more support in recent years due to the relative simplicity of the task and the fact that a payload that went to the end of the counterweight-cable would acquire considerable velocity relative to the Earth, allowing it to be launched into interplanetary space. However this idea cannot be completely shared by us due to following reason: <br />
<br />
It is well-known that the values of both '''Orbital''' and '''Escape Velocities''' decreases with increasing the altitude while the '''tangential velocity''' of Space Elevator’s cable increases. We can see the differences between them from the chart presented below:<br />
[[Image: Cxrili.gif]]<br />
<br />
As we see from this chart the ''tangential velocity'' of the Space Elevator even at its end (144 000 or 200 000 km altitude) is not very high to decrease the necessary time for covering the distance from the Earth to remote celestial bodies significantly. To achieve this, even the longer Space Elevator would be needed (its ''tangential velocity'' is directly proportional to its length) and this circumstance would complicate the technical task for building such Space Elevator. Because of this, there is no necessity to extend the cable itself far beyond geostationary orbit as proposed in the third variant. In any case, we have already seen that by means of Space Catapult it is possible to gain such huge velocities that are absolutely unachievable with other technologies, for example with Space Elevator. Therefore, using the counterweight and placing the Space Catapult there definitely has got some technical sense. <br />
<br />
However, we think that the question where the Space Catapult should be placed needs further discussion. Theoretically, the Space Catapult with its payload and nuclear reactor/solar panel needed for rotating the rod may be mounted not only at the counterweight, but on the Space Elevator’s cabin also that can carry all these goods to space in a usual way, as it should do it according to Space Elevator’s modern concepts. This option is quite possible, however for realizing this we need to know the mass of the payload, nuclear reactor/solar panels’ mass plus Space Catapult’s mass from one hand and Space Elevator’s lifting capacity (this ''must'' be more) from other hand, but these data are not available nowadays, therefore we think that the Space Catapult should be still mounted at the Space Elevator’s counterweight where it will be possible to send the payloads into deep space in ''continuous mode'' at high velocities.<br />
<br />
As we saw the Space Catapult is capable to gain very high velocities; however there is being developed other technologies and they in future will enable the spacecraft to fly at high speeds in space. These are Ion Drive systems, more precisely the most perspective one-''Variable Specific Impulse Magnetoplasma Rocket'' (VASIMR) which still under development can be used in future for deep space missions. Can these engines and Space Catapult be the rivals in space? Since none of them have been built and used in space yet we cannot give a persuasive answer to this question; however still it is possible to underline Space Catapult’s one significant advantage: if the future spacecraft uses the VASIMR (or any other kind of Ion Drive) engine it will definitely need to be equipped with nuclear reactor, otherwise the spacecraft will not be able to gain high speeds, also it will need to carry fuel tanks for this purpose. As for the Space Catapult, it can give much higher speed to spacecraft, besides it will have ''stationery'' power plant (see ''Energy source placed on the Space Elevator’s counterweight'') at the Space Elevator’s counterweight, so the payload will ''not'' have to carry the nuclear reactor onboard and this circumstance will lighten the work for deep space spacecraft. Besides, we should not forget that unlike the spacecrafts equipped with ion drive engines the Space Catapult will need no fuel for gaining high velocities. <br />
<br />
Briefly, Space Catapult’s advantages over any kind of propulsion systems are: <br />
<br />
1. Ability to gain any speed that is absolutely unachievable by means of other kinds of engines. <br />
<br />
2. No need by spacecraft to carry energy source that would make it too heavy and impracticable.<br />
<br />
=The Space Catapult needs long rod=<br />
<br />
When building the Space Catapult at Space Elevator’s counterweight we should install quite long rod there, the shorter the rod is, the easier would be installing it, however we should note that rod cannot be extremely short, let’s say 1 km length or so due to following reason:<br />
<br />
When we are going to send some payload into space, we need not only high velocity, but one certain direction also. The little inaccuracy in direction, inclination in several arcminutes is actually acceptable since the spacecraft would easily balance it with its engines; however great inclination from the initial direction would send the spacecraft into the completely different direction and in such case the whole mission will fail.<br />
<br />
If two Space Catapult’s rods have the length of let’s say 1 kilometer and 10 kilometers, then for giving to payload some certain linear speed (for instance 100 km/sec) these rods should rotate at different angular velocity. It is easy to ascertain that the shorter rod should rotate 10 times faster to gain the same linear speed than the rod with more length. But the faster the rod rotates, the more difficult will be to “catch” the needed moment for releasing the payload from the rod for sending it towards some certain direction. If the rod is too short, then it has to rotate very quickly for gaining some certain linear speed and therefore it will be extremely difficult catching the needed moment for releasing the payload. Hence, too short rod can make problem for sending the payload to some certain direction in space especially at high velocities. So, based on payload’s needed velocity we should find rod’s desired, minimal length that will enable us to send the payload in space to necessary direction without fear that it may yaw from the course. <br />
<br />
However, rod’s length will be crucial for payload’s abilities for withstanding the acceleration also. As an example, we can try to calculate its value which the payload will have to withstand during rod’s rotation. The acceleration of the body rotating at the circle with some constant velocity is calculated by the following formula:<br />
<br />
[[File: Acceleration - Copy.jpg]] <br />
<br />
Where a is acceleration in ''m/sec''<sup>2</sup>, ''v'' is payload’s linear velocity on the circle in ''m/sec'' and ''r'' is radius of the circle in ''meters'', in our case it is equal to rod’s length. Let’s assume that the rod is 100 km length and the electromotor rotates it so that payload’s speed is equal to 50 km/sec, in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design and manufacture the spacecraft’s subsystems (avionic and etc.) capable to withstand such acceleration. This circumstance somehow restricts the speeds that we can achieve, in any case their values actually depends on spacecrafts’ abilities for withstanding g-loads. But what can we do if much higher speeds are needed? The answer directly derives from that formula: the radius should be more; by the way note that this is additional reason why the longer rod is more useful. If we are able to make the extra long rod, then this will enable us to gain much higher velocities. <br />
<br />
What material should be used for manufacturing the rod? It is obvious that if very high speeds are needed the rod should be long and even in this case the acceleration at its end will be quite high, therefore ''sufficiently strong and light materials'' are needed for this purpose and making them is as similar challenge as in case of Space Elevator where the same requirements arises for the cable’s material. The lightness is needed because in case of heavy rod a lot of energy will be needed to rotate it; the strength is needed because in case of lack this property the rod will be destroyed due to great acceleration.<br />
<br />
=The mechanism for holding and releasing the payload=<br />
<br />
How the payload can be held by Space Catapult’s rod during rotation and how it can be released from the rod? We think that using ''electromagnet plus mechanical holding devices'' would be a good solution. More precisely, after the payload is attached to the rod it must be held by means of both methods until the rod accelerates and reaches necessary velocity (it may take even several days), but with approaching the desired speed the mechanical device should release the payload however the electromagnet(s) should still hold it. The explanation of such approach is following: generally the mechanical devices are much slower/sluggish in performance than electronic ones. We have already said that when releasing the payload the extreme accuracy is needed and mechanical devices cannot guarantee ''the exact time of releasing'' the payload unlike electronic ones. That is, it’s unlikely that mechanical devices can release the payload at some certain moment when needed while in case of electromagnet it would be enough to cease electric current there, it would lead to immediate vanishing of the magnetic field and sending the payload along the tangent from the point where the payload would be at the current moment. <br />
<br />
<br />
We think that the ''fastest control system'' would enable to release the payload to certain direction. This system (extremely fast-operating computer plus measuring equipments) should know the current position of the rod’s end, the current speed, the needed direction and be capable for computing the necessary moment for giving the order for diminishing the voltage for electromagnets and hence releasing the payload to desired direction and velocity.<br />
<br />
=Rod’s plane of rotation towards the Earth=<br />
<br />
The Space Catapult’s rod when rotating makes the circular plane/flatness in space and this plane may be horizontal/parallel to Earth surface, that is making the right angle to Space Elevator’s cable or it may be placed along the cable; see the both possible situations here:<br />
<br />
[[File: Planes-of-rotation - Copy.jpg]] <br />
<br />
Both approaches have got their advantages/disadvantages and here we will discuss this question, first of all from the point of view of safety.<br />
<br />
For gaining extremely high velocities quite long rod would be needed, maybe with the length of several thousand kilometers or even more. If such rod is placed ''along'' the Space Elevator’s cable then the rod during rotation will cross many orbits from the ''Medium Earth Orbit'' to ''High'' ones. When rotating, the rod may actually hit any satellite and/or space debris object and such collision can lead to rod’s complete destruction; therefore we should choose such plane which would be much more free from any artificial objects; hence if the rod rotates ''horizontally/parallel'' to Earth’s surface at high enough altitude where the satellites’ population is relatively low then this measurement would justify itself because under such circumstance the rod will not cross satellites’ orbits (rod’s plane of rotation will simply coincide to ''one'' orbit’s path). However, we should also note that this altitude actually depends on the Space Elevator’s proposed length. Indeed, the Space Catapult’s rod should be mounted at the Space Elevator’s counterweight; this counterweight from its side should be placed at the end of the Space Elevator at such altitude where the satellites’ population is as low as possible. This means that Space Elevator’s proposed height should be agreed with mounting Space Catapult on its counterweight. According to various databases the number of man-made objects at high orbits, more precisely beyond geostationary orbit is much less than on the lower orbits [3][4][5][6], therefore the Space Catapult with its rod should be located at the altitude of 50 000-60 000 km above the sea level. At such altitude the space is almost free and nothing will impede rod’s rapid rotation. Besides, the satellites at high orbits are orbiting around the Earth slower than on the lower orbits (as known any satellite orbits around its primary body slower in apogee than in perigee), therefore if some tracking system is mounted at Space Elevator’s counterweight then it will enable the Space Catapult to avoid undesired collision with satellites during Space Catapult’s performance. In other words, the Space Catapult should operate only when the there are no satellites near its vicinities.<br />
<br />
Now we will try to discuss this question from other side.<br />
<br />
How the payload can be transferred from the Space Elevator’s cabin to the Space Catapult’s rod? One way is following: cabin reaches the counterweight where the payload will be released, then payload will be mechanically conveyed to rod, continues its way ''on the rod'' (like the train rides on the rails) and after reaching rod’s end it stops, the rod begins rotating and after gaining necessary linear speed it releases the payload to needed direction. This method is generally realizable; however it seems to be too complicated and unpromising compare to the second one: the Space Catapult’s rod is stopped in space so that it to be directed downwards to the Earth and be parallel to Space Elevator’s cable. The Space Elevator’s cabin moving along the cable with payload stops at the cable ''near'' the end of the Space Catapult’s rod and releases the payload that will fly to the rod, attaches itself to the rod’s end (here the electromagnets would be useful), the rod begins rotating and after gaining needed linear speed will release the payload to necessary direction.<br />
<br />
This second way seems to be more promising because the first one is much more complicated as we have already said: first of all there would be needed some mechanical devices for transferring the payload from the Space Elevator’s cabin to counterweight, the counterweight should have the hole for the payload to move through it from below (we should not forget that the Space Catapult should be mounted ''at'' the counterweight, not ''beneath'' it), besides the rod should be made so that it to have some conveying surface (rails for instance) the payload to move on it. As we see it would be much more convenient if it is possible to convey the payload from the cabin to the rod directly and this would be feasible under the second method which is depicted below:<br />
<br />
[[File: Convey.jpg]] <br />
<br />
One more aspect regarding Space Catapult’s position. This structure, its rod, its electro motor and etc should be mounted at Space Elevator’s counterweight so that the rod to be placed westwards from the cable. The reason of it is following: when the Space Elevator’s cabin stops and releases the payload (which should fly to Space Catapult’s rod) the current speed of which will/should be more than the value of the ''Orbital/Escape Velocity'' at the current altitude. After releasing the payload will fly westwards and upwards because its orbit will be ellipse, under ellipse the payload will fly higher to apogee and at the speed less than Space Elevator’s current speed at the given altitude, in other words the released payload will “lag behind” the Space Elevator’s cable; therefore payloads’ ''stopping points'' at the cable and Space Catapult’s rod’s length should be calculated and chosen so that the payload to fly directly towards rod’s end. This process would be feasible in both cases-if the rod’s plane of rotation is parallel to Earth’s surface and if it is placed along the cable-but still this would be easier for the payload to achieve the rod’s end if the rod is placed along the cable because at least the distance that the payload should cover in space will be less.<br />
<br />
The length of the Space Catapult’s rod placed at the Space Elevator’s counterweight might vary since for various spaceflight purposes different initial speed will be needed and relatively low speed could be achieved by means of shorter rod. Because of this reason it might be necessary to change Space Catapult’s rod’s length, therefore it would be useful if the rod consists of two parts where the first part would be perpetually attached to electro motor and the second one will be attached to the first part if necessary. For this operation Space Catapult’s rod should be placed along the cable since the relative nearness would make this operation quite easy and it could be accomplished by the crew directly from the Space Elevator’s cabin stopped at the needed altitude. <br />
<br />
For deciding the question how the Space Catapult’s rod should be placed towards the Space Elevator’s cable we should take into consideration one substantial circumstance-to which direction do we plan to send the payload in space by means of Space Catapult? This circumstance will influence deciding this problem due to following reason:<br />
<br />
In case ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and if rod’s plane of rotation is parallel to Earth equator, then this plane will be orthogonal to Earth’s rotation axis. This axis from its side is tilted to ''ecliptic plane'' by 66° 34'. This means that Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 23°26'. Here follows very important consequence: under above-mentioned conditions the rod when rotating will be capable for covering only the part of the ''celestial sphere'' from 0° to 23°26' (counted from ''ecliptic plane'' northwards and southwards to ''Ecliptic poles''). This is about one fourth of the ''celestial sphere'' (23°/90°), this will not make problems if we intend to use the Space Catapult for exploring the solar system’s planets because their orbits’ tilts towards ''ecliptic plane'' do not exceed 7° (for planet Mercury, for other planets this tilt is even less); however we will not be able to send the payload for example to the nearest star ''Alpha Centaurs'' because this star is located at -42 degree according to ''ecliptic coordinate system'' in the celestial sphere.<br />
<br />
The situation will drastically change ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and ''if'' rod’s plane of rotation is orthogonal to Earth’s equator and therefore parallel to Earth’s axis of rotation. We have already discussed this option when we mentioned that the rod should be placed westwards from the cable and explained why it would be useful-for delivering the payload from Space Elevator’s cabin to Space Catapult’s rod. Under such conditions the Space Catapult will be capable to aim to any point on the ''celestial sphere''. Indeed, the Earth with the Space Elevator rotates around its axis and Space Elevator’s counterweight draws an imaginary circle in space. This circle is tilted to ''ecliptic plane'' at 23°26' and crosses this plane in two point called ''ascending'' and ''descending nodes''. The other points that are 90° away from these nodes we call point(s) of ''maximum elevation/depression'' (relative to ''ecliptic plane''). When the Space Elevator is at a''scending/descending node'' its rod and hence the payload can be directed to any point from 0º to 66º on the celestial sphere northwards and southwards from ecliptic plane. This makes about 75 % of celestial sphere. See the image depicting this situation:<br />
<br />
[[File: Node.jpg]]<br />
<br />
But when the space Elevator reaches the points of ''maximum elevation/depression'' then its rod during rapid rotation may be directed to any point from southern ''Ecliptic pole'' to ''Northern pole'' at the celestial sphere because at these points rod’s ''plane of rotation'' is orthogonal to ''ecliptic plane'' and thus the rotating rod can aim to ecliptic poles as well as other points. See this situation below:<br />
<br />
[[File: Elevation.jpg]] <br />
<br />
The situation will be similar if the Space Catapult’s rod is orthogonally placed towards cable. Under such approach Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 66° 34' and the Space Catapult will be capable to cover ''three fourths'' (66°/90°) of the ''celestial'' ''sphere'' when the Space Elevator is at the points of ''maximum elevation/depression'' and the whole celestial sphere when the Space Elevator is at ascending/descending nodes. For aiming the needed point on the celestial sphere the Earth should occupy the appropriate attitude towards the stars during the revolution around its axis, the same thing should be done under previous case described in the paragraph above. <br />
<br />
In conclusion, thinking about rod’s plane of rotation towards the Earth, we should note one important difference between above-mentioned approaches: if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, then in case of emergency during Space Catapult’s performance (for example if the Space Catapult’s rod is cut by sudden meteorite bombardment) the rod’s part with the payload may simply crash to the Earth at huge velocity if the rod at this moment is directed to the Earth. This cannot happen if Space Catapult’s rod’s plane of rotation is orthogonal to Space Elevator’s cable because payload’s rotational path will not be directed towards the Earth and hence its flying trajectory will never cross the Earth.<br />
<br />
=Braking the Space Catapult’s rod=<br />
<br />
After releasing the payload at necessary speed and direction, the Space Catapult’s rod will have a huge angular velocity that needs to be decreased to zero in order the Space Catapult’s rod to get another payload in motionless position and then to send it to space. <br />
What methods can we use to reduce Space Catapult’s rod’s rotation to zero? There are several possible ways: <br />
<br />
1. The electromotor designed for accelerating the rod may actually play a role of brakes, more precisely after releasing the payload to space the electromotor should operate/rotate in the opposite direction, hence rod’s rotational speed will be diminished to zero after that electromotor will stop operating. Under such method a bit less energy will be spent for decelerating the rod than in case of accelerating because when decelerating the rod is free from payload. <br />
<br />
2. An ordinary mechanical brakes, however due to electro motor’s and rod’s sizes a huge brake(s) would be needed to be installed on the Space Elevator’s counterweight and this circumstance would make additional problems from the engineering point of view. Nevertheless, we should admit that under such method we would not need as much energy as during accelerating; on the contrary, in this process the heat will be emitted as it generally happens during braking. <br />
<br />
3. For decelerating the rod we can use the well-known phenomenon in physics-''electromagnetic induction'': when the c''onductor/ closed circuit'' moves into the magnetic field the electric current is generated there. In case of Space Catapult we can use this phenomenon in the following manner: the conductor should be wrapped around the whole length of the rod like a helix and there should be possibility that this conductor to be turned into the ''closed circuit'' by means of mechanically connecting its ends (see the image below). After releasing the payload at necessary speed and direction this circuit should be closed, then according to ''electromagnetic induction'' the electric current will be generated in the conductor and the energy of this electric current will come from rod’s kinetic energy. Therefore, inducted electric current in the enclosed circuit will force this circuit and rod to lose kinetic energy and speed. The part of the generated electric current will be spent in prevailing conductor’s electric resistance:<br />
<br />
[[File: Helix.jpg]] <br />
<br />
The advantage of this method is that for decelerating the rod no energy will be required, as for drawback-much time will be required for this purpose because at the altitude of several ten thousand kilometers the Earth’s magnetic field is quite weak and the effect described in the paragraph above will need much time to operate and give necessary result. <br />
<br />
4. The above-described third method could be realized in a bit different way: if the conductor wrapped around the rod is a closed circuit and if we conduct the electricity there then the electric current will generate its own magnetic field that will counteract with Earth’s one. More precisely, according to ''Lenz's law'' induced current’s magnetic field will be in such a direction as to oppose the motion or change causing it, in other words induced current’s magnetic field will counteract outer magnetic field’s any change and this will cause decelerating rod’s rotation and finally its stopping. <br />
<br />
5. The obvious disadvantage of the third and fourth method described above is weakness of the Earth’s magnetic field because of which decelerating the rod may be delayed in time. For solving this problem we can create artificial magnetic field by means of electromagnets. Particularly, one electromagnet should be placed at the Space Elevator’s counterweight, very close to Space Catapult’s rod. The second electromagnet should be placed directly on the Space Catapult’s rod close to first electromagnet (actually, instead of this second electromagnet there could be used the conductor wrapped around the rod as we described above in previous methods). The reason of this nearness is that magnetic field generally weakens directly proportional to distance’s third power and much time will be needed for decelerating Space Catapult’s rod if two electromagnets are far from each other.<br />
<br />
This method probably will consume the most amount of energy but at the same time it will be the most effective because it does not depend on outer factors such as Earth’s magnetic field which is quite weak at the altitude of several ten thousand kilometers above the sea level. <br />
<br />
Eventually, which methods for decelerating the Space Catapult’s rod would be the best? As we see each one of them have got their advantages and disadvantages. We can state that we should choose one of them according to spaceflight’s profile and goal. Particularly, if we decide to send the spacecraft into the deep space mission where especially high speed is necessary then in this case ''longer/more massive'' rod would be needed rotating at very high speed. Under such circumstance much energy will be needed for accelerating/decelerating the rod. We should also take into consideration the fact how frequently the Space Catapult will operate, in other words how mane payloads it will have to send into space per some certain amount of time, week/month and etc. If time interval between two following missions is relatively high then we should choose the method that will consume less energy and more time for decelerating the rod. On the contrary, if the Space Catapult has to send payloads very often then we should choose the method that will consume more energy and enable the rod to decelerate faster. In other words, we should find ''golden mean'' between consuming time and energy. We should also take into account how much energy supply will be produced at the Space Elevator’s counterweight (see ''Energy source placed on the Space Elevator’s counterweight'') and what part of this energy can we spend for accelerating/decelerating the rod.<br />
<br />
The rod’s rotations can be decelerated much faster than accelerated; the reason of it is that when accelerating the rod has got some sophisticated device as payload and generally unmanned spacecrafts are capable to high g-loads, but still for them some restrictions exist. After the payload is released at needed direction and speed, the rod can decelerate much faster because the rod itself is quite simple device without any complex and sophisticated details. <br />
<br />
We can actually use several methods, such as the third one and then the first/fifth ones. This would be justified because of following reason: as we have already said when decelerating with the third/forth method the problem of weakness of the Earth’s magnetic field would occur, therefore much time would be necessary for described method(s) to perform and give us result. However, we should note that in the beginning when the rod rotates very quickly this method would still operate strong enough. This derives from Faraday's law of induction stating that “the electromotive force generated is proportional ''to the rate of change of the magnetic flux''”. Therefore, in the beginning when the rod is rotating very quickly we can use the third/forth method(s) and when the rod significantly brakes we can apply to the first/fifth ones-they do not depend on Earth magnetic field. In other words, such approach would greatly help us in finding the golden mean between spending energy and time necessary for decelerating the rod. <br />
<br />
And finally: after releasing the payload the Space Catapult’s rod can actually give us energy. More precisely, the electro motor itself can serve as electric generator also since we know that the same machine can operate as electric motor if it is fed with electricity and as generator for electricity if its rotor is rotated by other machines. Therefore after releasing the payload when the electro motor’s rotor is rotating very quickly it can give us energy, in result of which the rod will lose its kinetic energy and speed, as for generated energy it can be sent downwards to the Earth for our terrestrial needs (see the next section in this paper) or stored onboard the Space Elevator’s counterweight. This approach has got one substantial advantage: it does not imply additional mass (wrapped wire) that will cause problems because rotating heavier rod would consume more energy.<br />
<br />
=Energy source placed on the Space Elevator’s counterweight=<br />
<br />
As well-known, the Space Elevator’s cabin needs energy when moving along the cable and it can get it from the Earth by means of various ways, such as: laser beam, microwaves, through the cable itself and etc. On the other hand, Space Catapult also needs much energy for rotating the rod and for this purpose some energy source should be placed on the Space Elevator’s counterweight, presumably solar panels array. Doing this would demand additional funding and engineering work and this undertaking should be justified, so how can we prove that placing energy source on the counterweight would be necessary and useful? We should not forget that the energy generally could be simply transmitted from the Earth without carrying any material for energy source on counterweight; so we can justify this undertaking if we declare/prove that: <br />
<br />
1. Energy source should be designed for ''both'' Space Elevator’s cabin and Space Catapult’s rod. We can imagine it as array of numerous solar panels producing enough energy for both above-mentioned constructions. For this purpose solar panels would be better solution than nuclear reactor because they do not need nuclear fuel to be carried from the Earth to counterweight, also they are capable for producing energy in a continuous mode. By the way this circumstance will enable us to send the payload to space by Space Catapult whenever we want without depending existence nuclear fuel at the counterweight. <br />
<br />
2. Transmitting energy from the counterweight (“from above”) is better and advantageous than doing the same thing from Earth (“from below”). Indeed, when we try to transmit energy (laser or microwave beam) from the Earth to ascending cabin, the part of energy is inevitably lost and dispersed in the Earth’s atmosphere and (this is point of the question) this continues during the whole process of ascent. On the contrary, when transmitting the energy from counterweight to cabin the energy will be lost only on the little part of this voyage, more specifically until the cabin leaves the atmosphere (100 km in height) and when cabin leaves it the energy will be transmitted in vacuum without loss. <br />
<br />
3. For receiving the energy from the Earth the huge solar panels (in case of laser beam) or antennas (in case of microwaves) will be needed to be mounted on the counterweight and this is additional mass and additional engineering work.<br />
<br />
We think that these arguments given above are enough for shoving that placing energy source on the Space Elevator’s counterweight have advantages over transmitting energy from the Earth and as conclusion we can state that energy source on counterweight would serve both space transportation systems-Space Elevator and Space catapult. <br />
<br />
As addition, we could use the energy produced on the counterweight for terrestrial needs also. Indeed, there have been developed numerous projects for receiving energy from space since 60-ies implying producing it by means of solar panels and then transmitting to the Earth. Combining all these three goals we can conclude that placing solar power plant on the Space Elevator’s counterweight would be triply useful and advantageous. In other words, when the Space Catapult and Space Elevator do not function, the energy produced on the counterweight should be directly transmitted to the Earth for our terrestrial needs and thus the idea of Space Elevator, Space Catapult and space power plant will be combined in one project.<br />
<br />
=Assembling the Space Catapult=<br />
<br />
Assembling in space such a huge structure as Space Catapult will not be an easy task from the technical point of view and definitely needs special engineering approach. Besides, we think that Space Catapult’s rod should be mounted at the Space Elevator’s counterweight separately from every other parts of the Space Catapult (e.g. electro motor and etc.); this circumstance is caused by rod’s gigantic sizes. More precisely, electric motor and plus any other equipments necessary for Space Catapult’s performance should be delivered to space by means of Space Elevator in a usual way; as for Space Catapult’s rod, it is a different matter and it should be delivered and mounted separately in the end. <br />
<br />
Eventually, Space Catapult’s rod will be quite long, perhaps much more than 100 kilometers. It is obvious that delivering such a long rod as ''one single unit'' would be quite difficult task; also it is possible that due to its total mass the Space Elevator’s cabin will not be able to deliver such rod at all, but we have already mentioned that the Space Catapult may have the rod with various length; more precisely the rod may consist of two/more parts. In such case these parts should be delivered towards the counterweight separately and then assembled. <br />
<br />
But the Space Elevator’s cabin can actually deliver the Space Catapult’s rod as ''one single unit'' in space. We think that this would depend only on rod’s mass. The Space Elevator’s lifting capacity is not well-known yet; however apparently it will not exceed one hundred metric tons and if Space Catapult’s rod is made of extra light material then cabin will be able to deliver it in space and in such case the following question will arise: how the cabin will deliver such a huge object in space without any damage?<br />
<br />
This can be done by means of two cabins. Generally, Space Elevator’s conception implies only one cabin moving along the cable, but for some special purpose (like delivering Space Catapult’s rod in space) we can use the second cabin also that will descend downwards after finishing its job and will not participate in Space Elevator’s further performance. As for the process of delivering the rod, we can imagine it in a following manner: at first the rod will be placed horizontally on the Earth (thus it must be manufactured and then transported to the Space Elevator’s base station), then the Space Elevator’s first cabin will carry rod’s one end along the cable while the rod’s second end will be moved on the Earth so that the rod to take more and more vertical position. When the rod is in vertical position the second cabin will capture rod’s second end and will carry it in space. We think that without the second cabin it would be quite difficult for one cabin only to carry long/heavy rod because the rod may actually shake and crash to the Space Elevator’s cable and this is absolutely undesirable. <br />
<br />
So, as we see in principle it looks to be quite easy, however the assembling may complicate due to rod’s length. In this case it would be better to carry not the rod as ''one single unit'' but its parts and then to assemble them in space in the following manner: ''two'' cabins will carry the first part as described above, when this part is delivered to space and temporarily hung at the cable the next two cabins will carry the second part that will be attached to the first one from below; the other parts will be delivered to space and assembled into the rod in the same way. <br />
<br />
The obvious disadvantage of the above-described method is that each part needs two cabins on the Space Elevator’s cable, besides the humans will be needed for assembling the rod from these parts in the atmosphere’s upper layers; therefore we think that the first way-delivering the rod into space as one single unit still would be easier and more realistic; besides we should take into consideration the fact that if the rod is assembled the additional devices will be needed ''on the rod itself'' for joining these parts and this circumstance would lead to increasing the rod’s total mass and this is undesirable. See the image showing assembling process:<br />
<br />
[[File: Assembling.jpg]] <br />
<br />
Whatever design/structure the rod has-assembled from several parts or as one single unit, it must be delivered to its destination-Space Elevator’s counterweight and must be fastened to electro motor’s own axis. But the problem is that the rod will be quite long and also the fact that Space Catapult’s electro motor will be placed at counterweight’s upper side (or at the ''lateral'' side if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), so it will be necessary the rod coming from below to be moved to counterweight’s upper/lateral side, besides the rod should be docked with electro motor’s axis as accurately as possible. How is it possible to realize such complex engineering operation? Here we can indicate one possible theoretical way: <br />
<br />
The rod will be parallel to Space Elevator’s cable when carried by cabin, but later the cabin’s mechanisms should rotate it so that the rod to be orthogonal to Space Elevator’s cable (this will not be necessary if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), exactly in this position the rod should be delivered to counterweight, besides the rod when moving along the cable should be shifted a bit upwards (relative to the Earth) than the cabin itself. Under such conditions we will easily achieve docking the rod to electro motor’s own axis which from its side should have some trapping device (magnetic for example) to “catch” the rod and thus guarantee docking the rod to electro motor and finishing assembling the Space Catapult as a whole. But if the rod’s plane of rotation is parallel to cable then assembling process will be much easier because the ascending rod may directly dock to electro motor’s own axis. See the image showing this process:<br />
<br />
[[File: Deliver - Copy.jpg]] <br />
<br />
We think that it would be useful if one Space Elevator is built specially for Space Catapult with its base station located on the land, not the ocean. This would be justified because transporting Space Catapult’s rod from its place of manufacture to Space Elevator’s base station should occur on the land by means of several transports simultaneously (due to rod’s great length), this will enable us to deliver the rod to its destination without any damage while this kind of operation is hardly possible on the water.<br />
<br />
=The technical aspects regarding the Space Catapult=<br />
<br />
As an example, we can try to calculate/ascertain all possible kinds of aspects regarding the rod with some certain mass and sizes, for example we can assume the Space Catapult has got 100 km length rod. <br />
<br />
The circumference of the circle that this rod’s end will draw in space will be equal to 2πr=628 km. As we have already mentioned payload’s abilities for withstanding the g-load is restricted, so if the electromotor rotates the rod so that payload’s speed is equal to 50 km/sec (this means that it will take 12.56 seconds for the rod to make one complete revolution), in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design the spacecraft that will withstand such acceleration, but what about the rod itself? Which material can be used for designing this rod, what will be its mass and how much energy and time will be needed for the rod to reach this velocity? <br />
<br />
For manufacturing the rod we should choose the material with very low density and highest value of strength. Currently, the ''Carbon nanotubes'' are the best candidates for this purpose. What will the mass of the rod made of this material? This depends on width also and it should be as less as possible (otherwise the rod will be too heavy and too wide for transporting from manufacture place to Space Elevator’s base station and for delivering it to space by means of Space Elevator) but from the other hand the ''applied load'' will not let us to design very narrow rod.<br />
<br />
Let’s assume that we intend to launch the payload with the mass of 10 000 kg (during calculation we will use ''SI system'' only). To clarify what kind of material will be able to withstand the acceleration we should calculate and then compare two values: the ''applied load'' and ''tensile strength''. For calculating the first one we should multiply g-load (which we already know-2 550 g) to its mass-10 000 kg, we will get 25 500 000. As for calculating tensile strength, we should take its values (for Carbon nanotubes it varies from 11 000 MPa to 63 000, we will take some medium value-40 000 MPa) and multiply it to cross-section’s area, in our case rod is cylinder with circular cross-section. If radius of cross-section is 1 meters then its area is 3.14 square meters, multiplying this value to value of tensile strength (40 GPa as said) we will get 125 600 000 000 and this is significantly more than value of applied load-25 500 000. Of course, we should also take into consideration ''factor of safety'' which is generally equal to 2 and this indicates us that for safety the payload’s actual mass should be twice less but in our case as we see the rod will be able to accelerate the payload to above-mentioned speed. By the way, note that if that g-load ''2 550 g'' is almost at the payload’s withstanding limit this is not serious problem for the rod itself (we have already seen that value of tensile strength is much more than value of applied load) and this is clear why: payload generally contains sophisticated equipments (electrical circuit, optics an etc.) that will not be able to withstand very high g-loads while the rod will be made of some continuous solid substance, Carbon nanotubes is this case and of course it will be able to withstand much higher g-loads.<br />
<br />
<br />
What will be the mass of such rod? Knowing its volume (for this purpose its cross-section’s area 3.14 square meters should be multiplied to rod’s length-100 000 meters, we get 314 000 cubic meters) and taking the value of density (this also varies for Carbon nanotubes from 0.037 to 1.34 g/cm<sup>3</sup>, let’s take 0.1 g/cm<sup>3</sup>) we get rod’s mass as 31 400 000 kilograms. This is too heavy for Space Elevator’s modern concepts and for improving this situation we should either use many cabins for raising the rod as single unit or use nuclear energy for feeding the cabins instead of laser/microwave beams or deliver the rod’s parts separately in space and then assemble them (see ''Assembling the Space Catapult''). But if some advanced substances are chosen for this purpose (for example ''Silica aerogel'' the density of which is about 1.9 mg/cm<sup>3</sup>, this is 50 times less than the density of the Carbon nanotubes taken above-0.1 g/cm<sup>3</sup>) than problem may be lightened in spite of the fact that their current tensile strength is quite low-16 kPa for the density of 0.1 g/cm<sup>3</sup> <sup>7</sup>. So, we can conclude that we need the material with the density of ''Aerogels'' and tensile strength of Carbon nanotubes.<br />
<br />
How much energy and time will be needed for the rod to accelerate from zero to desired speed-50 km/sec? The amount of rotational energy of the rotating rod can be calculated by the following formula:<br />
Kinetic Energy<sub>rotational</sub>= (1/2)*I*ω2 <br />
<br />
Where:<br />
<br />
'''I'''=moment of inertia <br />
<br />
'''ω'''=angular velocity<br />
<br />
"I" depends on the shape of the mass under rotation. In the case of a uniform rod rotating from its end (axis of rotation is at the end of the rod) I = (m*L2)/3<br />
<br />
<br />
“ω” = V/R, where V = tangential velocity and R = radius<br />
<br />
In our case ''moment of inertia'' is equal to (31 400 000 kg*100 000 m2)/3=104 666 666 666 666 666<br />
ω is equal to (50 000 m/sec)/100 000 m=0.5<br />
<br />
So, Kinetic Energy<sub>rotational</sub>=(1/2)*104 666 666 666 666 666*(0.52)= 13 083 333 333 333 333.25 Joules<br />
<br />
Now, how much time and what amount of solar panels will be needed for accelerating this rod? The amount of Solar constant near the Earth is approximately equal to 1300 W/m2 [<sup>8</sup>], with assuming that ''coefficient of efficiency'' of solar panels is roughly 20 % we get 260 Watts per square meters and we can easily link amount energy (that we have already calculated) and power with the time needed. Particularly, ''Energy'' is equal to ''Power''’s multiplication to ''Time'':<br />
<br />
[[File: Formula - Copy.jpg]] <br />
<br />
So, Time is equal to 13 083 333 333 333 333.25 Joules/260 Watts=50320512820512.8 seconds, or 1 595 652 years. If we take much more area for solar panels, for example 10 millions square meters then 0.1595652 years or approximately 58 days will be needed and we think that this is acceptable time span.<br />
<br />
Actually, the time and energy will be needed a bit more for overcoming static friction in electro motor, for overcoming the rarified atmosphere’s resistance (we know that there no absolute vacuum in space), also we should take into consideration electric motors’ coefficient of efficiency that generally reaches 90-95 %, so some energy loss will occur here also. <br />
<br />
Now, what will be the total mass of solar panels producing the energy for Space Catapult? This depends on mass/power ratio, in near future it is expected that very lightweight designs could likely achieve 1 kg/kW [<sup>8</sup>] or 0.260 kg/ 260 W (per 1 square meter), so if for rotating the Space Catapult 10 millions square meters of solar panels are used then their total mass would be equal to 2 600 000 kg. We think that it is too heavy for Space Elevator the mass of which is expected to be equal around several hundred metric tons. If so, we will have to use fewer amounts of solar panels and therefore increase the time needed for accelerating the payload’s speed from zero to designed one. This will not make problems if the rod is accelerated only once and then keeps its constant rotation-for this purpose less energy will be needed and the payload will have to reach the rod’s end by first method as described earlier in this paper (see ''Rod’s plane of rotation towards the Earth'').<br />
<br />
We also need to take into consideration the value of deflection when the rod will be delivered to space by means of Space Elevator (see ''Assembling the Space Catapult''), in this case the thin and long rod will be bent due to its own weight and here we will try to calculate its value. This is quite complex problem that apparently cannot have an unambiguous solution because of many reasons, for example due to various temperatures in atmosphere’s different layers, various humidity and possible wind, but still we will try to calculate the value of ''Deflection'' that will occur in case when the rod’s one end is fastened to Space Elevator’s ascending cabin and the second end is fastened to the transport moving on the land, we discussed this option in above-mentioned section of our paper (see ''Assembling the Space Catapult''). The inclination angle for the rod will vary from 0º (rod is transported horizontally on the ground) to 90º (Space Elevator’s cabins are carrying the rod to space) and here we will discuss some medium case when the rod is semi-elevated in the air, when the angle between rod and ground/cable is equal to 45º. On the engineers’ ''eFunda'' web-site there is online calculator that enables to receive the value of ''Deflection'' (actually that site gives different term for this-''Displacement'') [10]:<br />
<br />
Here we need to enter the relevant values:<br />
<br />
''Length of beam'', ''L'': 100 000 meters<br />
<br />
''Line pressure load on beam'', p: In our case this is the weight per meter length. As we have already mentioned the radius of the rod’s cross-section is 1 meter, so the volume of rod’s 1 meter-length part will be 3.14 cubic meter. In case of using Carbon nanotubes with above-mentioned density-0.1 g/cm<sup>3</sup> the weight will be equal to 314 kg or 3 079 Newton. Since we have got the inclination of 45º we should multiply this value to cos45º- 0.707, so we get 2176 N/m.<br />
<br />
''Young's Modulus'', ''E'': This is equal to 1 000 GPa for Carbon nanotubes [11] <br />
<br />
''Distance from neutral axis to extreme fibers'', ''c'': In our case it is equal to the radius of the rod-1 meter<br />
<br />
''Moment of Inertia'', ''I'': It is equal to (pi*r<sup>4</sup>)/4, so it is equal to 0.785<br />
<br />
According to these initial data the calculator returns extremely high value of Deflection, much higher than the length of the rod itself: -3.61 × 10<sup>9</sup> meters. This result shows us that with the current materials (Carbon nanotubes in our case) it is impossible to raise the rod as ''one single unit'' to space by means of Space Elevator and we need other materials with less density and more ''Young's Modulus'' (or the rod should be much thicker but this will lead to increasing its mass). Therefore, we have got two options: either we should deliver the parts of that rod and then assemble them in space (we have already discussed this option) or completely different technologies for manufacturing the rod should be developed. Particularly, it would be very good if it was possible to manufacture the rod ''in continuous mode'' in vertical position and then uninterruptedly directly to carry it to space by means of Space Elevator’s cabins. Under such approach there will be no ''Deflection'' and several cabins will be able to deliver the rod in space. <br />
<br />
One note about transporting the rod from its place of manufacture to Space Elevator’s base station. We think that this process should be executed by many transports, in other words we are convinced that if the rod is carried by two trains only (or any other kind of transport) then the rod will continuously touch the ground since the ''Deflection'' occurs in any position-horizontal, inclined or vertical and this circumstance will lead to its damage, that’s why several transports will be needed to hold the rod at as many places as possible.<br />
<br />
=Stabilizing the counterweight=<br />
Stabilizing the Space Elevator’s counterweight is very important question during Space Catapult’s performance. Indeed, when the rod rotates it makes the imaginary circles in space and due to rod’s and payload’s masses the Space Catapult’s ''center of mass'' will be continuously shifted and if the counterweight is not somehow stabilized then it will make problems for accurate aiming to certain point at the celestial sphere. Also, if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable then there will be the danger that the rod may actually hit the cable and cut it. To avoid these problems we need to apply to serious measurements. <br />
<br />
First of all, the electro motor’s own axis can be quite long and this will diminish the chance to failure of the whole system. Actually, we are convinced that counterweight’s (where the electric motor will be placed) size will be quite large, mainly due to solar panels’ sizes and amount (this issue was discussed above), also the electromotor should be quite large and powerful to rotate the rod, and hence there will be enough distance between the rod and Space Elevator’s cable. <br />
<br />
The second serious problem is that the center of gravity of the system is not at the center of rotation, therefore it will be necessary to balance the rotating system when the payload is attached and when it is released.<br />
<br />
We think that the Space Catapult’s rod should not be deployed/directed to one side only but some counterweight of it should also exist. This is necessary since the unilaterally loaded (we mean the rod itself plus payload) rod will cause the counterweight to somersault. In other words, the rod should extend to other side and the ''moments of inertia'' of both sides should be the same as during rotating the rod as after releasing the payload when the rod still rotates. This is easily achievable if some additional, second payload is placed on the rod’s second end. Therefore, the Space Catapult will launch two payloads at the same time to the ''opposite'' directions but at various speeds if the second part/side of the rod is shorter.<br />
<br />
How the second payload should be placed on the rod and should we really send two payloads? Until we have got balanced rod this problem does not arise but as soon as the Space Catapult releases the payload this balance will be violated, how it can be restored? There are two theoretical ways for achieving this: reducing the ''mass'' or reducing the ''length''-with diminishing either one of them the ''moment of inertia'' will be decreased. We think that reducing the mass will be less practicable since this would require placing the second payload (spacecraft or anything else) on the rod’s second part and this cannot be done from the Space Elevator’s cabin-this is the easiest way for delivering the payload from Earth to Space Catapult’s rod; so we would have to (see ''Rod’s plane of rotation towards the Earth'') put the second payload on the electro motor and then send it rod’s second part’s end. This is quite complicated task; therefore we can apply to second approach-put some sliding object that will immediately move to electromotor as soon as the spacecraft is released.<br />
<br />
[[File: MOI.jpg]] <br />
<br />
The next problem that may occur is that when the electro motor rotates the rod this motion will make the Space Elevator to rotate to the opposite direction. The same problem arises when helicopter’s primary blade’s rotation forces the helicopter to rotate to opposite direction and this possible rotation is annulled by ''tail rotor''. We think that for balancing the counterweight the additional motor and rod should be installed and this rod should rotate to opposite direction and if their ''angular momentums'' are equal to each other, then their rotations will cancel each other. More precisely, the following equation should be fulfilled:<br />
<br />
[[File: Angular momentum.png]] <br />
<br />
Where ''m'' is mass of the rod, ''v'' is angular speed and ''L'' is rod’s length, the numbers ''1'' and ''2'' refer to first and second rods correspondingly. For balancing both rods’ rotation the multiplication at both sides of the counterweight should be equal, by the way this circumstance enables us to use the second rod with shorter length and even with less mass but rotating at more angular velocity.<br />
<br />
Such approach will effectively deal with other problem which will arise when the Space Catapult releases the payload(s), at this moment the second motor should instantly diminish its angular velocity to some certain level (an ordinary mechanical brakes could be used for this purpose), in this case ''angular momentums'' for both motors/rods will be equal again and Space Elevator’s counterweight will maintain its attitude in space. See the image below depicting the Space Catapult with two electro motors and rods:<br />
<br />
[[File: Two-rods.jpg]] <br />
<br />
Such approach will justify itself if rod’s plane of rotation is parallel to Space Elevator’s cable, but if this plane is orthogonal to cable (see ''Rod’s plane of rotation towards the Earth'') then the second/balancing electromotor cannot be placed under the counterweight because the cable will be cut when rod touches it. Therefore a bit different approach should used and we need to install two/four/eight electro motors with their own relatively shorter rods rotating to opposite direction. They should be placed at the counterweight’s lower side and on its edge (as we suppose the counterweight should be disc) so that their rods not to touch and cut Space Elevator’s cable. Also, total a''ngular momentums'' from these motors should be equal to the ''angular momentum'' from upper motor and thus the counterweight will not rotate and the Space Elevator’s cable will not be twisted. This situation is presented below:<br />
<br />
[[File: Modified-2.jpg]] <br />
<br />
We think that the array of gyroscopes would be also very useful to be installed at the counterweight since they can maintain the attitude of the whole system and this is important for precise aiming to certain point at the celestial sphere. As for the energy required for gyroscopes’ performance it could be received from the array of solar panels which as a result will generally serve Space Catapult’s precise performance.<br />
<br />
=Space Catapult placed at Lagrangian points-the way for gaining subluminal speeds=<br />
<br />
In our paper we discussed the Space Catapult based on the Space Elevator’s counterweight and concluded that this would be convenient when we intend to deliver the payload to space from the Earth. However, such Space Catapult cannot gain very high speeds and therefore we need to choose other way. It is obvious that we need to keep rod’s plane of rotation orthogonally relative to the ''Earth-Sun connecting line'' and hence we should place the rod on the celestial body which will be in synchronous rotation with the Sun but since there is no such body in the solar system we conclude that the Space Catapult for subluminal speeds (the speeds close to speed of light are in mind) should be placed at such point near the Earth where it will be easy to reach it from our planet and where the rotating rod will not hit the Earth and will be always at the same distance from the Sun to avoid the influence of its tidal forces. The examples of such places are '''Lagrangian''' L<sub>1</sub> and/or L<sub>2</sub> points at 1.5 million km away from the Earth. If the Space Catapult is placed at one of these points then its rod can be always orthogonal to the Sun in principle, at the same time it will never collide with the Earth and also it will be quite close to the Earth since 1.5 million km distance is very negligible in space.<br />
<br />
We have got several notes regarding such approach. First, when we mentioned that the rod’s various parts can be at the same distance from the Sun this strictly speaking is not very true because the Sun can be referred as little point where its gravity “comes out” from while the rod is quite long and its initial part (placed at one of the Lagrangian points) will be attracted stronger than the utmost one (for equal attracting the rod should the arc ''with the same curviness as Sun’s surface'' and not straight line); but still this is better than to direct the rod exactly towards the Sun where the tidal forces will try to tear the rod. Second, the Space Catapult should be placed at Lagrangian L1 point which is closer to the Sun than L2 one and therefore receives by 4 % more energy per area from the Sun. Third, the rod should be in constant rotation, this requires much less energy than accelerating it from zero, then stopping it and accelerating it again. Fourth, the existence of the asteroid belt in the solar system between Mars and Jupiter will somehow restrict the actual length of the rod. Indeed, the Space Catapult should be placed at one of the Lagrangian points at 1 AU distance from the Sun while asteroid belt approximately lays at 2.7 AU, from the simple geometry it is obvious that the length of the rod ''almost reaching'' the asteroid belt can be approximately equal to 390 million km, and if the rod is longer then it may simply hit any asteroid within that belt. For 390 million km length rod and for 100 000 m/sec2 acceleration at rod’s end (where the payload will be attached) the maximal speed that the spacecraft can gain will be approximately equal to 200 000 km/sec (two thirds of the speed of light) and this can be considered as enough for practical interstellar spaceflight. Fifth, the spacecraft should be directly put on the rotating rod’s initial end (near electromotor) and then slide towards the other end with its own rocket engines. To achieve this, the spacecraft will have to cover relatively less distance on the rod and then rod’s circular motion will accelerate the spacecraft further-we have already mentioned this in this paper when speaking about deploying the Lunar Space Catapult. This action-putting the spacecraft on the rod will not be difficult since rod’s angular velocity will be quite low due to rod’s huge length, particularly for 400 million km length rod and for 200 000 km/sec linear speed the rod’s angular velocity will be 0.0000796 revolutions/sec.<br />
<br />
[[File: Lagrangian-point.jpg]] <br />
<br />
We have already mentioned that to avoid the destructive influence of the Sun’s tidal forces the rod’s plane of rotation should be orthogonal to the Earth-Sun connecting line. By the way, note that under such approach we may have to wait one year until the Lagrangian Space Catapult occupies the relevant position towards the certain point at the celestial sphere where the spacecraft should be sent to. But from the other hand it would be useful if it is feasible to rotate this whole structure around the imaginary axis directed towards the ''ecliptic poles'' (depicted as faint green dash line on the image above), the reason if this is the possible danger when the rotating rod may hit Mars or asteroids that orbit around the Sun closer than 2.7 AU distance (for example ''433 Eros'' or ''1036 Ganymed''), hence for avoiding such undesired collision the Lagrangian Space Catapult should be slightly rotated by several degrees clockwise/counterclockwise so that the rod not to collide with any celestial object. We are convinced that rotation by several degrees will be absolutely enough measurement due to rod’s gigantic length and relatively less sizes of the celestial objects in the solar system.<br />
<br />
The next issue that we should discuss refers to stability of the Lagrangian Space Catapult placed at L<sub>1</sub> point. As we see this structure will have enormously gigantic size while the Lagrangian point is relatively little mathematical one in space, so what can be done to be convinced that this structure will remain at that point and do not shift aside? The body placed at one of the Lagrangian points is affected by other celestial objects’ gravity and therefore for achieving the balance the rod needs to have the counterweight with more mass if it (counterweight) is shorter. As we clearly see the rod needs the counterweight for two reasons: not to let the Space Catapult somersault and for maintaining it at the L1 point. We think that it would be very useful if the arrays of solar panels act as counterweight since exactly they can give us energy for rotating the rod. Also, we need the second, shorter, perhaps less massive but faster-rotating rod (again-solar panel arrays) the opposite rotation of which would cancel first rod’s rotation, this issue was discussed in this paper. These arrays of solar panels are depicted on the image shown above. <br />
<br />
How such a gigantic structure as Lagrangian Space Catapult can be assembled in space? In our paper we discussed the possible ways for delivering the rod from the Earth to the Space Elevator’s counterweight, now we will try to show that it is possible ''in principle'' to assemble the extra-long rod in space. <br />
<br />
If it is possible from the technical point of view to manufacture extra-long rod then we can use this approach and make 1.5 million km length rod (this is the distance between the Earth and Lagrangian L<sub>1</sub>/L<sub>2</sub> point) that will be mechanically directed to the base station at L<sub>1</sub> point. The capturing devices there will catch the rod and attach it to the electro motor’s shaft after which the rod should be spun by 90º so that it to be orthogonal to Earth-Sun connecting line (for this purpose the additional mechanisms will be needed), this spin is necessary because L<sub>1</sub> point is located on the Earth-Sun connecting line (that is towards the Sun if we look from the Earth) and when directing the rod from the Moon it will lay ''along'' this line while we need across. After this the rod should be slid to another side and then the next rod should be directed to the Lagrangian Space Catapult where it will be attached to the previous rod and etc. In other words, the extra-long rod will be assembled from one side and its length will “grow” from this side to other one, this is necessary because the distance between Moon (the rod should be manufactured exactly there and not on the Earth due to our planet’s relatively more gravity, atmosphere and problematic space debris belt around it) and L<sub>1</sub> point is constant and rod’s parts cannot be more. Due to whole rod’s and its parts’ lengths (400 million and 1.5 million km correspondingly) we think that about 260-270 such operations will be needed to finish assembling the rod (400/1.5). The process of assembling the Lagrangian Space Catapult is shown on the image below:<br />
<br />
[[File: Lagrangian-point-assemble.jpg]]<br />
<br />
=Conclusion=<br />
<br />
As we have seen, for leaving the Solar system and reaching the remote celestial bodies (stars, nebulas) there is no need to develop advanced and complicated technologies that mostly are not capable for gaining extra high velocities nevertheless. In any case, until the Space Elevator is really built (scheduled for construction by 2031) we have got much time for developing the idea of Space Catapult in technical aspect, like finding appropriate materials for the rod, perfect the ways how the Space Catapult can be assembled in space and etc. The concept of Space Catapult itself is the easiest one, does not need developing neither complex and sophisticated technologies, nor some exotic methods (such as ''Gravitoelectromagnetic toroidal launchers'', ''Antimatter rocket'' and etc.) and can be easily implemented in near future; in other words the Space Catapult is not some sophisticated structure that would need profound science research and the fact that it will enable us to gain whatever high speed will justify its developing and building by the humankind. As for other technologies like Ion Drive, they could be used by the spacecraft during flight for other purposes, for example for correcting/changing the flight direction.<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Space_Elevator<br />
<br />
2. http://www.isec.info/index.php?option=com_content&view=article&id=14&Itemid=9<br />
<br />
3. http://www.space-track.org/perl/geo_report.pl (provided data updates regularly, registering is needed) <br />
<br />
4. http://www.oosa.unvienna.org/pdf/reports/ac105/AC105_720E.pdf page 24 (data as at 21 August, 1997) <br />
<br />
5. http://www.amostech.com/ssw/presentations/Session7/S7-1Molotov.pdf page 16<br />
<br />
6. http://www.esa.int/SPECIALS/ESOC/SEMN2VM5NDF_mg_1_s_b.html <br />
<br />
7. http://eetd.lbl.gov/ecs/aerogels/sa-physical.html<br />
<br />
8. http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant<br />
<br />
9. http://www.you.com.au/news/2005.htm, http://www.spacedaily.com/news/ssp-03b.html<br />
<br />
10. http://www.efunda.com/formulae/solid_mechanics/beams/casestudy_display.cfm?case=simple_uniformload<br />
<br />
11. http://en.wikipedia.org/wiki/Young%27s_modulus<br />
<br />
<br />
'''Appendix''': <br />
<br />
Animation illustrating the payload’s departure from the Lagrangian Space Catapult:<br />
[[File: Lagrangian-point-animation.gif]]</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_5&diff=3669OpenSpace 52013-09-21T13:00:45Z<p>Eagle9: /* INTRODUCTION */</p>
<hr />
<div>== '''Space Catapult''' ==<br />
<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
=INTRODUCTION=<br />
<br />
<br />
The new method for sending the spacecrafts in deep space is presented here. The paper describes the long rod rotated by electro motor placed at the Space Elevator’s counterweight and at Lagrangian points. This simple structure will enable the rod to gain high velocity and carry the payload with it. After reaching the desired speed the rod will release the payload that will fly in space along the imaginary circle’s tangent. This structure we called Space Catapult and it should work with the assist of Space Elevator. This latter should be used for carrying the payload from the Earth to Space Catapult’s rod.<br />
<br />
For exploring the outer space the humankind generally uses the rocket engines, mostly chemical-propelled ones. They enable us the explore near-Earth celestial bodies and other planets in the solar system. They even enabled us to send several deep space missions beyond the solar system such as '''Pioneer-10''', '''Pioneer-11''', '''Voyager-1''', '''Voyager-2''', however by means of this technology the flight lasts undesirably long and it seems to be impossible to reach remote celestial bodies in space such as stars, so new technologies are necessary for this purpose. However new technologies do not necessary imply new kind of rocket engines, such as ''Ion Drives'' because they are capable for gaining several ten times higher speeds only, but for remote celestial bodies even they are not suitable. Besides, they need a huge amount of energy to be stored onboard the spacecraft and this will make additional problems. So, high speed should be achieved with absolutely different approach. How this can be done?<br />
<br />
High speed can be easily achieved by means of fast-rotating rod around the electric motor. The motor’s rotational speed can be very high; the rod also can be quite long, hence the rod’s end’s linear speed can be extremely high, absolutely unachievable for any other technologies nowadays. The payload should be fastened at the rod’s end where the linear speed generally reaches maximal value. After reaching the necessary speed the rod will release the payload that will fly along the tangent from the current position. Thus the electric energy can be turned into payload’s speed and its velocity could be as high as we wish (except the ''speed of light'' of course). In principle the '''Space Catapult''' (thus we call this structure) would be the simplest, the most convenient and direct way for converting the energy/electricity into speed and conveying it to payload. <br />
<br />
As we see the Space Catapult is quite uncomplicated structure, however if we wish to gain high speeds we should deploy it in space, not on the Earth. Indeed, our planet is surrounded with dense atmosphere that impedes any quick motion, so if we rotate the rod quickly the atmospheric drag and generated heat would burn it very soon, therefore the Space Catapult should be built and deployed in space only, and as we suppose-at the Space Elevator’s counterweight. In other words, the Space Elevator’s counterweight will operate as Space Catapult. See image below:<br />
[[File:Space-catapult.jpg]]<br />
Generally, what is the Space Elevator ['''1''']['''2''']? According to modern concepts it will be the tall vertical structure built on equator and will have height of several ten thousand kilometers with its thin cable fastened to the base station on the Earth and with counterweight placed higher geostationary orbit. Because of balance between centrifugal force and gravity this structure will be stretched and the cabin will move along its cable carrying the goods into high orbit. After delivering the payload, the cabin will descend and carry the next one.<br />
In Space Elevator’s concepts several solutions have been proposed to act as a counterweight: <br />
<br />
1. Heavy, captured asteroid <br />
<br />
2. Space dock, space station or spaceport positioned past geostationary orbit <br />
<br />
3. Extension of the cable itself far beyond geostationary orbit. <br />
<br />
The third idea has gained more support in recent years due to the relative simplicity of the task and the fact that a payload that went to the end of the counterweight-cable would acquire considerable velocity relative to the Earth, allowing it to be launched into interplanetary space. However this idea cannot be completely shared by us due to following reason: <br />
<br />
It is well-known that the values of both '''Orbital''' and '''Escape Velocities''' decreases with increasing the altitude while the '''tangential velocity''' of Space Elevator’s cable increases. We can see the differences between them from the chart presented below:<br />
[[Image: Cxrili.gif]]<br />
<br />
As we see from this chart the ''tangential velocity'' of the Space Elevator even at its end (144 000 or 200 000 km altitude) is not very high to decrease the necessary time for covering the distance from the Earth to remote celestial bodies significantly. To achieve this, even the longer Space Elevator would be needed (its ''tangential velocity'' is directly proportional to its length) and this circumstance would complicate the technical task for building such Space Elevator. Because of this, there is no necessity to extend the cable itself far beyond geostationary orbit as proposed in the third variant. In any case, we have already seen that by means of Space Catapult it is possible to gain such huge velocities that are absolutely unachievable with other technologies, for example with Space Elevator. Therefore, using the counterweight and placing the Space Catapult there definitely has got some technical sense. <br />
<br />
However, we think that the question where the Space Catapult should be placed needs further discussion. Theoretically, the Space Catapult with its payload and nuclear reactor/solar panel needed for rotating the rod may be mounted not only at the counterweight, but on the Space Elevator’s cabin also that can carry all these goods to space in a usual way, as it should do it according to Space Elevator’s modern concepts. This option is quite possible, however for realizing this we need to know the mass of the payload, nuclear reactor/solar panels’ mass plus Space Catapult’s mass from one hand and Space Elevator’s lifting capacity (this ''must'' be more) from other hand, but these data are not available nowadays, therefore we think that the Space Catapult should be still mounted at the Space Elevator’s counterweight where it will be possible to send the payloads into deep space in ''continuous mode'' at high velocities.<br />
<br />
As we saw the Space Catapult is capable to gain very high velocities; however there is being developed other technologies and they in future will enable the spacecraft to fly at high speeds in space. These are Ion Drive systems, more precisely the most perspective one-''Variable Specific Impulse Magnetoplasma Rocket'' (VASIMR) which still under development can be used in future for deep space missions. Can these engines and Space Catapult be the rivals in space? Since none of them have been built and used in space yet we cannot give a persuasive answer to this question; however still it is possible to underline Space Catapult’s one significant advantage: if the future spacecraft uses the VASIMR (or any other kind of Ion Drive) engine it will definitely need to be equipped with nuclear reactor, otherwise the spacecraft will not be able to gain high speeds, also it will need to carry fuel tanks for this purpose. As for the Space Catapult, it can give much higher speed to spacecraft, besides it will have ''stationery'' power plant (see ''Energy source placed on the Space Elevator’s counterweight'') at the Space Elevator’s counterweight, so the payload will ''not'' have to carry the nuclear reactor onboard and this circumstance will lighten the work for deep space spacecraft. Besides, we should not forget that unlike the spacecrafts equipped with ion drive engines the Space Catapult will need no fuel for gaining high velocities. <br />
<br />
Briefly, Space Catapult’s advantages over any kind of propulsion systems are: <br />
<br />
1. Ability to gain any speed that is absolutely unachievable by means of other kinds of engines. <br />
<br />
2. No need by spacecraft to carry energy source that would make it too heavy and impracticable.<br />
<br />
=The Space Catapult needs long rod=<br />
<br />
When building the Space Catapult at Space Elevator’s counterweight we should install quite long rod there, the shorter the rod is, the easier would be installing it, however we should note that rod cannot be extremely short, let’s say 1 km length or so due to following reason:<br />
<br />
When we are going to send some payload into space, we need not only high velocity, but one certain direction also. The little inaccuracy in direction, inclination in several arcminutes is actually acceptable since the spacecraft would easily balance it with its engines; however great inclination from the initial direction would send the spacecraft into the completely different direction and in such case the whole mission will fail.<br />
<br />
If two Space Catapult’s rods have the length of let’s say 1 kilometer and 10 kilometers, then for giving to payload some certain linear speed (for instance 100 km/sec) these rods should rotate at different angular velocity. It is easy to ascertain that the shorter rod should rotate 10 times faster to gain the same linear speed than the rod with more length. But the faster the rod rotates, the more difficult will be to “catch” the needed moment for releasing the payload from the rod for sending it towards some certain direction. If the rod is too short, then it has to rotate very quickly for gaining some certain linear speed and therefore it will be extremely difficult catching the needed moment for releasing the payload. Hence, too short rod can make problem for sending the payload to some certain direction in space especially at high velocities. So, based on payload’s needed velocity we should find rod’s desired, minimal length that will enable us to send the payload in space to necessary direction without fear that it may yaw from the course. <br />
<br />
However, rod’s length will be crucial for payload’s abilities for withstanding the acceleration also. As an example, we can try to calculate its value which the payload will have to withstand during rod’s rotation. The acceleration of the body rotating at the circle with some constant velocity is calculated by the following formula:<br />
<br />
[[File: Acceleration - Copy.jpg]] <br />
<br />
Where a is acceleration in ''m/sec''<sup>2</sup>, ''v'' is payload’s linear velocity on the circle in ''m/sec'' and ''r'' is radius of the circle in ''meters'', in our case it is equal to rod’s length. Let’s assume that the rod is 100 km length and the electromotor rotates it so that payload’s speed is equal to 50 km/sec, in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design and manufacture the spacecraft’s subsystems (avionic and etc.) capable to withstand such acceleration. This circumstance somehow restricts the speeds that we can achieve, in any case their values actually depends on spacecrafts’ abilities for withstanding g-loads. But what can we do if much higher speeds are needed? The answer directly derives from that formula: the radius should be more; by the way note that this is additional reason why the longer rod is more useful. If we are able to make the extra long rod, then this will enable us to gain much higher velocities. <br />
<br />
What material should be used for manufacturing the rod? It is obvious that if very high speeds are needed the rod should be long and even in this case the acceleration at its end will be quite high, therefore ''sufficiently strong and light materials'' are needed for this purpose and making them is as similar challenge as in case of Space Elevator where the same requirements arises for the cable’s material. The lightness is needed because in case of heavy rod a lot of energy will be needed to rotate it; the strength is needed because in case of lack this property the rod will be destroyed due to great acceleration.<br />
<br />
=The mechanism for holding and releasing the payload=<br />
<br />
How the payload can be held by Space Catapult’s rod during rotation and how it can be released from the rod? We think that using ''electromagnet plus mechanical holding devices'' would be a good solution. More precisely, after the payload is attached to the rod it must be held by means of both methods until the rod accelerates and reaches necessary velocity (it may take even several days), but with approaching the desired speed the mechanical device should release the payload however the electromagnet(s) should still hold it. The explanation of such approach is following: generally the mechanical devices are much slower/sluggish in performance than electronic ones. We have already said that when releasing the payload the extreme accuracy is needed and mechanical devices cannot guarantee ''the exact time of releasing'' the payload unlike electronic ones. That is, it’s unlikely that mechanical devices can release the payload at some certain moment when needed while in case of electromagnet it would be enough to cease electric current there, it would lead to immediate vanishing of the magnetic field and sending the payload along the tangent from the point where the payload would be at the current moment. <br />
<br />
<br />
We think that the ''fastest control system'' would enable to release the payload to certain direction. This system (extremely fast-operating computer plus measuring equipments) should know the current position of the rod’s end, the current speed, the needed direction and be capable for computing the necessary moment for giving the order for diminishing the voltage for electromagnets and hence releasing the payload to desired direction and velocity.<br />
<br />
=Rod’s plane of rotation towards the Earth=<br />
<br />
The Space Catapult’s rod when rotating makes the circular plane/flatness in space and this plane may be horizontal/parallel to Earth surface, that is making the right angle to Space Elevator’s cable or it may be placed along the cable; see the both possible situations here:<br />
<br />
[[File: Planes-of-rotation - Copy.jpg]] <br />
<br />
Both approaches have got their advantages/disadvantages and here we will discuss this question, first of all from the point of view of safety.<br />
<br />
For gaining extremely high velocities quite long rod would be needed, maybe with the length of several thousand kilometers or even more. If such rod is placed ''along'' the Space Elevator’s cable then the rod during rotation will cross many orbits from the ''Medium Earth Orbit'' to ''High'' ones. When rotating, the rod may actually hit any satellite and/or space debris object and such collision can lead to rod’s complete destruction; therefore we should choose such plane which would be much more free from any artificial objects; hence if the rod rotates ''horizontally/parallel'' to Earth’s surface at high enough altitude where the satellites’ population is relatively low then this measurement would justify itself because under such circumstance the rod will not cross satellites’ orbits (rod’s plane of rotation will simply coincide to ''one'' orbit’s path). However, we should also note that this altitude actually depends on the Space Elevator’s proposed length. Indeed, the Space Catapult’s rod should be mounted at the Space Elevator’s counterweight; this counterweight from its side should be placed at the end of the Space Elevator at such altitude where the satellites’ population is as low as possible. This means that Space Elevator’s proposed height should be agreed with mounting Space Catapult on its counterweight. According to various databases the number of man-made objects at high orbits, more precisely beyond geostationary orbit is much less than on the lower orbits <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup>, therefore the Space Catapult with its rod should be located at the altitude of 50 000-60 000 km above the sea level. At such altitude the space is almost free and nothing will impede rod’s rapid rotation. Besides, the satellites at high orbits are orbiting around the Earth slower than on the lower orbits (as known any satellite orbits around its primary body slower in apogee than in perigee), therefore if some tracking system is mounted at Space Elevator’s counterweight then it will enable the Space Catapult to avoid undesired collision with satellites during Space Catapult’s performance. In other words, the Space Catapult should operate only when the there are no satellites near its vicinities.<br />
<br />
Now we will try to discuss this question from other side.<br />
<br />
How the payload can be transferred from the Space Elevator’s cabin to the Space Catapult’s rod? One way is following: cabin reaches the counterweight where the payload will be released, then payload will be mechanically conveyed to rod, continues its way ''on the rod'' (like the train rides on the rails) and after reaching rod’s end it stops, the rod begins rotating and after gaining necessary linear speed it releases the payload to needed direction. This method is generally realizable; however it seems to be too complicated and unpromising compare to the second one: the Space Catapult’s rod is stopped in space so that it to be directed downwards to the Earth and be parallel to Space Elevator’s cable. The Space Elevator’s cabin moving along the cable with payload stops at the cable ''near'' the end of the Space Catapult’s rod and releases the payload that will fly to the rod, attaches itself to the rod’s end (here the electromagnets would be useful), the rod begins rotating and after gaining needed linear speed will release the payload to necessary direction.<br />
<br />
This second way seems to be more promising because the first one is much more complicated as we have already said: first of all there would be needed some mechanical devices for transferring the payload from the Space Elevator’s cabin to counterweight, the counterweight should have the hole for the payload to move through it from below (we should not forget that the Space Catapult should be mounted ''at'' the counterweight, not ''beneath'' it), besides the rod should be made so that it to have some conveying surface (rails for instance) the payload to move on it. As we see it would be much more convenient if it is possible to convey the payload from the cabin to the rod directly and this would be feasible under the second method which is depicted below:<br />
<br />
[[File: Convey.jpg]] <br />
<br />
One more aspect regarding Space Catapult’s position. This structure, its rod, its electro motor and etc should be mounted at Space Elevator’s counterweight so that the rod to be placed westwards from the cable. The reason of it is following: when the Space Elevator’s cabin stops and releases the payload (which should fly to Space Catapult’s rod) the current speed of which will/should be more than the value of the ''Orbital/Escape Velocity'' at the current altitude. After releasing the payload will fly westwards and upwards because its orbit will be ellipse, under ellipse the payload will fly higher to apogee and at the speed less than Space Elevator’s current speed at the given altitude, in other words the released payload will “lag behind” the Space Elevator’s cable; therefore payloads’ ''stopping points'' at the cable and Space Catapult’s rod’s length should be calculated and chosen so that the payload to fly directly towards rod’s end. This process would be feasible in both cases-if the rod’s plane of rotation is parallel to Earth’s surface and if it is placed along the cable-but still this would be easier for the payload to achieve the rod’s end if the rod is placed along the cable because at least the distance that the payload should cover in space will be less.<br />
<br />
The length of the Space Catapult’s rod placed at the Space Elevator’s counterweight might vary since for various spaceflight purposes different initial speed will be needed and relatively low speed could be achieved by means of shorter rod. Because of this reason it might be necessary to change Space Catapult’s rod’s length, therefore it would be useful if the rod consists of two parts where the first part would be perpetually attached to electro motor and the second one will be attached to the first part if necessary. For this operation Space Catapult’s rod should be placed along the cable since the relative nearness would make this operation quite easy and it could be accomplished by the crew directly from the Space Elevator’s cabin stopped at the needed altitude. <br />
<br />
For deciding the question how the Space Catapult’s rod should be placed towards the Space Elevator’s cable we should take into consideration one substantial circumstance-to which direction do we plan to send the payload in space by means of Space Catapult? This circumstance will influence deciding this problem due to following reason:<br />
<br />
In case ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and if rod’s plane of rotation is parallel to Earth equator, then this plane will be orthogonal to Earth’s rotation axis. This axis from its side is tilted to ''ecliptic plane'' by 66° 34'. This means that Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 23°26'. Here follows very important consequence: under above-mentioned conditions the rod when rotating will be capable for covering only the part of the ''celestial sphere'' from 0° to 23°26' (counted from ''ecliptic plane'' northwards and southwards to ''Ecliptic poles''). This is about one fourth of the ''celestial sphere'' (23°/90°), this will not make problems if we intend to use the Space Catapult for exploring the solar system’s planets because their orbits’ tilts towards ''ecliptic plane'' do not exceed 7° (for planet Mercury, for other planets this tilt is even less); however we will not be able to send the payload for example to the nearest star ''Alpha Centaurs'' because this star is located at -42 degree according to ''ecliptic coordinate system'' in the celestial sphere.<br />
<br />
The situation will drastically change ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and ''if'' rod’s plane of rotation is orthogonal to Earth’s equator and therefore parallel to Earth’s axis of rotation. We have already discussed this option when we mentioned that the rod should be placed westwards from the cable and explained why it would be useful-for delivering the payload from Space Elevator’s cabin to Space Catapult’s rod. Under such conditions the Space Catapult will be capable to aim to any point on the ''celestial sphere''. Indeed, the Earth with the Space Elevator rotates around its axis and Space Elevator’s counterweight draws an imaginary circle in space. This circle is tilted to ''ecliptic plane'' at 23°26' and crosses this plane in two point called ''ascending'' and ''descending nodes''. The other points that are 90° away from these nodes we call point(s) of ''maximum elevation/depression'' (relative to ''ecliptic plane''). When the Space Elevator is at a''scending/descending node'' its rod and hence the payload can be directed to any point from 0º to 66º on the celestial sphere northwards and southwards from ecliptic plane. This makes about 75 % of celestial sphere. See the image depicting this situation:<br />
<br />
[[File: Node.jpg]]<br />
<br />
But when the space Elevator reaches the points of ''maximum elevation/depression'' then its rod during rapid rotation may be directed to any point from southern ''Ecliptic pole'' to ''Northern pole'' at the celestial sphere because at these points rod’s ''plane of rotation'' is orthogonal to ''ecliptic plane'' and thus the rotating rod can aim to ecliptic poles as well as other points. See this situation below:<br />
<br />
[[File: Elevation.jpg]] <br />
<br />
The situation will be similar if the Space Catapult’s rod is orthogonally placed towards cable. Under such approach Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 66° 34' and the Space Catapult will be capable to cover ''three fourths'' (66°/90°) of the ''celestial'' ''sphere'' when the Space Elevator is at the points of ''maximum elevation/depression'' and the whole celestial sphere when the Space Elevator is at ascending/descending nodes. For aiming the needed point on the celestial sphere the Earth should occupy the appropriate attitude towards the stars during the revolution around its axis, the same thing should be done under previous case described in the paragraph above. <br />
<br />
In conclusion, thinking about rod’s plane of rotation towards the Earth, we should note one important difference between above-mentioned approaches: if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, then in case of emergency during Space Catapult’s performance (for example if the Space Catapult’s rod is cut by sudden meteorite bombardment) the rod’s part with the payload may simply crash to the Earth at huge velocity if the rod at this moment is directed to the Earth. This cannot happen if Space Catapult’s rod’s plane of rotation is orthogonal to Space Elevator’s cable because payload’s rotational path will not be directed towards the Earth and hence its flying trajectory will never cross the Earth.<br />
<br />
=Braking the Space Catapult’s rod=<br />
<br />
After releasing the payload at necessary speed and direction, the Space Catapult’s rod will have a huge angular velocity that needs to be decreased to zero in order the Space Catapult’s rod to get another payload in motionless position and then to send it to space. <br />
What methods can we use to reduce Space Catapult’s rod’s rotation to zero? There are several possible ways: <br />
<br />
1. The electromotor designed for accelerating the rod may actually play a role of brakes, more precisely after releasing the payload to space the electromotor should operate/rotate in the opposite direction, hence rod’s rotational speed will be diminished to zero after that electromotor will stop operating. Under such method a bit less energy will be spent for decelerating the rod than in case of accelerating because when decelerating the rod is free from payload. <br />
<br />
2. An ordinary mechanical brakes, however due to electro motor’s and rod’s sizes a huge brake(s) would be needed to be installed on the Space Elevator’s counterweight and this circumstance would make additional problems from the engineering point of view. Nevertheless, we should admit that under such method we would not need as much energy as during accelerating; on the contrary, in this process the heat will be emitted as it generally happens during braking. <br />
<br />
3. For decelerating the rod we can use the well-known phenomenon in physics-''electromagnetic induction'': when the c''onductor/ closed circuit'' moves into the magnetic field the electric current is generated there. In case of Space Catapult we can use this phenomenon in the following manner: the conductor should be wrapped around the whole length of the rod like a helix and there should be possibility that this conductor to be turned into the ''closed circuit'' by means of mechanically connecting its ends (see the image below). After releasing the payload at necessary speed and direction this circuit should be closed, then according to ''electromagnetic induction'' the electric current will be generated in the conductor and the energy of this electric current will come from rod’s kinetic energy. Therefore, inducted electric current in the enclosed circuit will force this circuit and rod to lose kinetic energy and speed. The part of the generated electric current will be spent in prevailing conductor’s electric resistance:<br />
<br />
[[File: Helix.jpg]] <br />
<br />
The advantage of this method is that for decelerating the rod no energy will be required, as for drawback-much time will be required for this purpose because at the altitude of several ten thousand kilometers the Earth’s magnetic field is quite weak and the effect described in the paragraph above will need much time to operate and give necessary result. <br />
<br />
4. The above-described third method could be realized in a bit different way: if the conductor wrapped around the rod is a closed circuit and if we conduct the electricity there then the electric current will generate its own magnetic field that will counteract with Earth’s one. More precisely, according to ''Lenz's law'' induced current’s magnetic field will be in such a direction as to oppose the motion or change causing it, in other words induced current’s magnetic field will counteract outer magnetic field’s any change and this will cause decelerating rod’s rotation and finally its stopping. <br />
<br />
5. The obvious disadvantage of the third and fourth method described above is weakness of the Earth’s magnetic field because of which decelerating the rod may be delayed in time. For solving this problem we can create artificial magnetic field by means of electromagnets. Particularly, one electromagnet should be placed at the Space Elevator’s counterweight, very close to Space Catapult’s rod. The second electromagnet should be placed directly on the Space Catapult’s rod close to first electromagnet (actually, instead of this second electromagnet there could be used the conductor wrapped around the rod as we described above in previous methods). The reason of this nearness is that magnetic field generally weakens directly proportional to distance’s third power and much time will be needed for decelerating Space Catapult’s rod if two electromagnets are far from each other.<br />
<br />
This method probably will consume the most amount of energy but at the same time it will be the most effective because it does not depend on outer factors such as Earth’s magnetic field which is quite weak at the altitude of several ten thousand kilometers above the sea level. <br />
<br />
Eventually, which methods for decelerating the Space Catapult’s rod would be the best? As we see each one of them have got their advantages and disadvantages. We can state that we should choose one of them according to spaceflight’s profile and goal. Particularly, if we decide to send the spacecraft into the deep space mission where especially high speed is necessary then in this case ''longer/more massive'' rod would be needed rotating at very high speed. Under such circumstance much energy will be needed for accelerating/decelerating the rod. We should also take into consideration the fact how frequently the Space Catapult will operate, in other words how mane payloads it will have to send into space per some certain amount of time, week/month and etc. If time interval between two following missions is relatively high then we should choose the method that will consume less energy and more time for decelerating the rod. On the contrary, if the Space Catapult has to send payloads very often then we should choose the method that will consume more energy and enable the rod to decelerate faster. In other words, we should find ''golden mean'' between consuming time and energy. We should also take into account how much energy supply will be produced at the Space Elevator’s counterweight (see ''Energy source placed on the Space Elevator’s counterweight'') and what part of this energy can we spend for accelerating/decelerating the rod.<br />
<br />
The rod’s rotations can be decelerated much faster than accelerated; the reason of it is that when accelerating the rod has got some sophisticated device as payload and generally unmanned spacecrafts are capable to high g-loads, but still for them some restrictions exist. After the payload is released at needed direction and speed, the rod can decelerate much faster because the rod itself is quite simple device without any complex and sophisticated details. <br />
<br />
We can actually use several methods, such as the third one and then the first/fifth ones. This would be justified because of following reason: as we have already said when decelerating with the third/forth method the problem of weakness of the Earth’s magnetic field would occur, therefore much time would be necessary for described method(s) to perform and give us result. However, we should note that in the beginning when the rod rotates very quickly this method would still operate strong enough. This derives from Faraday's law of induction stating that “the electromotive force generated is proportional ''to the rate of change of the magnetic flux''”. Therefore, in the beginning when the rod is rotating very quickly we can use the third/forth method(s) and when the rod significantly brakes we can apply to the first/fifth ones-they do not depend on Earth magnetic field. In other words, such approach would greatly help us in finding the golden mean between spending energy and time necessary for decelerating the rod. <br />
<br />
And finally: after releasing the payload the Space Catapult’s rod can actually give us energy. More precisely, the electro motor itself can serve as electric generator also since we know that the same machine can operate as electric motor if it is fed with electricity and as generator for electricity if its rotor is rotated by other machines. Therefore after releasing the payload when the electro motor’s rotor is rotating very quickly it can give us energy, in result of which the rod will lose its kinetic energy and speed, as for generated energy it can be sent downwards to the Earth for our terrestrial needs (see the next section in this paper) or stored onboard the Space Elevator’s counterweight. This approach has got one substantial advantage: it does not imply additional mass (wrapped wire) that will cause problems because rotating heavier rod would consume more energy.<br />
<br />
=Energy source placed on the Space Elevator’s counterweight=<br />
<br />
As well-known, the Space Elevator’s cabin needs energy when moving along the cable and it can get it from the Earth by means of various ways, such as: laser beam, microwaves, through the cable itself and etc. On the other hand, Space Catapult also needs much energy for rotating the rod and for this purpose some energy source should be placed on the Space Elevator’s counterweight, presumably solar panels array. Doing this would demand additional funding and engineering work and this undertaking should be justified, so how can we prove that placing energy source on the counterweight would be necessary and useful? We should not forget that the energy generally could be simply transmitted from the Earth without carrying any material for energy source on counterweight; so we can justify this undertaking if we declare/prove that: <br />
<br />
1. Energy source should be designed for ''both'' Space Elevator’s cabin and Space Catapult’s rod. We can imagine it as array of numerous solar panels producing enough energy for both above-mentioned constructions. For this purpose solar panels would be better solution than nuclear reactor because they do not need nuclear fuel to be carried from the Earth to counterweight, also they are capable for producing energy in a continuous mode. By the way this circumstance will enable us to send the payload to space by Space Catapult whenever we want without depending existence nuclear fuel at the counterweight. <br />
<br />
2. Transmitting energy from the counterweight (“from above”) is better and advantageous than doing the same thing from Earth (“from below”). Indeed, when we try to transmit energy (laser or microwave beam) from the Earth to ascending cabin, the part of energy is inevitably lost and dispersed in the Earth’s atmosphere and (this is point of the question) this continues during the whole process of ascent. On the contrary, when transmitting the energy from counterweight to cabin the energy will be lost only on the little part of this voyage, more specifically until the cabin leaves the atmosphere (100 km in height) and when cabin leaves it the energy will be transmitted in vacuum without loss. <br />
<br />
3. For receiving the energy from the Earth the huge solar panels (in case of laser beam) or antennas (in case of microwaves) will be needed to be mounted on the counterweight and this is additional mass and additional engineering work.<br />
<br />
We think that these arguments given above are enough for shoving that placing energy source on the Space Elevator’s counterweight have advantages over transmitting energy from the Earth and as conclusion we can state that energy source on counterweight would serve both space transportation systems-Space Elevator and Space catapult. <br />
<br />
As addition, we could use the energy produced on the counterweight for terrestrial needs also. Indeed, there have been developed numerous projects for receiving energy from space since 60-ies implying producing it by means of solar panels and then transmitting to the Earth. Combining all these three goals we can conclude that placing solar power plant on the Space Elevator’s counterweight would be triply useful and advantageous. In other words, when the Space Catapult and Space Elevator do not function, the energy produced on the counterweight should be directly transmitted to the Earth for our terrestrial needs and thus the idea of Space Elevator, Space Catapult and space power plant will be combined in one project.<br />
<br />
=Assembling the Space Catapult=<br />
<br />
Assembling in space such a huge structure as Space Catapult will not be an easy task from the technical point of view and definitely needs special engineering approach. Besides, we think that Space Catapult’s rod should be mounted at the Space Elevator’s counterweight separately from every other parts of the Space Catapult (e.g. electro motor and etc.); this circumstance is caused by rod’s gigantic sizes. More precisely, electric motor and plus any other equipments necessary for Space Catapult’s performance should be delivered to space by means of Space Elevator in a usual way; as for Space Catapult’s rod, it is a different matter and it should be delivered and mounted separately in the end. <br />
<br />
Eventually, Space Catapult’s rod will be quite long, perhaps much more than 100 kilometers. It is obvious that delivering such a long rod as ''one single unit'' would be quite difficult task; also it is possible that due to its total mass the Space Elevator’s cabin will not be able to deliver such rod at all, but we have already mentioned that the Space Catapult may have the rod with various length; more precisely the rod may consist of two/more parts. In such case these parts should be delivered towards the counterweight separately and then assembled. <br />
<br />
But the Space Elevator’s cabin can actually deliver the Space Catapult’s rod as ''one single unit'' in space. We think that this would depend only on rod’s mass. The Space Elevator’s lifting capacity is not well-known yet; however apparently it will not exceed one hundred metric tons and if Space Catapult’s rod is made of extra light material then cabin will be able to deliver it in space and in such case the following question will arise: how the cabin will deliver such a huge object in space without any damage?<br />
<br />
This can be done by means of two cabins. Generally, Space Elevator’s conception implies only one cabin moving along the cable, but for some special purpose (like delivering Space Catapult’s rod in space) we can use the second cabin also that will descend downwards after finishing its job and will not participate in Space Elevator’s further performance. As for the process of delivering the rod, we can imagine it in a following manner: at first the rod will be placed horizontally on the Earth (thus it must be manufactured and then transported to the Space Elevator’s base station), then the Space Elevator’s first cabin will carry rod’s one end along the cable while the rod’s second end will be moved on the Earth so that the rod to take more and more vertical position. When the rod is in vertical position the second cabin will capture rod’s second end and will carry it in space. We think that without the second cabin it would be quite difficult for one cabin only to carry long/heavy rod because the rod may actually shake and crash to the Space Elevator’s cable and this is absolutely undesirable. <br />
<br />
So, as we see in principle it looks to be quite easy, however the assembling may complicate due to rod’s length. In this case it would be better to carry not the rod as ''one single unit'' but its parts and then to assemble them in space in the following manner: ''two'' cabins will carry the first part as described above, when this part is delivered to space and temporarily hung at the cable the next two cabins will carry the second part that will be attached to the first one from below; the other parts will be delivered to space and assembled into the rod in the same way. <br />
<br />
The obvious disadvantage of the above-described method is that each part needs two cabins on the Space Elevator’s cable, besides the humans will be needed for assembling the rod from these parts in the atmosphere’s upper layers; therefore we think that the first way-delivering the rod into space as one single unit still would be easier and more realistic; besides we should take into consideration the fact that if the rod is assembled the additional devices will be needed ''on the rod itself'' for joining these parts and this circumstance would lead to increasing the rod’s total mass and this is undesirable. See the image showing assembling process:<br />
<br />
[[File: Assembling.jpg]] <br />
<br />
Whatever design/structure the rod has-assembled from several parts or as one single unit, it must be delivered to its destination-Space Elevator’s counterweight and must be fastened to electro motor’s own axis. But the problem is that the rod will be quite long and also the fact that Space Catapult’s electro motor will be placed at counterweight’s upper side (or at the ''lateral'' side if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), so it will be necessary the rod coming from below to be moved to counterweight’s upper/lateral side, besides the rod should be docked with electro motor’s axis as accurately as possible. How is it possible to realize such complex engineering operation? Here we can indicate one possible theoretical way: <br />
<br />
The rod will be parallel to Space Elevator’s cable when carried by cabin, but later the cabin’s mechanisms should rotate it so that the rod to be orthogonal to Space Elevator’s cable (this will not be necessary if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), exactly in this position the rod should be delivered to counterweight, besides the rod when moving along the cable should be shifted a bit upwards (relative to the Earth) than the cabin itself. Under such conditions we will easily achieve docking the rod to electro motor’s own axis which from its side should have some trapping device (magnetic for example) to “catch” the rod and thus guarantee docking the rod to electro motor and finishing assembling the Space Catapult as a whole. But if the rod’s plane of rotation is parallel to cable then assembling process will be much easier because the ascending rod may directly dock to electro motor’s own axis. See the image showing this process:<br />
<br />
[[File: Deliver - Copy.jpg]] <br />
<br />
We think that it would be useful if one Space Elevator is built specially for Space Catapult with its base station located on the land, not the ocean. This would be justified because transporting Space Catapult’s rod from its place of manufacture to Space Elevator’s base station should occur on the land by means of several transports simultaneously (due to rod’s great length), this will enable us to deliver the rod to its destination without any damage while this kind of operation is hardly possible on the water.<br />
<br />
=The technical aspects regarding the Space Catapult=<br />
<br />
As an example, we can try to calculate/ascertain all possible kinds of aspects regarding the rod with some certain mass and sizes, for example we can assume the Space Catapult has got 100 km length rod. <br />
<br />
The circumference of the circle that this rod’s end will draw in space will be equal to 2πr=628 km. As we have already mentioned payload’s abilities for withstanding the g-load is restricted, so if the electromotor rotates the rod so that payload’s speed is equal to 50 km/sec (this means that it will take 12.56 seconds for the rod to make one complete revolution), in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design the spacecraft that will withstand such acceleration, but what about the rod itself? Which material can be used for designing this rod, what will be its mass and how much energy and time will be needed for the rod to reach this velocity? <br />
<br />
For manufacturing the rod we should choose the material with very low density and highest value of strength. Currently, the ''Carbon nanotubes'' are the best candidates for this purpose. What will the mass of the rod made of this material? This depends on width also and it should be as less as possible (otherwise the rod will be too heavy and too wide for transporting from manufacture place to Space Elevator’s base station and for delivering it to space by means of Space Elevator) but from the other hand the ''applied load'' will not let us to design very narrow rod.<br />
<br />
Let’s assume that we intend to launch the payload with the mass of 10 000 kg (during calculation we will use ''SI system'' only). To clarify what kind of material will be able to withstand the acceleration we should calculate and then compare two values: the ''applied load'' and ''tensile strength''. For calculating the first one we should multiply g-load (which we already know-2 550 g) to its mass-10 000 kg, we will get 25 500 000. As for calculating tensile strength, we should take its values (for Carbon nanotubes it varies from 11 000 MPa to 63 000, we will take some medium value-40 000 MPa) and multiply it to cross-section’s area, in our case rod is cylinder with circular cross-section. If radius of cross-section is 1 meters then its area is 3.14 square meters, multiplying this value to value of tensile strength (40 GPa as said) we will get 125 600 000 000 and this is significantly more than value of applied load-25 500 000. Of course, we should also take into consideration ''factor of safety'' which is generally equal to 2 and this indicates us that for safety the payload’s actual mass should be twice less but in our case as we see the rod will be able to accelerate the payload to above-mentioned speed. By the way, note that if that g-load ''2 550 g'' is almost at the payload’s withstanding limit this is not serious problem for the rod itself (we have already seen that value of tensile strength is much more than value of applied load) and this is clear why: payload generally contains sophisticated equipments (electrical circuit, optics an etc.) that will not be able to withstand very high g-loads while the rod will be made of some continuous solid substance, Carbon nanotubes is this case and of course it will be able to withstand much higher g-loads.<br />
<br />
<br />
What will be the mass of such rod? Knowing its volume (for this purpose its cross-section’s area 3.14 square meters should be multiplied to rod’s length-100 000 meters, we get 314 000 cubic meters) and taking the value of density (this also varies for Carbon nanotubes from 0.037 to 1.34 g/cm<sup>3</sup>, let’s take 0.1 g/cm<sup>3</sup>) we get rod’s mass as 31 400 000 kilograms. This is too heavy for Space Elevator’s modern concepts and for improving this situation we should either use many cabins for raising the rod as single unit or use nuclear energy for feeding the cabins instead of laser/microwave beams or deliver the rod’s parts separately in space and then assemble them (see ''Assembling the Space Catapult''). But if some advanced substances are chosen for this purpose (for example ''Silica aerogel'' the density of which is about 1.9 mg/cm<sup>3</sup>, this is 50 times less than the density of the Carbon nanotubes taken above-0.1 g/cm<sup>3</sup>) than problem may be lightened in spite of the fact that their current tensile strength is quite low-16 kPa for the density of 0.1 g/cm<sup>3</sup> <sup>7</sup>. So, we can conclude that we need the material with the density of ''Aerogels'' and tensile strength of Carbon nanotubes.<br />
<br />
How much energy and time will be needed for the rod to accelerate from zero to desired speed-50 km/sec? The amount of rotational energy of the rotating rod can be calculated by the following formula:<br />
Kinetic Energy<sub>rotational</sub>= (1/2)*I*ω2 <br />
<br />
Where:<br />
<br />
'''I'''=moment of inertia <br />
<br />
'''ω'''=angular velocity<br />
<br />
"I" depends on the shape of the mass under rotation. In the case of a uniform rod rotating from its end (axis of rotation is at the end of the rod) I = (m*L2)/3<br />
<br />
<br />
“ω” = V/R, where V = tangential velocity and R = radius<br />
<br />
In our case ''moment of inertia'' is equal to (31 400 000 kg*100 000 m2)/3=104 666 666 666 666 666<br />
ω is equal to (50 000 m/sec)/100 000 m=0.5<br />
<br />
So, Kinetic Energy<sub>rotational</sub>=(1/2)*104 666 666 666 666 666*(0.52)= 13 083 333 333 333 333.25 Joules<br />
<br />
Now, how much time and what amount of solar panels will be needed for accelerating this rod? The amount of Solar constant near the Earth is approximately equal to 1300 W/m2 [<sup>8</sup>], with assuming that ''coefficient of efficiency'' of solar panels is roughly 20 % we get 260 Watts per square meters and we can easily link amount energy (that we have already calculated) and power with the time needed. Particularly, ''Energy'' is equal to ''Power''’s multiplication to ''Time'':<br />
<br />
[[File: Formula - Copy.jpg]] <br />
<br />
So, Time is equal to 13 083 333 333 333 333.25 Joules/260 Watts=50320512820512.8 seconds, or 1 595 652 years. If we take much more area for solar panels, for example 10 millions square meters then 0.1595652 years or approximately 58 days will be needed and we think that this is acceptable time span.<br />
<br />
Actually, the time and energy will be needed a bit more for overcoming static friction in electro motor, for overcoming the rarified atmosphere’s resistance (we know that there no absolute vacuum in space), also we should take into consideration electric motors’ coefficient of efficiency that generally reaches 90-95 %, so some energy loss will occur here also. <br />
<br />
Now, what will be the total mass of solar panels producing the energy for Space Catapult? This depends on mass/power ratio, in near future it is expected that very lightweight designs could likely achieve 1 kg/kW [<sup>8</sup>] or 0.260 kg/ 260 W (per 1 square meter), so if for rotating the Space Catapult 10 millions square meters of solar panels are used then their total mass would be equal to 2 600 000 kg. We think that it is too heavy for Space Elevator the mass of which is expected to be equal around several hundred metric tons. If so, we will have to use fewer amounts of solar panels and therefore increase the time needed for accelerating the payload’s speed from zero to designed one. This will not make problems if the rod is accelerated only once and then keeps its constant rotation-for this purpose less energy will be needed and the payload will have to reach the rod’s end by first method as described earlier in this paper (see ''Rod’s plane of rotation towards the Earth'').<br />
<br />
We also need to take into consideration the value of deflection when the rod will be delivered to space by means of Space Elevator (see ''Assembling the Space Catapult''), in this case the thin and long rod will be bent due to its own weight and here we will try to calculate its value. This is quite complex problem that apparently cannot have an unambiguous solution because of many reasons, for example due to various temperatures in atmosphere’s different layers, various humidity and possible wind, but still we will try to calculate the value of ''Deflection'' that will occur in case when the rod’s one end is fastened to Space Elevator’s ascending cabin and the second end is fastened to the transport moving on the land, we discussed this option in above-mentioned section of our paper (see ''Assembling the Space Catapult''). The inclination angle for the rod will vary from 0º (rod is transported horizontally on the ground) to 90º (Space Elevator’s cabins are carrying the rod to space) and here we will discuss some medium case when the rod is semi-elevated in the air, when the angle between rod and ground/cable is equal to 45º. On the engineers’ ''eFunda'' web-site there is online calculator that enables to receive the value of ''Deflection'' (actually that site gives different term for this-''Displacement'') [10]:<br />
<br />
Here we need to enter the relevant values:<br />
<br />
''Length of beam'', ''L'': 100 000 meters<br />
<br />
''Line pressure load on beam'', p: In our case this is the weight per meter length. As we have already mentioned the radius of the rod’s cross-section is 1 meter, so the volume of rod’s 1 meter-length part will be 3.14 cubic meter. In case of using Carbon nanotubes with above-mentioned density-0.1 g/cm<sup>3</sup> the weight will be equal to 314 kg or 3 079 Newton. Since we have got the inclination of 45º we should multiply this value to cos45º- 0.707, so we get 2176 N/m.<br />
<br />
''Young's Modulus'', ''E'': This is equal to 1 000 GPa for Carbon nanotubes [11] <br />
<br />
''Distance from neutral axis to extreme fibers'', ''c'': In our case it is equal to the radius of the rod-1 meter<br />
<br />
''Moment of Inertia'', ''I'': It is equal to (pi*r<sup>4</sup>)/4, so it is equal to 0.785<br />
<br />
According to these initial data the calculator returns extremely high value of Deflection, much higher than the length of the rod itself: -3.61 × 10<sup>9</sup> meters. This result shows us that with the current materials (Carbon nanotubes in our case) it is impossible to raise the rod as ''one single unit'' to space by means of Space Elevator and we need other materials with less density and more ''Young's Modulus'' (or the rod should be much thicker but this will lead to increasing its mass). Therefore, we have got two options: either we should deliver the parts of that rod and then assemble them in space (we have already discussed this option) or completely different technologies for manufacturing the rod should be developed. Particularly, it would be very good if it was possible to manufacture the rod ''in continuous mode'' in vertical position and then uninterruptedly directly to carry it to space by means of Space Elevator’s cabins. Under such approach there will be no ''Deflection'' and several cabins will be able to deliver the rod in space. <br />
<br />
One note about transporting the rod from its place of manufacture to Space Elevator’s base station. We think that this process should be executed by many transports, in other words we are convinced that if the rod is carried by two trains only (or any other kind of transport) then the rod will continuously touch the ground since the ''Deflection'' occurs in any position-horizontal, inclined or vertical and this circumstance will lead to its damage, that’s why several transports will be needed to hold the rod at as many places as possible.<br />
<br />
=Stabilizing the counterweight=<br />
Stabilizing the Space Elevator’s counterweight is very important question during Space Catapult’s performance. Indeed, when the rod rotates it makes the imaginary circles in space and due to rod’s and payload’s masses the Space Catapult’s ''center of mass'' will be continuously shifted and if the counterweight is not somehow stabilized then it will make problems for accurate aiming to certain point at the celestial sphere. Also, if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable then there will be the danger that the rod may actually hit the cable and cut it. To avoid these problems we need to apply to serious measurements. <br />
<br />
First of all, the electro motor’s own axis can be quite long and this will diminish the chance to failure of the whole system. Actually, we are convinced that counterweight’s (where the electric motor will be placed) size will be quite large, mainly due to solar panels’ sizes and amount (this issue was discussed above), also the electromotor should be quite large and powerful to rotate the rod, and hence there will be enough distance between the rod and Space Elevator’s cable. <br />
<br />
The second serious problem is that the center of gravity of the system is not at the center of rotation, therefore it will be necessary to balance the rotating system when the payload is attached and when it is released.<br />
<br />
We think that the Space Catapult’s rod should not be deployed/directed to one side only but some counterweight of it should also exist. This is necessary since the unilaterally loaded (we mean the rod itself plus payload) rod will cause the counterweight to somersault. In other words, the rod should extend to other side and the ''moments of inertia'' of both sides should be the same as during rotating the rod as after releasing the payload when the rod still rotates. This is easily achievable if some additional, second payload is placed on the rod’s second end. Therefore, the Space Catapult will launch two payloads at the same time to the ''opposite'' directions but at various speeds if the second part/side of the rod is shorter.<br />
<br />
How the second payload should be placed on the rod and should we really send two payloads? Until we have got balanced rod this problem does not arise but as soon as the Space Catapult releases the payload this balance will be violated, how it can be restored? There are two theoretical ways for achieving this: reducing the ''mass'' or reducing the ''length''-with diminishing either one of them the ''moment of inertia'' will be decreased. We think that reducing the mass will be less practicable since this would require placing the second payload (spacecraft or anything else) on the rod’s second part and this cannot be done from the Space Elevator’s cabin-this is the easiest way for delivering the payload from Earth to Space Catapult’s rod; so we would have to (see ''Rod’s plane of rotation towards the Earth'') put the second payload on the electro motor and then send it rod’s second part’s end. This is quite complicated task; therefore we can apply to second approach-put some sliding object that will immediately move to electromotor as soon as the spacecraft is released.<br />
<br />
[[File: MOI.jpg]] <br />
<br />
The next problem that may occur is that when the electro motor rotates the rod this motion will make the Space Elevator to rotate to the opposite direction. The same problem arises when helicopter’s primary blade’s rotation forces the helicopter to rotate to opposite direction and this possible rotation is annulled by ''tail rotor''. We think that for balancing the counterweight the additional motor and rod should be installed and this rod should rotate to opposite direction and if their ''angular momentums'' are equal to each other, then their rotations will cancel each other. More precisely, the following equation should be fulfilled:<br />
<br />
[[File: Angular momentum.png]] <br />
<br />
Where ''m'' is mass of the rod, ''v'' is angular speed and ''L'' is rod’s length, the numbers ''1'' and ''2'' refer to first and second rods correspondingly. For balancing both rods’ rotation the multiplication at both sides of the counterweight should be equal, by the way this circumstance enables us to use the second rod with shorter length and even with less mass but rotating at more angular velocity.<br />
<br />
Such approach will effectively deal with other problem which will arise when the Space Catapult releases the payload(s), at this moment the second motor should instantly diminish its angular velocity to some certain level (an ordinary mechanical brakes could be used for this purpose), in this case ''angular momentums'' for both motors/rods will be equal again and Space Elevator’s counterweight will maintain its attitude in space. See the image below depicting the Space Catapult with two electro motors and rods:<br />
<br />
[[File: Two-rods.jpg]] <br />
<br />
Such approach will justify itself if rod’s plane of rotation is parallel to Space Elevator’s cable, but if this plane is orthogonal to cable (see ''Rod’s plane of rotation towards the Earth'') then the second/balancing electromotor cannot be placed under the counterweight because the cable will be cut when rod touches it. Therefore a bit different approach should used and we need to install two/four/eight electro motors with their own relatively shorter rods rotating to opposite direction. They should be placed at the counterweight’s lower side and on its edge (as we suppose the counterweight should be disc) so that their rods not to touch and cut Space Elevator’s cable. Also, total a''ngular momentums'' from these motors should be equal to the ''angular momentum'' from upper motor and thus the counterweight will not rotate and the Space Elevator’s cable will not be twisted. This situation is presented below:<br />
<br />
[[File: Modified-2.jpg]] <br />
<br />
We think that the array of gyroscopes would be also very useful to be installed at the counterweight since they can maintain the attitude of the whole system and this is important for precise aiming to certain point at the celestial sphere. As for the energy required for gyroscopes’ performance it could be received from the array of solar panels which as a result will generally serve Space Catapult’s precise performance.<br />
<br />
=Space Catapult placed at Lagrangian points-the way for gaining subluminal speeds=<br />
<br />
In our paper we discussed the Space Catapult based on the Space Elevator’s counterweight and concluded that this would be convenient when we intend to deliver the payload to space from the Earth. However, such Space Catapult cannot gain very high speeds and therefore we need to choose other way. It is obvious that we need to keep rod’s plane of rotation orthogonally relative to the ''Earth-Sun connecting line'' and hence we should place the rod on the celestial body which will be in synchronous rotation with the Sun but since there is no such body in the solar system we conclude that the Space Catapult for subluminal speeds (the speeds close to speed of light are in mind) should be placed at such point near the Earth where it will be easy to reach it from our planet and where the rotating rod will not hit the Earth and will be always at the same distance from the Sun to avoid the influence of its tidal forces. The examples of such places are '''Lagrangian''' L<sub>1</sub> and/or L<sub>2</sub> points at 1.5 million km away from the Earth. If the Space Catapult is placed at one of these points then its rod can be always orthogonal to the Sun in principle, at the same time it will never collide with the Earth and also it will be quite close to the Earth since 1.5 million km distance is very negligible in space.<br />
<br />
We have got several notes regarding such approach. First, when we mentioned that the rod’s various parts can be at the same distance from the Sun this strictly speaking is not very true because the Sun can be referred as little point where its gravity “comes out” from while the rod is quite long and its initial part (placed at one of the Lagrangian points) will be attracted stronger than the utmost one (for equal attracting the rod should the arc ''with the same curviness as Sun’s surface'' and not straight line); but still this is better than to direct the rod exactly towards the Sun where the tidal forces will try to tear the rod. Second, the Space Catapult should be placed at Lagrangian L1 point which is closer to the Sun than L2 one and therefore receives by 4 % more energy per area from the Sun. Third, the rod should be in constant rotation, this requires much less energy than accelerating it from zero, then stopping it and accelerating it again. Fourth, the existence of the asteroid belt in the solar system between Mars and Jupiter will somehow restrict the actual length of the rod. Indeed, the Space Catapult should be placed at one of the Lagrangian points at 1 AU distance from the Sun while asteroid belt approximately lays at 2.7 AU, from the simple geometry it is obvious that the length of the rod ''almost reaching'' the asteroid belt can be approximately equal to 390 million km, and if the rod is longer then it may simply hit any asteroid within that belt. For 390 million km length rod and for 100 000 m/sec2 acceleration at rod’s end (where the payload will be attached) the maximal speed that the spacecraft can gain will be approximately equal to 200 000 km/sec (two thirds of the speed of light) and this can be considered as enough for practical interstellar spaceflight. Fifth, the spacecraft should be directly put on the rotating rod’s initial end (near electromotor) and then slide towards the other end with its own rocket engines. To achieve this, the spacecraft will have to cover relatively less distance on the rod and then rod’s circular motion will accelerate the spacecraft further-we have already mentioned this in this paper when speaking about deploying the Lunar Space Catapult. This action-putting the spacecraft on the rod will not be difficult since rod’s angular velocity will be quite low due to rod’s huge length, particularly for 400 million km length rod and for 200 000 km/sec linear speed the rod’s angular velocity will be 0.0000796 revolutions/sec.<br />
<br />
[[File: Lagrangian-point.jpg]] <br />
<br />
We have already mentioned that to avoid the destructive influence of the Sun’s tidal forces the rod’s plane of rotation should be orthogonal to the Earth-Sun connecting line. By the way, note that under such approach we may have to wait one year until the Lagrangian Space Catapult occupies the relevant position towards the certain point at the celestial sphere where the spacecraft should be sent to. But from the other hand it would be useful if it is feasible to rotate this whole structure around the imaginary axis directed towards the ''ecliptic poles'' (depicted as faint green dash line on the image above), the reason if this is the possible danger when the rotating rod may hit Mars or asteroids that orbit around the Sun closer than 2.7 AU distance (for example ''433 Eros'' or ''1036 Ganymed''), hence for avoiding such undesired collision the Lagrangian Space Catapult should be slightly rotated by several degrees clockwise/counterclockwise so that the rod not to collide with any celestial object. We are convinced that rotation by several degrees will be absolutely enough measurement due to rod’s gigantic length and relatively less sizes of the celestial objects in the solar system.<br />
<br />
The next issue that we should discuss refers to stability of the Lagrangian Space Catapult placed at L<sub>1</sub> point. As we see this structure will have enormously gigantic size while the Lagrangian point is relatively little mathematical one in space, so what can be done to be convinced that this structure will remain at that point and do not shift aside? The body placed at one of the Lagrangian points is affected by other celestial objects’ gravity and therefore for achieving the balance the rod needs to have the counterweight with more mass if it (counterweight) is shorter. As we clearly see the rod needs the counterweight for two reasons: not to let the Space Catapult somersault and for maintaining it at the L1 point. We think that it would be very useful if the arrays of solar panels act as counterweight since exactly they can give us energy for rotating the rod. Also, we need the second, shorter, perhaps less massive but faster-rotating rod (again-solar panel arrays) the opposite rotation of which would cancel first rod’s rotation, this issue was discussed in this paper. These arrays of solar panels are depicted on the image shown above. <br />
<br />
How such a gigantic structure as Lagrangian Space Catapult can be assembled in space? In our paper we discussed the possible ways for delivering the rod from the Earth to the Space Elevator’s counterweight, now we will try to show that it is possible ''in principle'' to assemble the extra-long rod in space. <br />
<br />
If it is possible from the technical point of view to manufacture extra-long rod then we can use this approach and make 1.5 million km length rod (this is the distance between the Earth and Lagrangian L<sub>1</sub>/L<sub>2</sub> point) that will be mechanically directed to the base station at L<sub>1</sub> point. The capturing devices there will catch the rod and attach it to the electro motor’s shaft after which the rod should be spun by 90º so that it to be orthogonal to Earth-Sun connecting line (for this purpose the additional mechanisms will be needed), this spin is necessary because L<sub>1</sub> point is located on the Earth-Sun connecting line (that is towards the Sun if we look from the Earth) and when directing the rod from the Moon it will lay ''along'' this line while we need across. After this the rod should be slid to another side and then the next rod should be directed to the Lagrangian Space Catapult where it will be attached to the previous rod and etc. In other words, the extra-long rod will be assembled from one side and its length will “grow” from this side to other one, this is necessary because the distance between Moon (the rod should be manufactured exactly there and not on the Earth due to our planet’s relatively more gravity, atmosphere and problematic space debris belt around it) and L<sub>1</sub> point is constant and rod’s parts cannot be more. Due to whole rod’s and its parts’ lengths (400 million and 1.5 million km correspondingly) we think that about 260-270 such operations will be needed to finish assembling the rod (400/1.5). The process of assembling the Lagrangian Space Catapult is shown on the image below:<br />
<br />
[[File: Lagrangian-point-assemble.jpg]]<br />
<br />
=Conclusion=<br />
<br />
As we have seen, for leaving the Solar system and reaching the remote celestial bodies (stars, nebulas) there is no need to develop advanced and complicated technologies that mostly are not capable for gaining extra high velocities nevertheless. In any case, until the Space Elevator is really built (scheduled for construction by 2031) we have got much time for developing the idea of Space Catapult in technical aspect, like finding appropriate materials for the rod, perfect the ways how the Space Catapult can be assembled in space and etc. The concept of Space Catapult itself is the easiest one, does not need developing neither complex and sophisticated technologies, nor some exotic methods (such as ''Gravitoelectromagnetic toroidal launchers'', ''Antimatter rocket'' and etc.) and can be easily implemented in near future; in other words the Space Catapult is not some sophisticated structure that would need profound science research and the fact that it will enable us to gain whatever high speed will justify its developing and building by the humankind. As for other technologies like Ion Drive, they could be used by the spacecraft during flight for other purposes, for example for correcting/changing the flight direction.<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Space_Elevator<br />
<br />
2. http://www.isec.info/index.php?option=com_content&view=article&id=14&Itemid=9<br />
<br />
3. http://www.space-track.org/perl/geo_report.pl (provided data updates regularly, registering is needed) <br />
<br />
4. http://www.oosa.unvienna.org/pdf/reports/ac105/AC105_720E.pdf page 24 (data as at 21 August, 1997) <br />
<br />
5. http://www.amostech.com/ssw/presentations/Session7/S7-1Molotov.pdf page 16<br />
<br />
6. http://www.esa.int/SPECIALS/ESOC/SEMN2VM5NDF_mg_1_s_b.html <br />
<br />
7. http://eetd.lbl.gov/ecs/aerogels/sa-physical.html<br />
<br />
8. http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant<br />
<br />
9. http://www.you.com.au/news/2005.htm, http://www.spacedaily.com/news/ssp-03b.html<br />
<br />
10. http://www.efunda.com/formulae/solid_mechanics/beams/casestudy_display.cfm?case=simple_uniformload<br />
<br />
11. http://en.wikipedia.org/wiki/Young%27s_modulus<br />
<br />
<br />
'''Appendix''': <br />
<br />
Animation illustrating the payload’s departure from the Lagrangian Space Catapult:<br />
[[File: Lagrangian-point-animation.gif]]</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_5&diff=3668OpenSpace 52013-09-21T12:59:38Z<p>Eagle9: </p>
<hr />
<div>== '''Space Catapult''' ==<br />
<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
=INTRODUCTION=<br />
<br />
<br />
The new method for sending the spacecrafts in deep space is presented here. The paper describes the long rod rotated by electro motor placed at the Space Elevator’s counterweight and at Lagrangian points. This simple structure will enable the rod to gain high velocity and carry the payload with it. After reaching the desired speed the rod will release the payload that will fly in space along the imaginary circle’s tangent. This structure we called Space Catapult and it should work with the assist of Space Elevator. This latter should be used for carrying the payload from the Earth to Space Catapult’s rod.<br />
<br />
For exploring the outer space the humankind generally uses the rocket engines, mostly chemical-propelled ones. They enable us the explore near-Earth celestial bodies and other planets in the solar system. They even enabled us to send several deep space missions beyond the solar system such as '''Pioneer-10''', '''Pioneer-11''', '''Voyager-1''', '''Voyager-2''', however by means of this technology the flight lasts undesirably long and it seems to be impossible to reach remote celestial bodies in space such as stars, so new technologies are necessary for this purpose. However new technologies do not necessary imply new kind of rocket engines, such as ''Ion Drives'' because they are capable for gaining several ten times higher speeds only, but for remote celestial bodies even they are not suitable. Besides, they need a huge amount of energy to be stored onboard the spacecraft and this will make additional problems. So, high speed should be achieved with absolutely different approach. How this can be done?<br />
<br />
High speed can be easily achieved by means of fast-rotating rod around the electric motor. The motor’s rotational speed can be very high; the rod also can be quite long, hence the rod’s end’s linear speed can be extremely high, absolutely unachievable for any other technologies nowadays. The payload should be fastened at the rod’s end where the linear speed generally reaches maximal value. After reaching the necessary speed the rod will release the payload that will fly along the tangent from the current position. Thus the electric energy can be turned into payload’s speed and its velocity could be as high as we wish (except the ''speed of light'' of course). In principle the '''Space Catapult''' (thus we call this structure) would be the simplest, the most convenient and direct way for converting the energy/electricity into speed and conveying it to payload. <br />
<br />
As we see the Space Catapult is quite uncomplicated structure, however if we wish to gain high speeds we should deploy it in space, not on the Earth. Indeed, our planet is surrounded with dense atmosphere that impedes any quick motion, so if we rotate the rod quickly the atmospheric drag and generated heat would burn it very soon, therefore the Space Catapult should be built and deployed in space only, and as we suppose-at the Space Elevator’s counterweight. In other words, the Space Elevator’s counterweight will operate as Space Catapult. See image below:<br />
[[File:Space-catapult.jpg]]<br />
Generally, what is the Space Elevator [1][2]? According to modern concepts it will be the tall vertical structure built on equator and will have height of several ten thousand kilometers with its thin cable fastened to the base station on the Earth and with counterweight placed higher geostationary orbit. Because of balance between centrifugal force and gravity this structure will be stretched and the cabin will move along its cable carrying the goods into high orbit. After delivering the payload, the cabin will descend and carry the next one.<br />
In Space Elevator’s concepts several solutions have been proposed to act as a counterweight: <br />
<br />
1. Heavy, captured asteroid <br />
<br />
2. Space dock, space station or spaceport positioned past geostationary orbit <br />
<br />
3. Extension of the cable itself far beyond geostationary orbit. <br />
<br />
The third idea has gained more support in recent years due to the relative simplicity of the task and the fact that a payload that went to the end of the counterweight-cable would acquire considerable velocity relative to the Earth, allowing it to be launched into interplanetary space. However this idea cannot be completely shared by us due to following reason: <br />
<br />
It is well-known that the values of both '''Orbital''' and '''Escape Velocities''' decreases with increasing the altitude while the '''tangential velocity''' of Space Elevator’s cable increases. We can see the differences between them from the chart presented below:<br />
[[Image: Cxrili.gif]]<br />
<br />
As we see from this chart the ''tangential velocity'' of the Space Elevator even at its end (144 000 or 200 000 km altitude) is not very high to decrease the necessary time for covering the distance from the Earth to remote celestial bodies significantly. To achieve this, even the longer Space Elevator would be needed (its ''tangential velocity'' is directly proportional to its length) and this circumstance would complicate the technical task for building such Space Elevator. Because of this, there is no necessity to extend the cable itself far beyond geostationary orbit as proposed in the third variant. In any case, we have already seen that by means of Space Catapult it is possible to gain such huge velocities that are absolutely unachievable with other technologies, for example with Space Elevator. Therefore, using the counterweight and placing the Space Catapult there definitely has got some technical sense. <br />
<br />
However, we think that the question where the Space Catapult should be placed needs further discussion. Theoretically, the Space Catapult with its payload and nuclear reactor/solar panel needed for rotating the rod may be mounted not only at the counterweight, but on the Space Elevator’s cabin also that can carry all these goods to space in a usual way, as it should do it according to Space Elevator’s modern concepts. This option is quite possible, however for realizing this we need to know the mass of the payload, nuclear reactor/solar panels’ mass plus Space Catapult’s mass from one hand and Space Elevator’s lifting capacity (this ''must'' be more) from other hand, but these data are not available nowadays, therefore we think that the Space Catapult should be still mounted at the Space Elevator’s counterweight where it will be possible to send the payloads into deep space in ''continuous mode'' at high velocities.<br />
<br />
As we saw the Space Catapult is capable to gain very high velocities; however there is being developed other technologies and they in future will enable the spacecraft to fly at high speeds in space. These are Ion Drive systems, more precisely the most perspective one-''Variable Specific Impulse Magnetoplasma Rocket'' (VASIMR) which still under development can be used in future for deep space missions. Can these engines and Space Catapult be the rivals in space? Since none of them have been built and used in space yet we cannot give a persuasive answer to this question; however still it is possible to underline Space Catapult’s one significant advantage: if the future spacecraft uses the VASIMR (or any other kind of Ion Drive) engine it will definitely need to be equipped with nuclear reactor, otherwise the spacecraft will not be able to gain high speeds, also it will need to carry fuel tanks for this purpose. As for the Space Catapult, it can give much higher speed to spacecraft, besides it will have ''stationery'' power plant (see ''Energy source placed on the Space Elevator’s counterweight'') at the Space Elevator’s counterweight, so the payload will ''not'' have to carry the nuclear reactor onboard and this circumstance will lighten the work for deep space spacecraft. Besides, we should not forget that unlike the spacecrafts equipped with ion drive engines the Space Catapult will need no fuel for gaining high velocities. <br />
<br />
Briefly, Space Catapult’s advantages over any kind of propulsion systems are: <br />
<br />
1. Ability to gain any speed that is absolutely unachievable by means of other kinds of engines. <br />
<br />
2. No need by spacecraft to carry energy source that would make it too heavy and impracticable.<br />
<br />
=The Space Catapult needs long rod=<br />
<br />
When building the Space Catapult at Space Elevator’s counterweight we should install quite long rod there, the shorter the rod is, the easier would be installing it, however we should note that rod cannot be extremely short, let’s say 1 km length or so due to following reason:<br />
<br />
When we are going to send some payload into space, we need not only high velocity, but one certain direction also. The little inaccuracy in direction, inclination in several arcminutes is actually acceptable since the spacecraft would easily balance it with its engines; however great inclination from the initial direction would send the spacecraft into the completely different direction and in such case the whole mission will fail.<br />
<br />
If two Space Catapult’s rods have the length of let’s say 1 kilometer and 10 kilometers, then for giving to payload some certain linear speed (for instance 100 km/sec) these rods should rotate at different angular velocity. It is easy to ascertain that the shorter rod should rotate 10 times faster to gain the same linear speed than the rod with more length. But the faster the rod rotates, the more difficult will be to “catch” the needed moment for releasing the payload from the rod for sending it towards some certain direction. If the rod is too short, then it has to rotate very quickly for gaining some certain linear speed and therefore it will be extremely difficult catching the needed moment for releasing the payload. Hence, too short rod can make problem for sending the payload to some certain direction in space especially at high velocities. So, based on payload’s needed velocity we should find rod’s desired, minimal length that will enable us to send the payload in space to necessary direction without fear that it may yaw from the course. <br />
<br />
However, rod’s length will be crucial for payload’s abilities for withstanding the acceleration also. As an example, we can try to calculate its value which the payload will have to withstand during rod’s rotation. The acceleration of the body rotating at the circle with some constant velocity is calculated by the following formula:<br />
<br />
[[File: Acceleration - Copy.jpg]] <br />
<br />
Where a is acceleration in ''m/sec''<sup>2</sup>, ''v'' is payload’s linear velocity on the circle in ''m/sec'' and ''r'' is radius of the circle in ''meters'', in our case it is equal to rod’s length. Let’s assume that the rod is 100 km length and the electromotor rotates it so that payload’s speed is equal to 50 km/sec, in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design and manufacture the spacecraft’s subsystems (avionic and etc.) capable to withstand such acceleration. This circumstance somehow restricts the speeds that we can achieve, in any case their values actually depends on spacecrafts’ abilities for withstanding g-loads. But what can we do if much higher speeds are needed? The answer directly derives from that formula: the radius should be more; by the way note that this is additional reason why the longer rod is more useful. If we are able to make the extra long rod, then this will enable us to gain much higher velocities. <br />
<br />
What material should be used for manufacturing the rod? It is obvious that if very high speeds are needed the rod should be long and even in this case the acceleration at its end will be quite high, therefore ''sufficiently strong and light materials'' are needed for this purpose and making them is as similar challenge as in case of Space Elevator where the same requirements arises for the cable’s material. The lightness is needed because in case of heavy rod a lot of energy will be needed to rotate it; the strength is needed because in case of lack this property the rod will be destroyed due to great acceleration.<br />
<br />
=The mechanism for holding and releasing the payload=<br />
<br />
How the payload can be held by Space Catapult’s rod during rotation and how it can be released from the rod? We think that using ''electromagnet plus mechanical holding devices'' would be a good solution. More precisely, after the payload is attached to the rod it must be held by means of both methods until the rod accelerates and reaches necessary velocity (it may take even several days), but with approaching the desired speed the mechanical device should release the payload however the electromagnet(s) should still hold it. The explanation of such approach is following: generally the mechanical devices are much slower/sluggish in performance than electronic ones. We have already said that when releasing the payload the extreme accuracy is needed and mechanical devices cannot guarantee ''the exact time of releasing'' the payload unlike electronic ones. That is, it’s unlikely that mechanical devices can release the payload at some certain moment when needed while in case of electromagnet it would be enough to cease electric current there, it would lead to immediate vanishing of the magnetic field and sending the payload along the tangent from the point where the payload would be at the current moment. <br />
<br />
<br />
We think that the ''fastest control system'' would enable to release the payload to certain direction. This system (extremely fast-operating computer plus measuring equipments) should know the current position of the rod’s end, the current speed, the needed direction and be capable for computing the necessary moment for giving the order for diminishing the voltage for electromagnets and hence releasing the payload to desired direction and velocity.<br />
<br />
=Rod’s plane of rotation towards the Earth=<br />
<br />
The Space Catapult’s rod when rotating makes the circular plane/flatness in space and this plane may be horizontal/parallel to Earth surface, that is making the right angle to Space Elevator’s cable or it may be placed along the cable; see the both possible situations here:<br />
<br />
[[File: Planes-of-rotation - Copy.jpg]] <br />
<br />
Both approaches have got their advantages/disadvantages and here we will discuss this question, first of all from the point of view of safety.<br />
<br />
For gaining extremely high velocities quite long rod would be needed, maybe with the length of several thousand kilometers or even more. If such rod is placed ''along'' the Space Elevator’s cable then the rod during rotation will cross many orbits from the ''Medium Earth Orbit'' to ''High'' ones. When rotating, the rod may actually hit any satellite and/or space debris object and such collision can lead to rod’s complete destruction; therefore we should choose such plane which would be much more free from any artificial objects; hence if the rod rotates ''horizontally/parallel'' to Earth’s surface at high enough altitude where the satellites’ population is relatively low then this measurement would justify itself because under such circumstance the rod will not cross satellites’ orbits (rod’s plane of rotation will simply coincide to ''one'' orbit’s path). However, we should also note that this altitude actually depends on the Space Elevator’s proposed length. Indeed, the Space Catapult’s rod should be mounted at the Space Elevator’s counterweight; this counterweight from its side should be placed at the end of the Space Elevator at such altitude where the satellites’ population is as low as possible. This means that Space Elevator’s proposed height should be agreed with mounting Space Catapult on its counterweight. According to various databases the number of man-made objects at high orbits, more precisely beyond geostationary orbit is much less than on the lower orbits <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup>, therefore the Space Catapult with its rod should be located at the altitude of 50 000-60 000 km above the sea level. At such altitude the space is almost free and nothing will impede rod’s rapid rotation. Besides, the satellites at high orbits are orbiting around the Earth slower than on the lower orbits (as known any satellite orbits around its primary body slower in apogee than in perigee), therefore if some tracking system is mounted at Space Elevator’s counterweight then it will enable the Space Catapult to avoid undesired collision with satellites during Space Catapult’s performance. In other words, the Space Catapult should operate only when the there are no satellites near its vicinities.<br />
<br />
Now we will try to discuss this question from other side.<br />
<br />
How the payload can be transferred from the Space Elevator’s cabin to the Space Catapult’s rod? One way is following: cabin reaches the counterweight where the payload will be released, then payload will be mechanically conveyed to rod, continues its way ''on the rod'' (like the train rides on the rails) and after reaching rod’s end it stops, the rod begins rotating and after gaining necessary linear speed it releases the payload to needed direction. This method is generally realizable; however it seems to be too complicated and unpromising compare to the second one: the Space Catapult’s rod is stopped in space so that it to be directed downwards to the Earth and be parallel to Space Elevator’s cable. The Space Elevator’s cabin moving along the cable with payload stops at the cable ''near'' the end of the Space Catapult’s rod and releases the payload that will fly to the rod, attaches itself to the rod’s end (here the electromagnets would be useful), the rod begins rotating and after gaining needed linear speed will release the payload to necessary direction.<br />
<br />
This second way seems to be more promising because the first one is much more complicated as we have already said: first of all there would be needed some mechanical devices for transferring the payload from the Space Elevator’s cabin to counterweight, the counterweight should have the hole for the payload to move through it from below (we should not forget that the Space Catapult should be mounted ''at'' the counterweight, not ''beneath'' it), besides the rod should be made so that it to have some conveying surface (rails for instance) the payload to move on it. As we see it would be much more convenient if it is possible to convey the payload from the cabin to the rod directly and this would be feasible under the second method which is depicted below:<br />
<br />
[[File: Convey.jpg]] <br />
<br />
One more aspect regarding Space Catapult’s position. This structure, its rod, its electro motor and etc should be mounted at Space Elevator’s counterweight so that the rod to be placed westwards from the cable. The reason of it is following: when the Space Elevator’s cabin stops and releases the payload (which should fly to Space Catapult’s rod) the current speed of which will/should be more than the value of the ''Orbital/Escape Velocity'' at the current altitude. After releasing the payload will fly westwards and upwards because its orbit will be ellipse, under ellipse the payload will fly higher to apogee and at the speed less than Space Elevator’s current speed at the given altitude, in other words the released payload will “lag behind” the Space Elevator’s cable; therefore payloads’ ''stopping points'' at the cable and Space Catapult’s rod’s length should be calculated and chosen so that the payload to fly directly towards rod’s end. This process would be feasible in both cases-if the rod’s plane of rotation is parallel to Earth’s surface and if it is placed along the cable-but still this would be easier for the payload to achieve the rod’s end if the rod is placed along the cable because at least the distance that the payload should cover in space will be less.<br />
<br />
The length of the Space Catapult’s rod placed at the Space Elevator’s counterweight might vary since for various spaceflight purposes different initial speed will be needed and relatively low speed could be achieved by means of shorter rod. Because of this reason it might be necessary to change Space Catapult’s rod’s length, therefore it would be useful if the rod consists of two parts where the first part would be perpetually attached to electro motor and the second one will be attached to the first part if necessary. For this operation Space Catapult’s rod should be placed along the cable since the relative nearness would make this operation quite easy and it could be accomplished by the crew directly from the Space Elevator’s cabin stopped at the needed altitude. <br />
<br />
For deciding the question how the Space Catapult’s rod should be placed towards the Space Elevator’s cable we should take into consideration one substantial circumstance-to which direction do we plan to send the payload in space by means of Space Catapult? This circumstance will influence deciding this problem due to following reason:<br />
<br />
In case ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and if rod’s plane of rotation is parallel to Earth equator, then this plane will be orthogonal to Earth’s rotation axis. This axis from its side is tilted to ''ecliptic plane'' by 66° 34'. This means that Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 23°26'. Here follows very important consequence: under above-mentioned conditions the rod when rotating will be capable for covering only the part of the ''celestial sphere'' from 0° to 23°26' (counted from ''ecliptic plane'' northwards and southwards to ''Ecliptic poles''). This is about one fourth of the ''celestial sphere'' (23°/90°), this will not make problems if we intend to use the Space Catapult for exploring the solar system’s planets because their orbits’ tilts towards ''ecliptic plane'' do not exceed 7° (for planet Mercury, for other planets this tilt is even less); however we will not be able to send the payload for example to the nearest star ''Alpha Centaurs'' because this star is located at -42 degree according to ''ecliptic coordinate system'' in the celestial sphere.<br />
<br />
The situation will drastically change ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and ''if'' rod’s plane of rotation is orthogonal to Earth’s equator and therefore parallel to Earth’s axis of rotation. We have already discussed this option when we mentioned that the rod should be placed westwards from the cable and explained why it would be useful-for delivering the payload from Space Elevator’s cabin to Space Catapult’s rod. Under such conditions the Space Catapult will be capable to aim to any point on the ''celestial sphere''. Indeed, the Earth with the Space Elevator rotates around its axis and Space Elevator’s counterweight draws an imaginary circle in space. This circle is tilted to ''ecliptic plane'' at 23°26' and crosses this plane in two point called ''ascending'' and ''descending nodes''. The other points that are 90° away from these nodes we call point(s) of ''maximum elevation/depression'' (relative to ''ecliptic plane''). When the Space Elevator is at a''scending/descending node'' its rod and hence the payload can be directed to any point from 0º to 66º on the celestial sphere northwards and southwards from ecliptic plane. This makes about 75 % of celestial sphere. See the image depicting this situation:<br />
<br />
[[File: Node.jpg]]<br />
<br />
But when the space Elevator reaches the points of ''maximum elevation/depression'' then its rod during rapid rotation may be directed to any point from southern ''Ecliptic pole'' to ''Northern pole'' at the celestial sphere because at these points rod’s ''plane of rotation'' is orthogonal to ''ecliptic plane'' and thus the rotating rod can aim to ecliptic poles as well as other points. See this situation below:<br />
<br />
[[File: Elevation.jpg]] <br />
<br />
The situation will be similar if the Space Catapult’s rod is orthogonally placed towards cable. Under such approach Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 66° 34' and the Space Catapult will be capable to cover ''three fourths'' (66°/90°) of the ''celestial'' ''sphere'' when the Space Elevator is at the points of ''maximum elevation/depression'' and the whole celestial sphere when the Space Elevator is at ascending/descending nodes. For aiming the needed point on the celestial sphere the Earth should occupy the appropriate attitude towards the stars during the revolution around its axis, the same thing should be done under previous case described in the paragraph above. <br />
<br />
In conclusion, thinking about rod’s plane of rotation towards the Earth, we should note one important difference between above-mentioned approaches: if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, then in case of emergency during Space Catapult’s performance (for example if the Space Catapult’s rod is cut by sudden meteorite bombardment) the rod’s part with the payload may simply crash to the Earth at huge velocity if the rod at this moment is directed to the Earth. This cannot happen if Space Catapult’s rod’s plane of rotation is orthogonal to Space Elevator’s cable because payload’s rotational path will not be directed towards the Earth and hence its flying trajectory will never cross the Earth.<br />
<br />
=Braking the Space Catapult’s rod=<br />
<br />
After releasing the payload at necessary speed and direction, the Space Catapult’s rod will have a huge angular velocity that needs to be decreased to zero in order the Space Catapult’s rod to get another payload in motionless position and then to send it to space. <br />
What methods can we use to reduce Space Catapult’s rod’s rotation to zero? There are several possible ways: <br />
<br />
1. The electromotor designed for accelerating the rod may actually play a role of brakes, more precisely after releasing the payload to space the electromotor should operate/rotate in the opposite direction, hence rod’s rotational speed will be diminished to zero after that electromotor will stop operating. Under such method a bit less energy will be spent for decelerating the rod than in case of accelerating because when decelerating the rod is free from payload. <br />
<br />
2. An ordinary mechanical brakes, however due to electro motor’s and rod’s sizes a huge brake(s) would be needed to be installed on the Space Elevator’s counterweight and this circumstance would make additional problems from the engineering point of view. Nevertheless, we should admit that under such method we would not need as much energy as during accelerating; on the contrary, in this process the heat will be emitted as it generally happens during braking. <br />
<br />
3. For decelerating the rod we can use the well-known phenomenon in physics-''electromagnetic induction'': when the c''onductor/ closed circuit'' moves into the magnetic field the electric current is generated there. In case of Space Catapult we can use this phenomenon in the following manner: the conductor should be wrapped around the whole length of the rod like a helix and there should be possibility that this conductor to be turned into the ''closed circuit'' by means of mechanically connecting its ends (see the image below). After releasing the payload at necessary speed and direction this circuit should be closed, then according to ''electromagnetic induction'' the electric current will be generated in the conductor and the energy of this electric current will come from rod’s kinetic energy. Therefore, inducted electric current in the enclosed circuit will force this circuit and rod to lose kinetic energy and speed. The part of the generated electric current will be spent in prevailing conductor’s electric resistance:<br />
<br />
[[File: Helix.jpg]] <br />
<br />
The advantage of this method is that for decelerating the rod no energy will be required, as for drawback-much time will be required for this purpose because at the altitude of several ten thousand kilometers the Earth’s magnetic field is quite weak and the effect described in the paragraph above will need much time to operate and give necessary result. <br />
<br />
4. The above-described third method could be realized in a bit different way: if the conductor wrapped around the rod is a closed circuit and if we conduct the electricity there then the electric current will generate its own magnetic field that will counteract with Earth’s one. More precisely, according to ''Lenz's law'' induced current’s magnetic field will be in such a direction as to oppose the motion or change causing it, in other words induced current’s magnetic field will counteract outer magnetic field’s any change and this will cause decelerating rod’s rotation and finally its stopping. <br />
<br />
5. The obvious disadvantage of the third and fourth method described above is weakness of the Earth’s magnetic field because of which decelerating the rod may be delayed in time. For solving this problem we can create artificial magnetic field by means of electromagnets. Particularly, one electromagnet should be placed at the Space Elevator’s counterweight, very close to Space Catapult’s rod. The second electromagnet should be placed directly on the Space Catapult’s rod close to first electromagnet (actually, instead of this second electromagnet there could be used the conductor wrapped around the rod as we described above in previous methods). The reason of this nearness is that magnetic field generally weakens directly proportional to distance’s third power and much time will be needed for decelerating Space Catapult’s rod if two electromagnets are far from each other.<br />
<br />
This method probably will consume the most amount of energy but at the same time it will be the most effective because it does not depend on outer factors such as Earth’s magnetic field which is quite weak at the altitude of several ten thousand kilometers above the sea level. <br />
<br />
Eventually, which methods for decelerating the Space Catapult’s rod would be the best? As we see each one of them have got their advantages and disadvantages. We can state that we should choose one of them according to spaceflight’s profile and goal. Particularly, if we decide to send the spacecraft into the deep space mission where especially high speed is necessary then in this case ''longer/more massive'' rod would be needed rotating at very high speed. Under such circumstance much energy will be needed for accelerating/decelerating the rod. We should also take into consideration the fact how frequently the Space Catapult will operate, in other words how mane payloads it will have to send into space per some certain amount of time, week/month and etc. If time interval between two following missions is relatively high then we should choose the method that will consume less energy and more time for decelerating the rod. On the contrary, if the Space Catapult has to send payloads very often then we should choose the method that will consume more energy and enable the rod to decelerate faster. In other words, we should find ''golden mean'' between consuming time and energy. We should also take into account how much energy supply will be produced at the Space Elevator’s counterweight (see ''Energy source placed on the Space Elevator’s counterweight'') and what part of this energy can we spend for accelerating/decelerating the rod.<br />
<br />
The rod’s rotations can be decelerated much faster than accelerated; the reason of it is that when accelerating the rod has got some sophisticated device as payload and generally unmanned spacecrafts are capable to high g-loads, but still for them some restrictions exist. After the payload is released at needed direction and speed, the rod can decelerate much faster because the rod itself is quite simple device without any complex and sophisticated details. <br />
<br />
We can actually use several methods, such as the third one and then the first/fifth ones. This would be justified because of following reason: as we have already said when decelerating with the third/forth method the problem of weakness of the Earth’s magnetic field would occur, therefore much time would be necessary for described method(s) to perform and give us result. However, we should note that in the beginning when the rod rotates very quickly this method would still operate strong enough. This derives from Faraday's law of induction stating that “the electromotive force generated is proportional ''to the rate of change of the magnetic flux''”. Therefore, in the beginning when the rod is rotating very quickly we can use the third/forth method(s) and when the rod significantly brakes we can apply to the first/fifth ones-they do not depend on Earth magnetic field. In other words, such approach would greatly help us in finding the golden mean between spending energy and time necessary for decelerating the rod. <br />
<br />
And finally: after releasing the payload the Space Catapult’s rod can actually give us energy. More precisely, the electro motor itself can serve as electric generator also since we know that the same machine can operate as electric motor if it is fed with electricity and as generator for electricity if its rotor is rotated by other machines. Therefore after releasing the payload when the electro motor’s rotor is rotating very quickly it can give us energy, in result of which the rod will lose its kinetic energy and speed, as for generated energy it can be sent downwards to the Earth for our terrestrial needs (see the next section in this paper) or stored onboard the Space Elevator’s counterweight. This approach has got one substantial advantage: it does not imply additional mass (wrapped wire) that will cause problems because rotating heavier rod would consume more energy.<br />
<br />
=Energy source placed on the Space Elevator’s counterweight=<br />
<br />
As well-known, the Space Elevator’s cabin needs energy when moving along the cable and it can get it from the Earth by means of various ways, such as: laser beam, microwaves, through the cable itself and etc. On the other hand, Space Catapult also needs much energy for rotating the rod and for this purpose some energy source should be placed on the Space Elevator’s counterweight, presumably solar panels array. Doing this would demand additional funding and engineering work and this undertaking should be justified, so how can we prove that placing energy source on the counterweight would be necessary and useful? We should not forget that the energy generally could be simply transmitted from the Earth without carrying any material for energy source on counterweight; so we can justify this undertaking if we declare/prove that: <br />
<br />
1. Energy source should be designed for ''both'' Space Elevator’s cabin and Space Catapult’s rod. We can imagine it as array of numerous solar panels producing enough energy for both above-mentioned constructions. For this purpose solar panels would be better solution than nuclear reactor because they do not need nuclear fuel to be carried from the Earth to counterweight, also they are capable for producing energy in a continuous mode. By the way this circumstance will enable us to send the payload to space by Space Catapult whenever we want without depending existence nuclear fuel at the counterweight. <br />
<br />
2. Transmitting energy from the counterweight (“from above”) is better and advantageous than doing the same thing from Earth (“from below”). Indeed, when we try to transmit energy (laser or microwave beam) from the Earth to ascending cabin, the part of energy is inevitably lost and dispersed in the Earth’s atmosphere and (this is point of the question) this continues during the whole process of ascent. On the contrary, when transmitting the energy from counterweight to cabin the energy will be lost only on the little part of this voyage, more specifically until the cabin leaves the atmosphere (100 km in height) and when cabin leaves it the energy will be transmitted in vacuum without loss. <br />
<br />
3. For receiving the energy from the Earth the huge solar panels (in case of laser beam) or antennas (in case of microwaves) will be needed to be mounted on the counterweight and this is additional mass and additional engineering work.<br />
<br />
We think that these arguments given above are enough for shoving that placing energy source on the Space Elevator’s counterweight have advantages over transmitting energy from the Earth and as conclusion we can state that energy source on counterweight would serve both space transportation systems-Space Elevator and Space catapult. <br />
<br />
As addition, we could use the energy produced on the counterweight for terrestrial needs also. Indeed, there have been developed numerous projects for receiving energy from space since 60-ies implying producing it by means of solar panels and then transmitting to the Earth. Combining all these three goals we can conclude that placing solar power plant on the Space Elevator’s counterweight would be triply useful and advantageous. In other words, when the Space Catapult and Space Elevator do not function, the energy produced on the counterweight should be directly transmitted to the Earth for our terrestrial needs and thus the idea of Space Elevator, Space Catapult and space power plant will be combined in one project.<br />
<br />
=Assembling the Space Catapult=<br />
<br />
Assembling in space such a huge structure as Space Catapult will not be an easy task from the technical point of view and definitely needs special engineering approach. Besides, we think that Space Catapult’s rod should be mounted at the Space Elevator’s counterweight separately from every other parts of the Space Catapult (e.g. electro motor and etc.); this circumstance is caused by rod’s gigantic sizes. More precisely, electric motor and plus any other equipments necessary for Space Catapult’s performance should be delivered to space by means of Space Elevator in a usual way; as for Space Catapult’s rod, it is a different matter and it should be delivered and mounted separately in the end. <br />
<br />
Eventually, Space Catapult’s rod will be quite long, perhaps much more than 100 kilometers. It is obvious that delivering such a long rod as ''one single unit'' would be quite difficult task; also it is possible that due to its total mass the Space Elevator’s cabin will not be able to deliver such rod at all, but we have already mentioned that the Space Catapult may have the rod with various length; more precisely the rod may consist of two/more parts. In such case these parts should be delivered towards the counterweight separately and then assembled. <br />
<br />
But the Space Elevator’s cabin can actually deliver the Space Catapult’s rod as ''one single unit'' in space. We think that this would depend only on rod’s mass. The Space Elevator’s lifting capacity is not well-known yet; however apparently it will not exceed one hundred metric tons and if Space Catapult’s rod is made of extra light material then cabin will be able to deliver it in space and in such case the following question will arise: how the cabin will deliver such a huge object in space without any damage?<br />
<br />
This can be done by means of two cabins. Generally, Space Elevator’s conception implies only one cabin moving along the cable, but for some special purpose (like delivering Space Catapult’s rod in space) we can use the second cabin also that will descend downwards after finishing its job and will not participate in Space Elevator’s further performance. As for the process of delivering the rod, we can imagine it in a following manner: at first the rod will be placed horizontally on the Earth (thus it must be manufactured and then transported to the Space Elevator’s base station), then the Space Elevator’s first cabin will carry rod’s one end along the cable while the rod’s second end will be moved on the Earth so that the rod to take more and more vertical position. When the rod is in vertical position the second cabin will capture rod’s second end and will carry it in space. We think that without the second cabin it would be quite difficult for one cabin only to carry long/heavy rod because the rod may actually shake and crash to the Space Elevator’s cable and this is absolutely undesirable. <br />
<br />
So, as we see in principle it looks to be quite easy, however the assembling may complicate due to rod’s length. In this case it would be better to carry not the rod as ''one single unit'' but its parts and then to assemble them in space in the following manner: ''two'' cabins will carry the first part as described above, when this part is delivered to space and temporarily hung at the cable the next two cabins will carry the second part that will be attached to the first one from below; the other parts will be delivered to space and assembled into the rod in the same way. <br />
<br />
The obvious disadvantage of the above-described method is that each part needs two cabins on the Space Elevator’s cable, besides the humans will be needed for assembling the rod from these parts in the atmosphere’s upper layers; therefore we think that the first way-delivering the rod into space as one single unit still would be easier and more realistic; besides we should take into consideration the fact that if the rod is assembled the additional devices will be needed ''on the rod itself'' for joining these parts and this circumstance would lead to increasing the rod’s total mass and this is undesirable. See the image showing assembling process:<br />
<br />
[[File: Assembling.jpg]] <br />
<br />
Whatever design/structure the rod has-assembled from several parts or as one single unit, it must be delivered to its destination-Space Elevator’s counterweight and must be fastened to electro motor’s own axis. But the problem is that the rod will be quite long and also the fact that Space Catapult’s electro motor will be placed at counterweight’s upper side (or at the ''lateral'' side if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), so it will be necessary the rod coming from below to be moved to counterweight’s upper/lateral side, besides the rod should be docked with electro motor’s axis as accurately as possible. How is it possible to realize such complex engineering operation? Here we can indicate one possible theoretical way: <br />
<br />
The rod will be parallel to Space Elevator’s cable when carried by cabin, but later the cabin’s mechanisms should rotate it so that the rod to be orthogonal to Space Elevator’s cable (this will not be necessary if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), exactly in this position the rod should be delivered to counterweight, besides the rod when moving along the cable should be shifted a bit upwards (relative to the Earth) than the cabin itself. Under such conditions we will easily achieve docking the rod to electro motor’s own axis which from its side should have some trapping device (magnetic for example) to “catch” the rod and thus guarantee docking the rod to electro motor and finishing assembling the Space Catapult as a whole. But if the rod’s plane of rotation is parallel to cable then assembling process will be much easier because the ascending rod may directly dock to electro motor’s own axis. See the image showing this process:<br />
<br />
[[File: Deliver - Copy.jpg]] <br />
<br />
We think that it would be useful if one Space Elevator is built specially for Space Catapult with its base station located on the land, not the ocean. This would be justified because transporting Space Catapult’s rod from its place of manufacture to Space Elevator’s base station should occur on the land by means of several transports simultaneously (due to rod’s great length), this will enable us to deliver the rod to its destination without any damage while this kind of operation is hardly possible on the water.<br />
<br />
=The technical aspects regarding the Space Catapult=<br />
<br />
As an example, we can try to calculate/ascertain all possible kinds of aspects regarding the rod with some certain mass and sizes, for example we can assume the Space Catapult has got 100 km length rod. <br />
<br />
The circumference of the circle that this rod’s end will draw in space will be equal to 2πr=628 km. As we have already mentioned payload’s abilities for withstanding the g-load is restricted, so if the electromotor rotates the rod so that payload’s speed is equal to 50 km/sec (this means that it will take 12.56 seconds for the rod to make one complete revolution), in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design the spacecraft that will withstand such acceleration, but what about the rod itself? Which material can be used for designing this rod, what will be its mass and how much energy and time will be needed for the rod to reach this velocity? <br />
<br />
For manufacturing the rod we should choose the material with very low density and highest value of strength. Currently, the ''Carbon nanotubes'' are the best candidates for this purpose. What will the mass of the rod made of this material? This depends on width also and it should be as less as possible (otherwise the rod will be too heavy and too wide for transporting from manufacture place to Space Elevator’s base station and for delivering it to space by means of Space Elevator) but from the other hand the ''applied load'' will not let us to design very narrow rod.<br />
<br />
Let’s assume that we intend to launch the payload with the mass of 10 000 kg (during calculation we will use ''SI system'' only). To clarify what kind of material will be able to withstand the acceleration we should calculate and then compare two values: the ''applied load'' and ''tensile strength''. For calculating the first one we should multiply g-load (which we already know-2 550 g) to its mass-10 000 kg, we will get 25 500 000. As for calculating tensile strength, we should take its values (for Carbon nanotubes it varies from 11 000 MPa to 63 000, we will take some medium value-40 000 MPa) and multiply it to cross-section’s area, in our case rod is cylinder with circular cross-section. If radius of cross-section is 1 meters then its area is 3.14 square meters, multiplying this value to value of tensile strength (40 GPa as said) we will get 125 600 000 000 and this is significantly more than value of applied load-25 500 000. Of course, we should also take into consideration ''factor of safety'' which is generally equal to 2 and this indicates us that for safety the payload’s actual mass should be twice less but in our case as we see the rod will be able to accelerate the payload to above-mentioned speed. By the way, note that if that g-load ''2 550 g'' is almost at the payload’s withstanding limit this is not serious problem for the rod itself (we have already seen that value of tensile strength is much more than value of applied load) and this is clear why: payload generally contains sophisticated equipments (electrical circuit, optics an etc.) that will not be able to withstand very high g-loads while the rod will be made of some continuous solid substance, Carbon nanotubes is this case and of course it will be able to withstand much higher g-loads.<br />
<br />
<br />
What will be the mass of such rod? Knowing its volume (for this purpose its cross-section’s area 3.14 square meters should be multiplied to rod’s length-100 000 meters, we get 314 000 cubic meters) and taking the value of density (this also varies for Carbon nanotubes from 0.037 to 1.34 g/cm<sup>3</sup>, let’s take 0.1 g/cm<sup>3</sup>) we get rod’s mass as 31 400 000 kilograms. This is too heavy for Space Elevator’s modern concepts and for improving this situation we should either use many cabins for raising the rod as single unit or use nuclear energy for feeding the cabins instead of laser/microwave beams or deliver the rod’s parts separately in space and then assemble them (see ''Assembling the Space Catapult''). But if some advanced substances are chosen for this purpose (for example ''Silica aerogel'' the density of which is about 1.9 mg/cm<sup>3</sup>, this is 50 times less than the density of the Carbon nanotubes taken above-0.1 g/cm<sup>3</sup>) than problem may be lightened in spite of the fact that their current tensile strength is quite low-16 kPa for the density of 0.1 g/cm<sup>3</sup> <sup>7</sup>. So, we can conclude that we need the material with the density of ''Aerogels'' and tensile strength of Carbon nanotubes.<br />
<br />
How much energy and time will be needed for the rod to accelerate from zero to desired speed-50 km/sec? The amount of rotational energy of the rotating rod can be calculated by the following formula:<br />
Kinetic Energy<sub>rotational</sub>= (1/2)*I*ω2 <br />
<br />
Where:<br />
<br />
'''I'''=moment of inertia <br />
<br />
'''ω'''=angular velocity<br />
<br />
"I" depends on the shape of the mass under rotation. In the case of a uniform rod rotating from its end (axis of rotation is at the end of the rod) I = (m*L2)/3<br />
<br />
<br />
“ω” = V/R, where V = tangential velocity and R = radius<br />
<br />
In our case ''moment of inertia'' is equal to (31 400 000 kg*100 000 m2)/3=104 666 666 666 666 666<br />
ω is equal to (50 000 m/sec)/100 000 m=0.5<br />
<br />
So, Kinetic Energy<sub>rotational</sub>=(1/2)*104 666 666 666 666 666*(0.52)= 13 083 333 333 333 333.25 Joules<br />
<br />
Now, how much time and what amount of solar panels will be needed for accelerating this rod? The amount of Solar constant near the Earth is approximately equal to 1300 W/m2 [<sup>8</sup>], with assuming that ''coefficient of efficiency'' of solar panels is roughly 20 % we get 260 Watts per square meters and we can easily link amount energy (that we have already calculated) and power with the time needed. Particularly, ''Energy'' is equal to ''Power''’s multiplication to ''Time'':<br />
<br />
[[File: Formula - Copy.jpg]] <br />
<br />
So, Time is equal to 13 083 333 333 333 333.25 Joules/260 Watts=50320512820512.8 seconds, or 1 595 652 years. If we take much more area for solar panels, for example 10 millions square meters then 0.1595652 years or approximately 58 days will be needed and we think that this is acceptable time span.<br />
<br />
Actually, the time and energy will be needed a bit more for overcoming static friction in electro motor, for overcoming the rarified atmosphere’s resistance (we know that there no absolute vacuum in space), also we should take into consideration electric motors’ coefficient of efficiency that generally reaches 90-95 %, so some energy loss will occur here also. <br />
<br />
Now, what will be the total mass of solar panels producing the energy for Space Catapult? This depends on mass/power ratio, in near future it is expected that very lightweight designs could likely achieve 1 kg/kW [<sup>8</sup>] or 0.260 kg/ 260 W (per 1 square meter), so if for rotating the Space Catapult 10 millions square meters of solar panels are used then their total mass would be equal to 2 600 000 kg. We think that it is too heavy for Space Elevator the mass of which is expected to be equal around several hundred metric tons. If so, we will have to use fewer amounts of solar panels and therefore increase the time needed for accelerating the payload’s speed from zero to designed one. This will not make problems if the rod is accelerated only once and then keeps its constant rotation-for this purpose less energy will be needed and the payload will have to reach the rod’s end by first method as described earlier in this paper (see ''Rod’s plane of rotation towards the Earth'').<br />
<br />
We also need to take into consideration the value of deflection when the rod will be delivered to space by means of Space Elevator (see ''Assembling the Space Catapult''), in this case the thin and long rod will be bent due to its own weight and here we will try to calculate its value. This is quite complex problem that apparently cannot have an unambiguous solution because of many reasons, for example due to various temperatures in atmosphere’s different layers, various humidity and possible wind, but still we will try to calculate the value of ''Deflection'' that will occur in case when the rod’s one end is fastened to Space Elevator’s ascending cabin and the second end is fastened to the transport moving on the land, we discussed this option in above-mentioned section of our paper (see ''Assembling the Space Catapult''). The inclination angle for the rod will vary from 0º (rod is transported horizontally on the ground) to 90º (Space Elevator’s cabins are carrying the rod to space) and here we will discuss some medium case when the rod is semi-elevated in the air, when the angle between rod and ground/cable is equal to 45º. On the engineers’ ''eFunda'' web-site there is online calculator that enables to receive the value of ''Deflection'' (actually that site gives different term for this-''Displacement'') [10]:<br />
<br />
Here we need to enter the relevant values:<br />
<br />
''Length of beam'', ''L'': 100 000 meters<br />
<br />
''Line pressure load on beam'', p: In our case this is the weight per meter length. As we have already mentioned the radius of the rod’s cross-section is 1 meter, so the volume of rod’s 1 meter-length part will be 3.14 cubic meter. In case of using Carbon nanotubes with above-mentioned density-0.1 g/cm<sup>3</sup> the weight will be equal to 314 kg or 3 079 Newton. Since we have got the inclination of 45º we should multiply this value to cos45º- 0.707, so we get 2176 N/m.<br />
<br />
''Young's Modulus'', ''E'': This is equal to 1 000 GPa for Carbon nanotubes [11] <br />
<br />
''Distance from neutral axis to extreme fibers'', ''c'': In our case it is equal to the radius of the rod-1 meter<br />
<br />
''Moment of Inertia'', ''I'': It is equal to (pi*r<sup>4</sup>)/4, so it is equal to 0.785<br />
<br />
According to these initial data the calculator returns extremely high value of Deflection, much higher than the length of the rod itself: -3.61 × 10<sup>9</sup> meters. This result shows us that with the current materials (Carbon nanotubes in our case) it is impossible to raise the rod as ''one single unit'' to space by means of Space Elevator and we need other materials with less density and more ''Young's Modulus'' (or the rod should be much thicker but this will lead to increasing its mass). Therefore, we have got two options: either we should deliver the parts of that rod and then assemble them in space (we have already discussed this option) or completely different technologies for manufacturing the rod should be developed. Particularly, it would be very good if it was possible to manufacture the rod ''in continuous mode'' in vertical position and then uninterruptedly directly to carry it to space by means of Space Elevator’s cabins. Under such approach there will be no ''Deflection'' and several cabins will be able to deliver the rod in space. <br />
<br />
One note about transporting the rod from its place of manufacture to Space Elevator’s base station. We think that this process should be executed by many transports, in other words we are convinced that if the rod is carried by two trains only (or any other kind of transport) then the rod will continuously touch the ground since the ''Deflection'' occurs in any position-horizontal, inclined or vertical and this circumstance will lead to its damage, that’s why several transports will be needed to hold the rod at as many places as possible.<br />
<br />
=Stabilizing the counterweight=<br />
Stabilizing the Space Elevator’s counterweight is very important question during Space Catapult’s performance. Indeed, when the rod rotates it makes the imaginary circles in space and due to rod’s and payload’s masses the Space Catapult’s ''center of mass'' will be continuously shifted and if the counterweight is not somehow stabilized then it will make problems for accurate aiming to certain point at the celestial sphere. Also, if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable then there will be the danger that the rod may actually hit the cable and cut it. To avoid these problems we need to apply to serious measurements. <br />
<br />
First of all, the electro motor’s own axis can be quite long and this will diminish the chance to failure of the whole system. Actually, we are convinced that counterweight’s (where the electric motor will be placed) size will be quite large, mainly due to solar panels’ sizes and amount (this issue was discussed above), also the electromotor should be quite large and powerful to rotate the rod, and hence there will be enough distance between the rod and Space Elevator’s cable. <br />
<br />
The second serious problem is that the center of gravity of the system is not at the center of rotation, therefore it will be necessary to balance the rotating system when the payload is attached and when it is released.<br />
<br />
We think that the Space Catapult’s rod should not be deployed/directed to one side only but some counterweight of it should also exist. This is necessary since the unilaterally loaded (we mean the rod itself plus payload) rod will cause the counterweight to somersault. In other words, the rod should extend to other side and the ''moments of inertia'' of both sides should be the same as during rotating the rod as after releasing the payload when the rod still rotates. This is easily achievable if some additional, second payload is placed on the rod’s second end. Therefore, the Space Catapult will launch two payloads at the same time to the ''opposite'' directions but at various speeds if the second part/side of the rod is shorter.<br />
<br />
How the second payload should be placed on the rod and should we really send two payloads? Until we have got balanced rod this problem does not arise but as soon as the Space Catapult releases the payload this balance will be violated, how it can be restored? There are two theoretical ways for achieving this: reducing the ''mass'' or reducing the ''length''-with diminishing either one of them the ''moment of inertia'' will be decreased. We think that reducing the mass will be less practicable since this would require placing the second payload (spacecraft or anything else) on the rod’s second part and this cannot be done from the Space Elevator’s cabin-this is the easiest way for delivering the payload from Earth to Space Catapult’s rod; so we would have to (see ''Rod’s plane of rotation towards the Earth'') put the second payload on the electro motor and then send it rod’s second part’s end. This is quite complicated task; therefore we can apply to second approach-put some sliding object that will immediately move to electromotor as soon as the spacecraft is released.<br />
<br />
[[File: MOI.jpg]] <br />
<br />
The next problem that may occur is that when the electro motor rotates the rod this motion will make the Space Elevator to rotate to the opposite direction. The same problem arises when helicopter’s primary blade’s rotation forces the helicopter to rotate to opposite direction and this possible rotation is annulled by ''tail rotor''. We think that for balancing the counterweight the additional motor and rod should be installed and this rod should rotate to opposite direction and if their ''angular momentums'' are equal to each other, then their rotations will cancel each other. More precisely, the following equation should be fulfilled:<br />
<br />
[[File: Angular momentum.png]] <br />
<br />
Where ''m'' is mass of the rod, ''v'' is angular speed and ''L'' is rod’s length, the numbers ''1'' and ''2'' refer to first and second rods correspondingly. For balancing both rods’ rotation the multiplication at both sides of the counterweight should be equal, by the way this circumstance enables us to use the second rod with shorter length and even with less mass but rotating at more angular velocity.<br />
<br />
Such approach will effectively deal with other problem which will arise when the Space Catapult releases the payload(s), at this moment the second motor should instantly diminish its angular velocity to some certain level (an ordinary mechanical brakes could be used for this purpose), in this case ''angular momentums'' for both motors/rods will be equal again and Space Elevator’s counterweight will maintain its attitude in space. See the image below depicting the Space Catapult with two electro motors and rods:<br />
<br />
[[File: Two-rods.jpg]] <br />
<br />
Such approach will justify itself if rod’s plane of rotation is parallel to Space Elevator’s cable, but if this plane is orthogonal to cable (see ''Rod’s plane of rotation towards the Earth'') then the second/balancing electromotor cannot be placed under the counterweight because the cable will be cut when rod touches it. Therefore a bit different approach should used and we need to install two/four/eight electro motors with their own relatively shorter rods rotating to opposite direction. They should be placed at the counterweight’s lower side and on its edge (as we suppose the counterweight should be disc) so that their rods not to touch and cut Space Elevator’s cable. Also, total a''ngular momentums'' from these motors should be equal to the ''angular momentum'' from upper motor and thus the counterweight will not rotate and the Space Elevator’s cable will not be twisted. This situation is presented below:<br />
<br />
[[File: Modified-2.jpg]] <br />
<br />
We think that the array of gyroscopes would be also very useful to be installed at the counterweight since they can maintain the attitude of the whole system and this is important for precise aiming to certain point at the celestial sphere. As for the energy required for gyroscopes’ performance it could be received from the array of solar panels which as a result will generally serve Space Catapult’s precise performance.<br />
<br />
=Space Catapult placed at Lagrangian points-the way for gaining subluminal speeds=<br />
<br />
In our paper we discussed the Space Catapult based on the Space Elevator’s counterweight and concluded that this would be convenient when we intend to deliver the payload to space from the Earth. However, such Space Catapult cannot gain very high speeds and therefore we need to choose other way. It is obvious that we need to keep rod’s plane of rotation orthogonally relative to the ''Earth-Sun connecting line'' and hence we should place the rod on the celestial body which will be in synchronous rotation with the Sun but since there is no such body in the solar system we conclude that the Space Catapult for subluminal speeds (the speeds close to speed of light are in mind) should be placed at such point near the Earth where it will be easy to reach it from our planet and where the rotating rod will not hit the Earth and will be always at the same distance from the Sun to avoid the influence of its tidal forces. The examples of such places are '''Lagrangian''' L<sub>1</sub> and/or L<sub>2</sub> points at 1.5 million km away from the Earth. If the Space Catapult is placed at one of these points then its rod can be always orthogonal to the Sun in principle, at the same time it will never collide with the Earth and also it will be quite close to the Earth since 1.5 million km distance is very negligible in space.<br />
<br />
We have got several notes regarding such approach. First, when we mentioned that the rod’s various parts can be at the same distance from the Sun this strictly speaking is not very true because the Sun can be referred as little point where its gravity “comes out” from while the rod is quite long and its initial part (placed at one of the Lagrangian points) will be attracted stronger than the utmost one (for equal attracting the rod should the arc ''with the same curviness as Sun’s surface'' and not straight line); but still this is better than to direct the rod exactly towards the Sun where the tidal forces will try to tear the rod. Second, the Space Catapult should be placed at Lagrangian L1 point which is closer to the Sun than L2 one and therefore receives by 4 % more energy per area from the Sun. Third, the rod should be in constant rotation, this requires much less energy than accelerating it from zero, then stopping it and accelerating it again. Fourth, the existence of the asteroid belt in the solar system between Mars and Jupiter will somehow restrict the actual length of the rod. Indeed, the Space Catapult should be placed at one of the Lagrangian points at 1 AU distance from the Sun while asteroid belt approximately lays at 2.7 AU, from the simple geometry it is obvious that the length of the rod ''almost reaching'' the asteroid belt can be approximately equal to 390 million km, and if the rod is longer then it may simply hit any asteroid within that belt. For 390 million km length rod and for 100 000 m/sec2 acceleration at rod’s end (where the payload will be attached) the maximal speed that the spacecraft can gain will be approximately equal to 200 000 km/sec (two thirds of the speed of light) and this can be considered as enough for practical interstellar spaceflight. Fifth, the spacecraft should be directly put on the rotating rod’s initial end (near electromotor) and then slide towards the other end with its own rocket engines. To achieve this, the spacecraft will have to cover relatively less distance on the rod and then rod’s circular motion will accelerate the spacecraft further-we have already mentioned this in this paper when speaking about deploying the Lunar Space Catapult. This action-putting the spacecraft on the rod will not be difficult since rod’s angular velocity will be quite low due to rod’s huge length, particularly for 400 million km length rod and for 200 000 km/sec linear speed the rod’s angular velocity will be 0.0000796 revolutions/sec.<br />
<br />
[[File: Lagrangian-point.jpg]] <br />
<br />
We have already mentioned that to avoid the destructive influence of the Sun’s tidal forces the rod’s plane of rotation should be orthogonal to the Earth-Sun connecting line. By the way, note that under such approach we may have to wait one year until the Lagrangian Space Catapult occupies the relevant position towards the certain point at the celestial sphere where the spacecraft should be sent to. But from the other hand it would be useful if it is feasible to rotate this whole structure around the imaginary axis directed towards the ''ecliptic poles'' (depicted as faint green dash line on the image above), the reason if this is the possible danger when the rotating rod may hit Mars or asteroids that orbit around the Sun closer than 2.7 AU distance (for example ''433 Eros'' or ''1036 Ganymed''), hence for avoiding such undesired collision the Lagrangian Space Catapult should be slightly rotated by several degrees clockwise/counterclockwise so that the rod not to collide with any celestial object. We are convinced that rotation by several degrees will be absolutely enough measurement due to rod’s gigantic length and relatively less sizes of the celestial objects in the solar system.<br />
<br />
The next issue that we should discuss refers to stability of the Lagrangian Space Catapult placed at L<sub>1</sub> point. As we see this structure will have enormously gigantic size while the Lagrangian point is relatively little mathematical one in space, so what can be done to be convinced that this structure will remain at that point and do not shift aside? The body placed at one of the Lagrangian points is affected by other celestial objects’ gravity and therefore for achieving the balance the rod needs to have the counterweight with more mass if it (counterweight) is shorter. As we clearly see the rod needs the counterweight for two reasons: not to let the Space Catapult somersault and for maintaining it at the L1 point. We think that it would be very useful if the arrays of solar panels act as counterweight since exactly they can give us energy for rotating the rod. Also, we need the second, shorter, perhaps less massive but faster-rotating rod (again-solar panel arrays) the opposite rotation of which would cancel first rod’s rotation, this issue was discussed in this paper. These arrays of solar panels are depicted on the image shown above. <br />
<br />
How such a gigantic structure as Lagrangian Space Catapult can be assembled in space? In our paper we discussed the possible ways for delivering the rod from the Earth to the Space Elevator’s counterweight, now we will try to show that it is possible ''in principle'' to assemble the extra-long rod in space. <br />
<br />
If it is possible from the technical point of view to manufacture extra-long rod then we can use this approach and make 1.5 million km length rod (this is the distance between the Earth and Lagrangian L<sub>1</sub>/L<sub>2</sub> point) that will be mechanically directed to the base station at L<sub>1</sub> point. The capturing devices there will catch the rod and attach it to the electro motor’s shaft after which the rod should be spun by 90º so that it to be orthogonal to Earth-Sun connecting line (for this purpose the additional mechanisms will be needed), this spin is necessary because L<sub>1</sub> point is located on the Earth-Sun connecting line (that is towards the Sun if we look from the Earth) and when directing the rod from the Moon it will lay ''along'' this line while we need across. After this the rod should be slid to another side and then the next rod should be directed to the Lagrangian Space Catapult where it will be attached to the previous rod and etc. In other words, the extra-long rod will be assembled from one side and its length will “grow” from this side to other one, this is necessary because the distance between Moon (the rod should be manufactured exactly there and not on the Earth due to our planet’s relatively more gravity, atmosphere and problematic space debris belt around it) and L<sub>1</sub> point is constant and rod’s parts cannot be more. Due to whole rod’s and its parts’ lengths (400 million and 1.5 million km correspondingly) we think that about 260-270 such operations will be needed to finish assembling the rod (400/1.5). The process of assembling the Lagrangian Space Catapult is shown on the image below:<br />
<br />
[[File: Lagrangian-point-assemble.jpg]]<br />
<br />
=Conclusion=<br />
<br />
As we have seen, for leaving the Solar system and reaching the remote celestial bodies (stars, nebulas) there is no need to develop advanced and complicated technologies that mostly are not capable for gaining extra high velocities nevertheless. In any case, until the Space Elevator is really built (scheduled for construction by 2031) we have got much time for developing the idea of Space Catapult in technical aspect, like finding appropriate materials for the rod, perfect the ways how the Space Catapult can be assembled in space and etc. The concept of Space Catapult itself is the easiest one, does not need developing neither complex and sophisticated technologies, nor some exotic methods (such as ''Gravitoelectromagnetic toroidal launchers'', ''Antimatter rocket'' and etc.) and can be easily implemented in near future; in other words the Space Catapult is not some sophisticated structure that would need profound science research and the fact that it will enable us to gain whatever high speed will justify its developing and building by the humankind. As for other technologies like Ion Drive, they could be used by the spacecraft during flight for other purposes, for example for correcting/changing the flight direction.<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Space_Elevator<br />
<br />
2. http://www.isec.info/index.php?option=com_content&view=article&id=14&Itemid=9<br />
<br />
3. http://www.space-track.org/perl/geo_report.pl (provided data updates regularly, registering is needed) <br />
<br />
4. http://www.oosa.unvienna.org/pdf/reports/ac105/AC105_720E.pdf page 24 (data as at 21 August, 1997) <br />
<br />
5. http://www.amostech.com/ssw/presentations/Session7/S7-1Molotov.pdf page 16<br />
<br />
6. http://www.esa.int/SPECIALS/ESOC/SEMN2VM5NDF_mg_1_s_b.html <br />
<br />
7. http://eetd.lbl.gov/ecs/aerogels/sa-physical.html<br />
<br />
8. http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant<br />
<br />
9. http://www.you.com.au/news/2005.htm, http://www.spacedaily.com/news/ssp-03b.html<br />
<br />
10. http://www.efunda.com/formulae/solid_mechanics/beams/casestudy_display.cfm?case=simple_uniformload<br />
<br />
11. http://en.wikipedia.org/wiki/Young%27s_modulus<br />
<br />
<br />
'''Appendix''': <br />
<br />
Animation illustrating the payload’s departure from the Lagrangian Space Catapult:<br />
[[File: Lagrangian-point-animation.gif]]</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_5&diff=3667OpenSpace 52013-09-21T12:56:14Z<p>Eagle9: </p>
<hr />
<div>== '''Space Catapult''' ==<br />
<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
=INTRODUCTION=<br />
<br />
<br />
The new method for sending the spacecrafts in deep space is presented here. The paper describes the long rod rotated by electro motor placed at the Space Elevator’s counterweight and at Lagrangian points. This simple structure will enable the rod to gain high velocity and carry the payload with it. After reaching the desired speed the rod will release the payload that will fly in space along the imaginary circle’s tangent. This structure we called Space Catapult and it should work with the assist of Space Elevator. This latter should be used for carrying the payload from the Earth to Space Catapult’s rod.<br />
<br />
For exploring the outer space the humankind generally uses the rocket engines, mostly chemical-propelled ones. They enable us the explore near-Earth celestial bodies and other planets in the solar system. They even enabled us to send several deep space missions beyond the solar system such as '''Pioneer-10''', '''Pioneer-11''', '''Voyager-1''', '''Voyager-2''', however by means of this technology the flight lasts undesirably long and it seems to be impossible to reach remote celestial bodies in space such as stars, so new technologies are necessary for this purpose. However new technologies do not necessary imply new kind of rocket engines, such as ''Ion Drives'' because they are capable for gaining several ten times higher speeds only, but for remote celestial bodies even they are not suitable. Besides, they need a huge amount of energy to be stored onboard the spacecraft and this will make additional problems. So, high speed should be achieved with absolutely different approach. How this can be done?<br />
<br />
High speed can be easily achieved by means of fast-rotating rod around the electric motor. The motor’s rotational speed can be very high; the rod also can be quite long, hence the rod’s end’s linear speed can be extremely high, absolutely unachievable for any other technologies nowadays. The payload should be fastened at the rod’s end where the linear speed generally reaches maximal value. After reaching the necessary speed the rod will release the payload that will fly along the tangent from the current position. Thus the electric energy can be turned into payload’s speed and its velocity could be as high as we wish (except the ''speed of light'' of course). In principle the '''Space Catapult''' (thus we call this structure) would be the simplest, the most convenient and direct way for converting the energy/electricity into speed and conveying it to payload. <br />
<br />
As we see the Space Catapult is quite uncomplicated structure, however if we wish to gain high speeds we should deploy it in space, not on the Earth. Indeed, our planet is surrounded with dense atmosphere that impedes any quick motion, so if we rotate the rod quickly the atmospheric drag and generated heat would burn it very soon, therefore the Space Catapult should be built and deployed in space only, and as we suppose-at the Space Elevator’s counterweight. In other words, the Space Elevator’s counterweight will operate as Space Catapult. See image below:<br />
[[File:Space-catapult.jpg]]<br />
Generally, what is the Space Elevator <sup>1</sup> <sup>2</sup>? According to modern concepts it will be the tall vertical structure built on equator and will have height of several ten thousand kilometers with its thin cable fastened to the base station on the Earth and with counterweight placed higher geostationary orbit. Because of balance between centrifugal force and gravity this structure will be stretched and the cabin will move along its cable carrying the goods into high orbit. After delivering the payload, the cabin will descend and carry the next one.<br />
In Space Elevator’s concepts several solutions have been proposed to act as a counterweight: <br />
<br />
1. Heavy, captured asteroid <br />
<br />
2. Space dock, space station or spaceport positioned past geostationary orbit <br />
<br />
3. Extension of the cable itself far beyond geostationary orbit. <br />
<br />
The third idea has gained more support in recent years due to the relative simplicity of the task and the fact that a payload that went to the end of the counterweight-cable would acquire considerable velocity relative to the Earth, allowing it to be launched into interplanetary space. However this idea cannot be completely shared by us due to following reason: <br />
<br />
It is well-known that the values of both '''Orbital''' and '''Escape Velocities''' decreases with increasing the altitude while the '''tangential velocity''' of Space Elevator’s cable increases. We can see the differences between them from the chart presented below:<br />
[[Image: Cxrili.gif]]<br />
<br />
As we see from this chart the ''tangential velocity'' of the Space Elevator even at its end (144 000 or 200 000 km altitude) is not very high to decrease the necessary time for covering the distance from the Earth to remote celestial bodies significantly. To achieve this, even the longer Space Elevator would be needed (its ''tangential velocity'' is directly proportional to its length) and this circumstance would complicate the technical task for building such Space Elevator. Because of this, there is no necessity to extend the cable itself far beyond geostationary orbit as proposed in the third variant. In any case, we have already seen that by means of Space Catapult it is possible to gain such huge velocities that are absolutely unachievable with other technologies, for example with Space Elevator. Therefore, using the counterweight and placing the Space Catapult there definitely has got some technical sense. <br />
<br />
However, we think that the question where the Space Catapult should be placed needs further discussion. Theoretically, the Space Catapult with its payload and nuclear reactor/solar panel needed for rotating the rod may be mounted not only at the counterweight, but on the Space Elevator’s cabin also that can carry all these goods to space in a usual way, as it should do it according to Space Elevator’s modern concepts. This option is quite possible, however for realizing this we need to know the mass of the payload, nuclear reactor/solar panels’ mass plus Space Catapult’s mass from one hand and Space Elevator’s lifting capacity (this ''must'' be more) from other hand, but these data are not available nowadays, therefore we think that the Space Catapult should be still mounted at the Space Elevator’s counterweight where it will be possible to send the payloads into deep space in ''continuous mode'' at high velocities.<br />
<br />
As we saw the Space Catapult is capable to gain very high velocities; however there is being developed other technologies and they in future will enable the spacecraft to fly at high speeds in space. These are Ion Drive systems, more precisely the most perspective one-''Variable Specific Impulse Magnetoplasma Rocket'' (VASIMR) which still under development can be used in future for deep space missions. Can these engines and Space Catapult be the rivals in space? Since none of them have been built and used in space yet we cannot give a persuasive answer to this question; however still it is possible to underline Space Catapult’s one significant advantage: if the future spacecraft uses the VASIMR (or any other kind of Ion Drive) engine it will definitely need to be equipped with nuclear reactor, otherwise the spacecraft will not be able to gain high speeds, also it will need to carry fuel tanks for this purpose. As for the Space Catapult, it can give much higher speed to spacecraft, besides it will have ''stationery'' power plant (see ''Energy source placed on the Space Elevator’s counterweight'') at the Space Elevator’s counterweight, so the payload will ''not'' have to carry the nuclear reactor onboard and this circumstance will lighten the work for deep space spacecraft. Besides, we should not forget that unlike the spacecrafts equipped with ion drive engines the Space Catapult will need no fuel for gaining high velocities. <br />
<br />
Briefly, Space Catapult’s advantages over any kind of propulsion systems are: <br />
<br />
1. Ability to gain any speed that is absolutely unachievable by means of other kinds of engines. <br />
<br />
2. No need by spacecraft to carry energy source that would make it too heavy and impracticable.<br />
<br />
=The Space Catapult needs long rod=<br />
<br />
When building the Space Catapult at Space Elevator’s counterweight we should install quite long rod there, the shorter the rod is, the easier would be installing it, however we should note that rod cannot be extremely short, let’s say 1 km length or so due to following reason:<br />
<br />
When we are going to send some payload into space, we need not only high velocity, but one certain direction also. The little inaccuracy in direction, inclination in several arcminutes is actually acceptable since the spacecraft would easily balance it with its engines; however great inclination from the initial direction would send the spacecraft into the completely different direction and in such case the whole mission will fail.<br />
<br />
If two Space Catapult’s rods have the length of let’s say 1 kilometer and 10 kilometers, then for giving to payload some certain linear speed (for instance 100 km/sec) these rods should rotate at different angular velocity. It is easy to ascertain that the shorter rod should rotate 10 times faster to gain the same linear speed than the rod with more length. But the faster the rod rotates, the more difficult will be to “catch” the needed moment for releasing the payload from the rod for sending it towards some certain direction. If the rod is too short, then it has to rotate very quickly for gaining some certain linear speed and therefore it will be extremely difficult catching the needed moment for releasing the payload. Hence, too short rod can make problem for sending the payload to some certain direction in space especially at high velocities. So, based on payload’s needed velocity we should find rod’s desired, minimal length that will enable us to send the payload in space to necessary direction without fear that it may yaw from the course. <br />
<br />
However, rod’s length will be crucial for payload’s abilities for withstanding the acceleration also. As an example, we can try to calculate its value which the payload will have to withstand during rod’s rotation. The acceleration of the body rotating at the circle with some constant velocity is calculated by the following formula:<br />
<br />
[[File: Acceleration - Copy.jpg]] <br />
<br />
Where a is acceleration in ''m/sec''<sup>2</sup>, ''v'' is payload’s linear velocity on the circle in ''m/sec'' and ''r'' is radius of the circle in ''meters'', in our case it is equal to rod’s length. Let’s assume that the rod is 100 km length and the electromotor rotates it so that payload’s speed is equal to 50 km/sec, in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design and manufacture the spacecraft’s subsystems (avionic and etc.) capable to withstand such acceleration. This circumstance somehow restricts the speeds that we can achieve, in any case their values actually depends on spacecrafts’ abilities for withstanding g-loads. But what can we do if much higher speeds are needed? The answer directly derives from that formula: the radius should be more; by the way note that this is additional reason why the longer rod is more useful. If we are able to make the extra long rod, then this will enable us to gain much higher velocities. <br />
<br />
What material should be used for manufacturing the rod? It is obvious that if very high speeds are needed the rod should be long and even in this case the acceleration at its end will be quite high, therefore ''sufficiently strong and light materials'' are needed for this purpose and making them is as similar challenge as in case of Space Elevator where the same requirements arises for the cable’s material. The lightness is needed because in case of heavy rod a lot of energy will be needed to rotate it; the strength is needed because in case of lack this property the rod will be destroyed due to great acceleration.<br />
<br />
=The mechanism for holding and releasing the payload=<br />
<br />
How the payload can be held by Space Catapult’s rod during rotation and how it can be released from the rod? We think that using ''electromagnet plus mechanical holding devices'' would be a good solution. More precisely, after the payload is attached to the rod it must be held by means of both methods until the rod accelerates and reaches necessary velocity (it may take even several days), but with approaching the desired speed the mechanical device should release the payload however the electromagnet(s) should still hold it. The explanation of such approach is following: generally the mechanical devices are much slower/sluggish in performance than electronic ones. We have already said that when releasing the payload the extreme accuracy is needed and mechanical devices cannot guarantee ''the exact time of releasing'' the payload unlike electronic ones. That is, it’s unlikely that mechanical devices can release the payload at some certain moment when needed while in case of electromagnet it would be enough to cease electric current there, it would lead to immediate vanishing of the magnetic field and sending the payload along the tangent from the point where the payload would be at the current moment. <br />
<br />
<br />
We think that the ''fastest control system'' would enable to release the payload to certain direction. This system (extremely fast-operating computer plus measuring equipments) should know the current position of the rod’s end, the current speed, the needed direction and be capable for computing the necessary moment for giving the order for diminishing the voltage for electromagnets and hence releasing the payload to desired direction and velocity.<br />
<br />
=Rod’s plane of rotation towards the Earth=<br />
<br />
The Space Catapult’s rod when rotating makes the circular plane/flatness in space and this plane may be horizontal/parallel to Earth surface, that is making the right angle to Space Elevator’s cable or it may be placed along the cable; see the both possible situations here:<br />
<br />
[[File: Planes-of-rotation - Copy.jpg]] <br />
<br />
Both approaches have got their advantages/disadvantages and here we will discuss this question, first of all from the point of view of safety.<br />
<br />
For gaining extremely high velocities quite long rod would be needed, maybe with the length of several thousand kilometers or even more. If such rod is placed ''along'' the Space Elevator’s cable then the rod during rotation will cross many orbits from the ''Medium Earth Orbit'' to ''High'' ones. When rotating, the rod may actually hit any satellite and/or space debris object and such collision can lead to rod’s complete destruction; therefore we should choose such plane which would be much more free from any artificial objects; hence if the rod rotates ''horizontally/parallel'' to Earth’s surface at high enough altitude where the satellites’ population is relatively low then this measurement would justify itself because under such circumstance the rod will not cross satellites’ orbits (rod’s plane of rotation will simply coincide to ''one'' orbit’s path). However, we should also note that this altitude actually depends on the Space Elevator’s proposed length. Indeed, the Space Catapult’s rod should be mounted at the Space Elevator’s counterweight; this counterweight from its side should be placed at the end of the Space Elevator at such altitude where the satellites’ population is as low as possible. This means that Space Elevator’s proposed height should be agreed with mounting Space Catapult on its counterweight. According to various databases the number of man-made objects at high orbits, more precisely beyond geostationary orbit is much less than on the lower orbits <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup>, therefore the Space Catapult with its rod should be located at the altitude of 50 000-60 000 km above the sea level. At such altitude the space is almost free and nothing will impede rod’s rapid rotation. Besides, the satellites at high orbits are orbiting around the Earth slower than on the lower orbits (as known any satellite orbits around its primary body slower in apogee than in perigee), therefore if some tracking system is mounted at Space Elevator’s counterweight then it will enable the Space Catapult to avoid undesired collision with satellites during Space Catapult’s performance. In other words, the Space Catapult should operate only when the there are no satellites near its vicinities.<br />
<br />
Now we will try to discuss this question from other side.<br />
<br />
How the payload can be transferred from the Space Elevator’s cabin to the Space Catapult’s rod? One way is following: cabin reaches the counterweight where the payload will be released, then payload will be mechanically conveyed to rod, continues its way ''on the rod'' (like the train rides on the rails) and after reaching rod’s end it stops, the rod begins rotating and after gaining necessary linear speed it releases the payload to needed direction. This method is generally realizable; however it seems to be too complicated and unpromising compare to the second one: the Space Catapult’s rod is stopped in space so that it to be directed downwards to the Earth and be parallel to Space Elevator’s cable. The Space Elevator’s cabin moving along the cable with payload stops at the cable ''near'' the end of the Space Catapult’s rod and releases the payload that will fly to the rod, attaches itself to the rod’s end (here the electromagnets would be useful), the rod begins rotating and after gaining needed linear speed will release the payload to necessary direction.<br />
<br />
This second way seems to be more promising because the first one is much more complicated as we have already said: first of all there would be needed some mechanical devices for transferring the payload from the Space Elevator’s cabin to counterweight, the counterweight should have the hole for the payload to move through it from below (we should not forget that the Space Catapult should be mounted ''at'' the counterweight, not ''beneath'' it), besides the rod should be made so that it to have some conveying surface (rails for instance) the payload to move on it. As we see it would be much more convenient if it is possible to convey the payload from the cabin to the rod directly and this would be feasible under the second method which is depicted below:<br />
<br />
[[File: Convey.jpg]] <br />
<br />
One more aspect regarding Space Catapult’s position. This structure, its rod, its electro motor and etc should be mounted at Space Elevator’s counterweight so that the rod to be placed westwards from the cable. The reason of it is following: when the Space Elevator’s cabin stops and releases the payload (which should fly to Space Catapult’s rod) the current speed of which will/should be more than the value of the ''Orbital/Escape Velocity'' at the current altitude. After releasing the payload will fly westwards and upwards because its orbit will be ellipse, under ellipse the payload will fly higher to apogee and at the speed less than Space Elevator’s current speed at the given altitude, in other words the released payload will “lag behind” the Space Elevator’s cable; therefore payloads’ ''stopping points'' at the cable and Space Catapult’s rod’s length should be calculated and chosen so that the payload to fly directly towards rod’s end. This process would be feasible in both cases-if the rod’s plane of rotation is parallel to Earth’s surface and if it is placed along the cable-but still this would be easier for the payload to achieve the rod’s end if the rod is placed along the cable because at least the distance that the payload should cover in space will be less.<br />
<br />
The length of the Space Catapult’s rod placed at the Space Elevator’s counterweight might vary since for various spaceflight purposes different initial speed will be needed and relatively low speed could be achieved by means of shorter rod. Because of this reason it might be necessary to change Space Catapult’s rod’s length, therefore it would be useful if the rod consists of two parts where the first part would be perpetually attached to electro motor and the second one will be attached to the first part if necessary. For this operation Space Catapult’s rod should be placed along the cable since the relative nearness would make this operation quite easy and it could be accomplished by the crew directly from the Space Elevator’s cabin stopped at the needed altitude. <br />
<br />
For deciding the question how the Space Catapult’s rod should be placed towards the Space Elevator’s cable we should take into consideration one substantial circumstance-to which direction do we plan to send the payload in space by means of Space Catapult? This circumstance will influence deciding this problem due to following reason:<br />
<br />
In case ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and if rod’s plane of rotation is parallel to Earth equator, then this plane will be orthogonal to Earth’s rotation axis. This axis from its side is tilted to ''ecliptic plane'' by 66° 34'. This means that Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 23°26'. Here follows very important consequence: under above-mentioned conditions the rod when rotating will be capable for covering only the part of the ''celestial sphere'' from 0° to 23°26' (counted from ''ecliptic plane'' northwards and southwards to ''Ecliptic poles''). This is about one fourth of the ''celestial sphere'' (23°/90°), this will not make problems if we intend to use the Space Catapult for exploring the solar system’s planets because their orbits’ tilts towards ''ecliptic plane'' do not exceed 7° (for planet Mercury, for other planets this tilt is even less); however we will not be able to send the payload for example to the nearest star ''Alpha Centaurs'' because this star is located at -42 degree according to ''ecliptic coordinate system'' in the celestial sphere.<br />
<br />
The situation will drastically change ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and ''if'' rod’s plane of rotation is orthogonal to Earth’s equator and therefore parallel to Earth’s axis of rotation. We have already discussed this option when we mentioned that the rod should be placed westwards from the cable and explained why it would be useful-for delivering the payload from Space Elevator’s cabin to Space Catapult’s rod. Under such conditions the Space Catapult will be capable to aim to any point on the ''celestial sphere''. Indeed, the Earth with the Space Elevator rotates around its axis and Space Elevator’s counterweight draws an imaginary circle in space. This circle is tilted to ''ecliptic plane'' at 23°26' and crosses this plane in two point called ''ascending'' and ''descending nodes''. The other points that are 90° away from these nodes we call point(s) of ''maximum elevation/depression'' (relative to ''ecliptic plane''). When the Space Elevator is at a''scending/descending node'' its rod and hence the payload can be directed to any point from 0º to 66º on the celestial sphere northwards and southwards from ecliptic plane. This makes about 75 % of celestial sphere. See the image depicting this situation:<br />
<br />
[[File: Node.jpg]]<br />
<br />
But when the space Elevator reaches the points of ''maximum elevation/depression'' then its rod during rapid rotation may be directed to any point from southern ''Ecliptic pole'' to ''Northern pole'' at the celestial sphere because at these points rod’s ''plane of rotation'' is orthogonal to ''ecliptic plane'' and thus the rotating rod can aim to ecliptic poles as well as other points. See this situation below:<br />
<br />
[[File: Elevation.jpg]] <br />
<br />
The situation will be similar if the Space Catapult’s rod is orthogonally placed towards cable. Under such approach Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 66° 34' and the Space Catapult will be capable to cover ''three fourths'' (66°/90°) of the ''celestial'' ''sphere'' when the Space Elevator is at the points of ''maximum elevation/depression'' and the whole celestial sphere when the Space Elevator is at ascending/descending nodes. For aiming the needed point on the celestial sphere the Earth should occupy the appropriate attitude towards the stars during the revolution around its axis, the same thing should be done under previous case described in the paragraph above. <br />
<br />
In conclusion, thinking about rod’s plane of rotation towards the Earth, we should note one important difference between above-mentioned approaches: if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, then in case of emergency during Space Catapult’s performance (for example if the Space Catapult’s rod is cut by sudden meteorite bombardment) the rod’s part with the payload may simply crash to the Earth at huge velocity if the rod at this moment is directed to the Earth. This cannot happen if Space Catapult’s rod’s plane of rotation is orthogonal to Space Elevator’s cable because payload’s rotational path will not be directed towards the Earth and hence its flying trajectory will never cross the Earth.<br />
<br />
=Braking the Space Catapult’s rod=<br />
<br />
After releasing the payload at necessary speed and direction, the Space Catapult’s rod will have a huge angular velocity that needs to be decreased to zero in order the Space Catapult’s rod to get another payload in motionless position and then to send it to space. <br />
What methods can we use to reduce Space Catapult’s rod’s rotation to zero? There are several possible ways: <br />
<br />
1. The electromotor designed for accelerating the rod may actually play a role of brakes, more precisely after releasing the payload to space the electromotor should operate/rotate in the opposite direction, hence rod’s rotational speed will be diminished to zero after that electromotor will stop operating. Under such method a bit less energy will be spent for decelerating the rod than in case of accelerating because when decelerating the rod is free from payload. <br />
<br />
2. An ordinary mechanical brakes, however due to electro motor’s and rod’s sizes a huge brake(s) would be needed to be installed on the Space Elevator’s counterweight and this circumstance would make additional problems from the engineering point of view. Nevertheless, we should admit that under such method we would not need as much energy as during accelerating; on the contrary, in this process the heat will be emitted as it generally happens during braking. <br />
<br />
3. For decelerating the rod we can use the well-known phenomenon in physics-''electromagnetic induction'': when the c''onductor/ closed circuit'' moves into the magnetic field the electric current is generated there. In case of Space Catapult we can use this phenomenon in the following manner: the conductor should be wrapped around the whole length of the rod like a helix and there should be possibility that this conductor to be turned into the ''closed circuit'' by means of mechanically connecting its ends (see the image below). After releasing the payload at necessary speed and direction this circuit should be closed, then according to ''electromagnetic induction'' the electric current will be generated in the conductor and the energy of this electric current will come from rod’s kinetic energy. Therefore, inducted electric current in the enclosed circuit will force this circuit and rod to lose kinetic energy and speed. The part of the generated electric current will be spent in prevailing conductor’s electric resistance:<br />
<br />
[[File: Helix.jpg]] <br />
<br />
The advantage of this method is that for decelerating the rod no energy will be required, as for drawback-much time will be required for this purpose because at the altitude of several ten thousand kilometers the Earth’s magnetic field is quite weak and the effect described in the paragraph above will need much time to operate and give necessary result. <br />
<br />
4. The above-described third method could be realized in a bit different way: if the conductor wrapped around the rod is a closed circuit and if we conduct the electricity there then the electric current will generate its own magnetic field that will counteract with Earth’s one. More precisely, according to ''Lenz's law'' induced current’s magnetic field will be in such a direction as to oppose the motion or change causing it, in other words induced current’s magnetic field will counteract outer magnetic field’s any change and this will cause decelerating rod’s rotation and finally its stopping. <br />
<br />
5. The obvious disadvantage of the third and fourth method described above is weakness of the Earth’s magnetic field because of which decelerating the rod may be delayed in time. For solving this problem we can create artificial magnetic field by means of electromagnets. Particularly, one electromagnet should be placed at the Space Elevator’s counterweight, very close to Space Catapult’s rod. The second electromagnet should be placed directly on the Space Catapult’s rod close to first electromagnet (actually, instead of this second electromagnet there could be used the conductor wrapped around the rod as we described above in previous methods). The reason of this nearness is that magnetic field generally weakens directly proportional to distance’s third power and much time will be needed for decelerating Space Catapult’s rod if two electromagnets are far from each other.<br />
<br />
This method probably will consume the most amount of energy but at the same time it will be the most effective because it does not depend on outer factors such as Earth’s magnetic field which is quite weak at the altitude of several ten thousand kilometers above the sea level. <br />
<br />
Eventually, which methods for decelerating the Space Catapult’s rod would be the best? As we see each one of them have got their advantages and disadvantages. We can state that we should choose one of them according to spaceflight’s profile and goal. Particularly, if we decide to send the spacecraft into the deep space mission where especially high speed is necessary then in this case ''longer/more massive'' rod would be needed rotating at very high speed. Under such circumstance much energy will be needed for accelerating/decelerating the rod. We should also take into consideration the fact how frequently the Space Catapult will operate, in other words how mane payloads it will have to send into space per some certain amount of time, week/month and etc. If time interval between two following missions is relatively high then we should choose the method that will consume less energy and more time for decelerating the rod. On the contrary, if the Space Catapult has to send payloads very often then we should choose the method that will consume more energy and enable the rod to decelerate faster. In other words, we should find ''golden mean'' between consuming time and energy. We should also take into account how much energy supply will be produced at the Space Elevator’s counterweight (see ''Energy source placed on the Space Elevator’s counterweight'') and what part of this energy can we spend for accelerating/decelerating the rod.<br />
<br />
The rod’s rotations can be decelerated much faster than accelerated; the reason of it is that when accelerating the rod has got some sophisticated device as payload and generally unmanned spacecrafts are capable to high g-loads, but still for them some restrictions exist. After the payload is released at needed direction and speed, the rod can decelerate much faster because the rod itself is quite simple device without any complex and sophisticated details. <br />
<br />
We can actually use several methods, such as the third one and then the first/fifth ones. This would be justified because of following reason: as we have already said when decelerating with the third/forth method the problem of weakness of the Earth’s magnetic field would occur, therefore much time would be necessary for described method(s) to perform and give us result. However, we should note that in the beginning when the rod rotates very quickly this method would still operate strong enough. This derives from Faraday's law of induction stating that “the electromotive force generated is proportional ''to the rate of change of the magnetic flux''”. Therefore, in the beginning when the rod is rotating very quickly we can use the third/forth method(s) and when the rod significantly brakes we can apply to the first/fifth ones-they do not depend on Earth magnetic field. In other words, such approach would greatly help us in finding the golden mean between spending energy and time necessary for decelerating the rod. <br />
<br />
And finally: after releasing the payload the Space Catapult’s rod can actually give us energy. More precisely, the electro motor itself can serve as electric generator also since we know that the same machine can operate as electric motor if it is fed with electricity and as generator for electricity if its rotor is rotated by other machines. Therefore after releasing the payload when the electro motor’s rotor is rotating very quickly it can give us energy, in result of which the rod will lose its kinetic energy and speed, as for generated energy it can be sent downwards to the Earth for our terrestrial needs (see the next section in this paper) or stored onboard the Space Elevator’s counterweight. This approach has got one substantial advantage: it does not imply additional mass (wrapped wire) that will cause problems because rotating heavier rod would consume more energy.<br />
<br />
=Energy source placed on the Space Elevator’s counterweight=<br />
<br />
As well-known, the Space Elevator’s cabin needs energy when moving along the cable and it can get it from the Earth by means of various ways, such as: laser beam, microwaves, through the cable itself and etc. On the other hand, Space Catapult also needs much energy for rotating the rod and for this purpose some energy source should be placed on the Space Elevator’s counterweight, presumably solar panels array. Doing this would demand additional funding and engineering work and this undertaking should be justified, so how can we prove that placing energy source on the counterweight would be necessary and useful? We should not forget that the energy generally could be simply transmitted from the Earth without carrying any material for energy source on counterweight; so we can justify this undertaking if we declare/prove that: <br />
<br />
1. Energy source should be designed for ''both'' Space Elevator’s cabin and Space Catapult’s rod. We can imagine it as array of numerous solar panels producing enough energy for both above-mentioned constructions. For this purpose solar panels would be better solution than nuclear reactor because they do not need nuclear fuel to be carried from the Earth to counterweight, also they are capable for producing energy in a continuous mode. By the way this circumstance will enable us to send the payload to space by Space Catapult whenever we want without depending existence nuclear fuel at the counterweight. <br />
<br />
2. Transmitting energy from the counterweight (“from above”) is better and advantageous than doing the same thing from Earth (“from below”). Indeed, when we try to transmit energy (laser or microwave beam) from the Earth to ascending cabin, the part of energy is inevitably lost and dispersed in the Earth’s atmosphere and (this is point of the question) this continues during the whole process of ascent. On the contrary, when transmitting the energy from counterweight to cabin the energy will be lost only on the little part of this voyage, more specifically until the cabin leaves the atmosphere (100 km in height) and when cabin leaves it the energy will be transmitted in vacuum without loss. <br />
<br />
3. For receiving the energy from the Earth the huge solar panels (in case of laser beam) or antennas (in case of microwaves) will be needed to be mounted on the counterweight and this is additional mass and additional engineering work.<br />
<br />
We think that these arguments given above are enough for shoving that placing energy source on the Space Elevator’s counterweight have advantages over transmitting energy from the Earth and as conclusion we can state that energy source on counterweight would serve both space transportation systems-Space Elevator and Space catapult. <br />
<br />
As addition, we could use the energy produced on the counterweight for terrestrial needs also. Indeed, there have been developed numerous projects for receiving energy from space since 60-ies implying producing it by means of solar panels and then transmitting to the Earth. Combining all these three goals we can conclude that placing solar power plant on the Space Elevator’s counterweight would be triply useful and advantageous. In other words, when the Space Catapult and Space Elevator do not function, the energy produced on the counterweight should be directly transmitted to the Earth for our terrestrial needs and thus the idea of Space Elevator, Space Catapult and space power plant will be combined in one project.<br />
<br />
=Assembling the Space Catapult=<br />
<br />
Assembling in space such a huge structure as Space Catapult will not be an easy task from the technical point of view and definitely needs special engineering approach. Besides, we think that Space Catapult’s rod should be mounted at the Space Elevator’s counterweight separately from every other parts of the Space Catapult (e.g. electro motor and etc.); this circumstance is caused by rod’s gigantic sizes. More precisely, electric motor and plus any other equipments necessary for Space Catapult’s performance should be delivered to space by means of Space Elevator in a usual way; as for Space Catapult’s rod, it is a different matter and it should be delivered and mounted separately in the end. <br />
<br />
Eventually, Space Catapult’s rod will be quite long, perhaps much more than 100 kilometers. It is obvious that delivering such a long rod as ''one single unit'' would be quite difficult task; also it is possible that due to its total mass the Space Elevator’s cabin will not be able to deliver such rod at all, but we have already mentioned that the Space Catapult may have the rod with various length; more precisely the rod may consist of two/more parts. In such case these parts should be delivered towards the counterweight separately and then assembled. <br />
<br />
But the Space Elevator’s cabin can actually deliver the Space Catapult’s rod as ''one single unit'' in space. We think that this would depend only on rod’s mass. The Space Elevator’s lifting capacity is not well-known yet; however apparently it will not exceed one hundred metric tons and if Space Catapult’s rod is made of extra light material then cabin will be able to deliver it in space and in such case the following question will arise: how the cabin will deliver such a huge object in space without any damage?<br />
<br />
This can be done by means of two cabins. Generally, Space Elevator’s conception implies only one cabin moving along the cable, but for some special purpose (like delivering Space Catapult’s rod in space) we can use the second cabin also that will descend downwards after finishing its job and will not participate in Space Elevator’s further performance. As for the process of delivering the rod, we can imagine it in a following manner: at first the rod will be placed horizontally on the Earth (thus it must be manufactured and then transported to the Space Elevator’s base station), then the Space Elevator’s first cabin will carry rod’s one end along the cable while the rod’s second end will be moved on the Earth so that the rod to take more and more vertical position. When the rod is in vertical position the second cabin will capture rod’s second end and will carry it in space. We think that without the second cabin it would be quite difficult for one cabin only to carry long/heavy rod because the rod may actually shake and crash to the Space Elevator’s cable and this is absolutely undesirable. <br />
<br />
So, as we see in principle it looks to be quite easy, however the assembling may complicate due to rod’s length. In this case it would be better to carry not the rod as ''one single unit'' but its parts and then to assemble them in space in the following manner: ''two'' cabins will carry the first part as described above, when this part is delivered to space and temporarily hung at the cable the next two cabins will carry the second part that will be attached to the first one from below; the other parts will be delivered to space and assembled into the rod in the same way. <br />
<br />
The obvious disadvantage of the above-described method is that each part needs two cabins on the Space Elevator’s cable, besides the humans will be needed for assembling the rod from these parts in the atmosphere’s upper layers; therefore we think that the first way-delivering the rod into space as one single unit still would be easier and more realistic; besides we should take into consideration the fact that if the rod is assembled the additional devices will be needed ''on the rod itself'' for joining these parts and this circumstance would lead to increasing the rod’s total mass and this is undesirable. See the image showing assembling process:<br />
<br />
[[File: Assembling.jpg]] <br />
<br />
Whatever design/structure the rod has-assembled from several parts or as one single unit, it must be delivered to its destination-Space Elevator’s counterweight and must be fastened to electro motor’s own axis. But the problem is that the rod will be quite long and also the fact that Space Catapult’s electro motor will be placed at counterweight’s upper side (or at the ''lateral'' side if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), so it will be necessary the rod coming from below to be moved to counterweight’s upper/lateral side, besides the rod should be docked with electro motor’s axis as accurately as possible. How is it possible to realize such complex engineering operation? Here we can indicate one possible theoretical way: <br />
<br />
The rod will be parallel to Space Elevator’s cable when carried by cabin, but later the cabin’s mechanisms should rotate it so that the rod to be orthogonal to Space Elevator’s cable (this will not be necessary if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), exactly in this position the rod should be delivered to counterweight, besides the rod when moving along the cable should be shifted a bit upwards (relative to the Earth) than the cabin itself. Under such conditions we will easily achieve docking the rod to electro motor’s own axis which from its side should have some trapping device (magnetic for example) to “catch” the rod and thus guarantee docking the rod to electro motor and finishing assembling the Space Catapult as a whole. But if the rod’s plane of rotation is parallel to cable then assembling process will be much easier because the ascending rod may directly dock to electro motor’s own axis. See the image showing this process:<br />
<br />
[[File: Deliver - Copy.jpg]] <br />
<br />
We think that it would be useful if one Space Elevator is built specially for Space Catapult with its base station located on the land, not the ocean. This would be justified because transporting Space Catapult’s rod from its place of manufacture to Space Elevator’s base station should occur on the land by means of several transports simultaneously (due to rod’s great length), this will enable us to deliver the rod to its destination without any damage while this kind of operation is hardly possible on the water.<br />
<br />
=The technical aspects regarding the Space Catapult=<br />
<br />
As an example, we can try to calculate/ascertain all possible kinds of aspects regarding the rod with some certain mass and sizes, for example we can assume the Space Catapult has got 100 km length rod. <br />
<br />
The circumference of the circle that this rod’s end will draw in space will be equal to 2πr=628 km. As we have already mentioned payload’s abilities for withstanding the g-load is restricted, so if the electromotor rotates the rod so that payload’s speed is equal to 50 km/sec (this means that it will take 12.56 seconds for the rod to make one complete revolution), in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design the spacecraft that will withstand such acceleration, but what about the rod itself? Which material can be used for designing this rod, what will be its mass and how much energy and time will be needed for the rod to reach this velocity? <br />
<br />
For manufacturing the rod we should choose the material with very low density and highest value of strength. Currently, the ''Carbon nanotubes'' are the best candidates for this purpose. What will the mass of the rod made of this material? This depends on width also and it should be as less as possible (otherwise the rod will be too heavy and too wide for transporting from manufacture place to Space Elevator’s base station and for delivering it to space by means of Space Elevator) but from the other hand the ''applied load'' will not let us to design very narrow rod.<br />
<br />
Let’s assume that we intend to launch the payload with the mass of 10 000 kg (during calculation we will use ''SI system'' only). To clarify what kind of material will be able to withstand the acceleration we should calculate and then compare two values: the ''applied load'' and ''tensile strength''. For calculating the first one we should multiply g-load (which we already know-2 550 g) to its mass-10 000 kg, we will get 25 500 000. As for calculating tensile strength, we should take its values (for Carbon nanotubes it varies from 11 000 MPa to 63 000, we will take some medium value-40 000 MPa) and multiply it to cross-section’s area, in our case rod is cylinder with circular cross-section. If radius of cross-section is 1 meters then its area is 3.14 square meters, multiplying this value to value of tensile strength (40 GPa as said) we will get 125 600 000 000 and this is significantly more than value of applied load-25 500 000. Of course, we should also take into consideration ''factor of safety'' which is generally equal to 2 and this indicates us that for safety the payload’s actual mass should be twice less but in our case as we see the rod will be able to accelerate the payload to above-mentioned speed. By the way, note that if that g-load ''2 550 g'' is almost at the payload’s withstanding limit this is not serious problem for the rod itself (we have already seen that value of tensile strength is much more than value of applied load) and this is clear why: payload generally contains sophisticated equipments (electrical circuit, optics an etc.) that will not be able to withstand very high g-loads while the rod will be made of some continuous solid substance, Carbon nanotubes is this case and of course it will be able to withstand much higher g-loads.<br />
<br />
<br />
What will be the mass of such rod? Knowing its volume (for this purpose its cross-section’s area 3.14 square meters should be multiplied to rod’s length-100 000 meters, we get 314 000 cubic meters) and taking the value of density (this also varies for Carbon nanotubes from 0.037 to 1.34 g/cm<sup>3</sup>, let’s take 0.1 g/cm<sup>3</sup>) we get rod’s mass as 31 400 000 kilograms. This is too heavy for Space Elevator’s modern concepts and for improving this situation we should either use many cabins for raising the rod as single unit or use nuclear energy for feeding the cabins instead of laser/microwave beams or deliver the rod’s parts separately in space and then assemble them (see ''Assembling the Space Catapult''). But if some advanced substances are chosen for this purpose (for example ''Silica aerogel'' the density of which is about 1.9 mg/cm<sup>3</sup>, this is 50 times less than the density of the Carbon nanotubes taken above-0.1 g/cm<sup>3</sup>) than problem may be lightened in spite of the fact that their current tensile strength is quite low-16 kPa for the density of 0.1 g/cm<sup>3</sup> <sup>7</sup>. So, we can conclude that we need the material with the density of ''Aerogels'' and tensile strength of Carbon nanotubes.<br />
<br />
How much energy and time will be needed for the rod to accelerate from zero to desired speed-50 km/sec? The amount of rotational energy of the rotating rod can be calculated by the following formula:<br />
Kinetic Energy<sub>rotational</sub>= (1/2)*I*ω2 <br />
<br />
Where:<br />
<br />
'''I'''=moment of inertia <br />
<br />
'''ω'''=angular velocity<br />
<br />
"I" depends on the shape of the mass under rotation. In the case of a uniform rod rotating from its end (axis of rotation is at the end of the rod) I = (m*L2)/3<br />
<br />
<br />
“ω” = V/R, where V = tangential velocity and R = radius<br />
<br />
In our case ''moment of inertia'' is equal to (31 400 000 kg*100 000 m2)/3=104 666 666 666 666 666<br />
ω is equal to (50 000 m/sec)/100 000 m=0.5<br />
<br />
So, Kinetic Energy<sub>rotational</sub>=(1/2)*104 666 666 666 666 666*(0.52)= 13 083 333 333 333 333.25 Joules<br />
<br />
Now, how much time and what amount of solar panels will be needed for accelerating this rod? The amount of Solar constant near the Earth is approximately equal to 1300 W/m2 [<sup>8</sup>], with assuming that ''coefficient of efficiency'' of solar panels is roughly 20 % we get 260 Watts per square meters and we can easily link amount energy (that we have already calculated) and power with the time needed. Particularly, ''Energy'' is equal to ''Power''’s multiplication to ''Time'':<br />
<br />
[[File: Formula - Copy.jpg]] <br />
<br />
So, Time is equal to 13 083 333 333 333 333.25 Joules/260 Watts=50320512820512.8 seconds, or 1 595 652 years. If we take much more area for solar panels, for example 10 millions square meters then 0.1595652 years or approximately 58 days will be needed and we think that this is acceptable time span.<br />
<br />
Actually, the time and energy will be needed a bit more for overcoming static friction in electro motor, for overcoming the rarified atmosphere’s resistance (we know that there no absolute vacuum in space), also we should take into consideration electric motors’ coefficient of efficiency that generally reaches 90-95 %, so some energy loss will occur here also. <br />
<br />
Now, what will be the total mass of solar panels producing the energy for Space Catapult? This depends on mass/power ratio, in near future it is expected that very lightweight designs could likely achieve 1 kg/kW [<sup>8</sup>] or 0.260 kg/ 260 W (per 1 square meter), so if for rotating the Space Catapult 10 millions square meters of solar panels are used then their total mass would be equal to 2 600 000 kg. We think that it is too heavy for Space Elevator the mass of which is expected to be equal around several hundred metric tons. If so, we will have to use fewer amounts of solar panels and therefore increase the time needed for accelerating the payload’s speed from zero to designed one. This will not make problems if the rod is accelerated only once and then keeps its constant rotation-for this purpose less energy will be needed and the payload will have to reach the rod’s end by first method as described earlier in this paper (see ''Rod’s plane of rotation towards the Earth'').<br />
<br />
We also need to take into consideration the value of deflection when the rod will be delivered to space by means of Space Elevator (see ''Assembling the Space Catapult''), in this case the thin and long rod will be bent due to its own weight and here we will try to calculate its value. This is quite complex problem that apparently cannot have an unambiguous solution because of many reasons, for example due to various temperatures in atmosphere’s different layers, various humidity and possible wind, but still we will try to calculate the value of ''Deflection'' that will occur in case when the rod’s one end is fastened to Space Elevator’s ascending cabin and the second end is fastened to the transport moving on the land, we discussed this option in above-mentioned section of our paper (see ''Assembling the Space Catapult''). The inclination angle for the rod will vary from 0º (rod is transported horizontally on the ground) to 90º (Space Elevator’s cabins are carrying the rod to space) and here we will discuss some medium case when the rod is semi-elevated in the air, when the angle between rod and ground/cable is equal to 45º. On the engineers’ ''eFunda'' web-site there is online calculator that enables to receive the value of ''Deflection'' (actually that site gives different term for this-''Displacement'') [10]:<br />
<br />
Here we need to enter the relevant values:<br />
<br />
''Length of beam'', ''L'': 100 000 meters<br />
<br />
''Line pressure load on beam'', p: In our case this is the weight per meter length. As we have already mentioned the radius of the rod’s cross-section is 1 meter, so the volume of rod’s 1 meter-length part will be 3.14 cubic meter. In case of using Carbon nanotubes with above-mentioned density-0.1 g/cm<sup>3</sup> the weight will be equal to 314 kg or 3 079 Newton. Since we have got the inclination of 45º we should multiply this value to cos45º- 0.707, so we get 2176 N/m.<br />
<br />
''Young's Modulus'', ''E'': This is equal to 1 000 GPa for Carbon nanotubes [11] <br />
<br />
''Distance from neutral axis to extreme fibers'', ''c'': In our case it is equal to the radius of the rod-1 meter<br />
<br />
''Moment of Inertia'', ''I'': It is equal to (pi*r<sup>4</sup>)/4, so it is equal to 0.785<br />
<br />
According to these initial data the calculator returns extremely high value of Deflection, much higher than the length of the rod itself: -3.61 × 10<sup>9</sup> meters. This result shows us that with the current materials (Carbon nanotubes in our case) it is impossible to raise the rod as ''one single unit'' to space by means of Space Elevator and we need other materials with less density and more ''Young's Modulus'' (or the rod should be much thicker but this will lead to increasing its mass). Therefore, we have got two options: either we should deliver the parts of that rod and then assemble them in space (we have already discussed this option) or completely different technologies for manufacturing the rod should be developed. Particularly, it would be very good if it was possible to manufacture the rod ''in continuous mode'' in vertical position and then uninterruptedly directly to carry it to space by means of Space Elevator’s cabins. Under such approach there will be no ''Deflection'' and several cabins will be able to deliver the rod in space. <br />
<br />
One note about transporting the rod from its place of manufacture to Space Elevator’s base station. We think that this process should be executed by many transports, in other words we are convinced that if the rod is carried by two trains only (or any other kind of transport) then the rod will continuously touch the ground since the ''Deflection'' occurs in any position-horizontal, inclined or vertical and this circumstance will lead to its damage, that’s why several transports will be needed to hold the rod at as many places as possible.<br />
<br />
=Stabilizing the counterweight=<br />
Stabilizing the Space Elevator’s counterweight is very important question during Space Catapult’s performance. Indeed, when the rod rotates it makes the imaginary circles in space and due to rod’s and payload’s masses the Space Catapult’s ''center of mass'' will be continuously shifted and if the counterweight is not somehow stabilized then it will make problems for accurate aiming to certain point at the celestial sphere. Also, if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable then there will be the danger that the rod may actually hit the cable and cut it. To avoid these problems we need to apply to serious measurements. <br />
<br />
First of all, the electro motor’s own axis can be quite long and this will diminish the chance to failure of the whole system. Actually, we are convinced that counterweight’s (where the electric motor will be placed) size will be quite large, mainly due to solar panels’ sizes and amount (this issue was discussed above), also the electromotor should be quite large and powerful to rotate the rod, and hence there will be enough distance between the rod and Space Elevator’s cable. <br />
<br />
The second serious problem is that the center of gravity of the system is not at the center of rotation, therefore it will be necessary to balance the rotating system when the payload is attached and when it is released.<br />
<br />
We think that the Space Catapult’s rod should not be deployed/directed to one side only but some counterweight of it should also exist. This is necessary since the unilaterally loaded (we mean the rod itself plus payload) rod will cause the counterweight to somersault. In other words, the rod should extend to other side and the ''moments of inertia'' of both sides should be the same as during rotating the rod as after releasing the payload when the rod still rotates. This is easily achievable if some additional, second payload is placed on the rod’s second end. Therefore, the Space Catapult will launch two payloads at the same time to the ''opposite'' directions but at various speeds if the second part/side of the rod is shorter.<br />
<br />
How the second payload should be placed on the rod and should we really send two payloads? Until we have got balanced rod this problem does not arise but as soon as the Space Catapult releases the payload this balance will be violated, how it can be restored? There are two theoretical ways for achieving this: reducing the ''mass'' or reducing the ''length''-with diminishing either one of them the ''moment of inertia'' will be decreased. We think that reducing the mass will be less practicable since this would require placing the second payload (spacecraft or anything else) on the rod’s second part and this cannot be done from the Space Elevator’s cabin-this is the easiest way for delivering the payload from Earth to Space Catapult’s rod; so we would have to (see ''Rod’s plane of rotation towards the Earth'') put the second payload on the electro motor and then send it rod’s second part’s end. This is quite complicated task; therefore we can apply to second approach-put some sliding object that will immediately move to electromotor as soon as the spacecraft is released.<br />
<br />
[[File: MOI.jpg]] <br />
<br />
The next problem that may occur is that when the electro motor rotates the rod this motion will make the Space Elevator to rotate to the opposite direction. The same problem arises when helicopter’s primary blade’s rotation forces the helicopter to rotate to opposite direction and this possible rotation is annulled by ''tail rotor''. We think that for balancing the counterweight the additional motor and rod should be installed and this rod should rotate to opposite direction and if their ''angular momentums'' are equal to each other, then their rotations will cancel each other. More precisely, the following equation should be fulfilled:<br />
<br />
[[File: Angular momentum.png]] <br />
<br />
Where ''m'' is mass of the rod, ''v'' is angular speed and ''L'' is rod’s length, the numbers ''1'' and ''2'' refer to first and second rods correspondingly. For balancing both rods’ rotation the multiplication at both sides of the counterweight should be equal, by the way this circumstance enables us to use the second rod with shorter length and even with less mass but rotating at more angular velocity.<br />
<br />
Such approach will effectively deal with other problem which will arise when the Space Catapult releases the payload(s), at this moment the second motor should instantly diminish its angular velocity to some certain level (an ordinary mechanical brakes could be used for this purpose), in this case ''angular momentums'' for both motors/rods will be equal again and Space Elevator’s counterweight will maintain its attitude in space. See the image below depicting the Space Catapult with two electro motors and rods:<br />
<br />
[[File: Two-rods.jpg]] <br />
<br />
Such approach will justify itself if rod’s plane of rotation is parallel to Space Elevator’s cable, but if this plane is orthogonal to cable (see ''Rod’s plane of rotation towards the Earth'') then the second/balancing electromotor cannot be placed under the counterweight because the cable will be cut when rod touches it. Therefore a bit different approach should used and we need to install two/four/eight electro motors with their own relatively shorter rods rotating to opposite direction. They should be placed at the counterweight’s lower side and on its edge (as we suppose the counterweight should be disc) so that their rods not to touch and cut Space Elevator’s cable. Also, total a''ngular momentums'' from these motors should be equal to the ''angular momentum'' from upper motor and thus the counterweight will not rotate and the Space Elevator’s cable will not be twisted. This situation is presented below:<br />
<br />
[[File: Modified-2.jpg]] <br />
<br />
We think that the array of gyroscopes would be also very useful to be installed at the counterweight since they can maintain the attitude of the whole system and this is important for precise aiming to certain point at the celestial sphere. As for the energy required for gyroscopes’ performance it could be received from the array of solar panels which as a result will generally serve Space Catapult’s precise performance.<br />
<br />
=Space Catapult placed at Lagrangian points-the way for gaining subluminal speeds=<br />
<br />
In our paper we discussed the Space Catapult based on the Space Elevator’s counterweight and concluded that this would be convenient when we intend to deliver the payload to space from the Earth. However, such Space Catapult cannot gain very high speeds and therefore we need to choose other way. It is obvious that we need to keep rod’s plane of rotation orthogonally relative to the ''Earth-Sun connecting line'' and hence we should place the rod on the celestial body which will be in synchronous rotation with the Sun but since there is no such body in the solar system we conclude that the Space Catapult for subluminal speeds (the speeds close to speed of light are in mind) should be placed at such point near the Earth where it will be easy to reach it from our planet and where the rotating rod will not hit the Earth and will be always at the same distance from the Sun to avoid the influence of its tidal forces. The examples of such places are '''Lagrangian''' L<sub>1</sub> and/or L<sub>2</sub> points at 1.5 million km away from the Earth. If the Space Catapult is placed at one of these points then its rod can be always orthogonal to the Sun in principle, at the same time it will never collide with the Earth and also it will be quite close to the Earth since 1.5 million km distance is very negligible in space.<br />
<br />
We have got several notes regarding such approach. First, when we mentioned that the rod’s various parts can be at the same distance from the Sun this strictly speaking is not very true because the Sun can be referred as little point where its gravity “comes out” from while the rod is quite long and its initial part (placed at one of the Lagrangian points) will be attracted stronger than the utmost one (for equal attracting the rod should the arc ''with the same curviness as Sun’s surface'' and not straight line); but still this is better than to direct the rod exactly towards the Sun where the tidal forces will try to tear the rod. Second, the Space Catapult should be placed at Lagrangian L1 point which is closer to the Sun than L2 one and therefore receives by 4 % more energy per area from the Sun. Third, the rod should be in constant rotation, this requires much less energy than accelerating it from zero, then stopping it and accelerating it again. Fourth, the existence of the asteroid belt in the solar system between Mars and Jupiter will somehow restrict the actual length of the rod. Indeed, the Space Catapult should be placed at one of the Lagrangian points at 1 AU distance from the Sun while asteroid belt approximately lays at 2.7 AU, from the simple geometry it is obvious that the length of the rod ''almost reaching'' the asteroid belt can be approximately equal to 390 million km, and if the rod is longer then it may simply hit any asteroid within that belt. For 390 million km length rod and for 100 000 m/sec2 acceleration at rod’s end (where the payload will be attached) the maximal speed that the spacecraft can gain will be approximately equal to 200 000 km/sec (two thirds of the speed of light) and this can be considered as enough for practical interstellar spaceflight. Fifth, the spacecraft should be directly put on the rotating rod’s initial end (near electromotor) and then slide towards the other end with its own rocket engines. To achieve this, the spacecraft will have to cover relatively less distance on the rod and then rod’s circular motion will accelerate the spacecraft further-we have already mentioned this in this paper when speaking about deploying the Lunar Space Catapult. This action-putting the spacecraft on the rod will not be difficult since rod’s angular velocity will be quite low due to rod’s huge length, particularly for 400 million km length rod and for 200 000 km/sec linear speed the rod’s angular velocity will be 0.0000796 revolutions/sec.<br />
<br />
[[File: Lagrangian-point.jpg]] <br />
<br />
We have already mentioned that to avoid the destructive influence of the Sun’s tidal forces the rod’s plane of rotation should be orthogonal to the Earth-Sun connecting line. By the way, note that under such approach we may have to wait one year until the Lagrangian Space Catapult occupies the relevant position towards the certain point at the celestial sphere where the spacecraft should be sent to. But from the other hand it would be useful if it is feasible to rotate this whole structure around the imaginary axis directed towards the ''ecliptic poles'' (depicted as faint green dash line on the image above), the reason if this is the possible danger when the rotating rod may hit Mars or asteroids that orbit around the Sun closer than 2.7 AU distance (for example ''433 Eros'' or ''1036 Ganymed''), hence for avoiding such undesired collision the Lagrangian Space Catapult should be slightly rotated by several degrees clockwise/counterclockwise so that the rod not to collide with any celestial object. We are convinced that rotation by several degrees will be absolutely enough measurement due to rod’s gigantic length and relatively less sizes of the celestial objects in the solar system.<br />
<br />
The next issue that we should discuss refers to stability of the Lagrangian Space Catapult placed at L<sub>1</sub> point. As we see this structure will have enormously gigantic size while the Lagrangian point is relatively little mathematical one in space, so what can be done to be convinced that this structure will remain at that point and do not shift aside? The body placed at one of the Lagrangian points is affected by other celestial objects’ gravity and therefore for achieving the balance the rod needs to have the counterweight with more mass if it (counterweight) is shorter. As we clearly see the rod needs the counterweight for two reasons: not to let the Space Catapult somersault and for maintaining it at the L1 point. We think that it would be very useful if the arrays of solar panels act as counterweight since exactly they can give us energy for rotating the rod. Also, we need the second, shorter, perhaps less massive but faster-rotating rod (again-solar panel arrays) the opposite rotation of which would cancel first rod’s rotation, this issue was discussed in this paper. These arrays of solar panels are depicted on the image shown above. <br />
<br />
How such a gigantic structure as Lagrangian Space Catapult can be assembled in space? In our paper we discussed the possible ways for delivering the rod from the Earth to the Space Elevator’s counterweight, now we will try to show that it is possible ''in principle'' to assemble the extra-long rod in space. <br />
<br />
If it is possible from the technical point of view to manufacture extra-long rod then we can use this approach and make 1.5 million km length rod (this is the distance between the Earth and Lagrangian L<sub>1</sub>/L<sub>2</sub> point) that will be mechanically directed to the base station at L<sub>1</sub> point. The capturing devices there will catch the rod and attach it to the electro motor’s shaft after which the rod should be spun by 90º so that it to be orthogonal to Earth-Sun connecting line (for this purpose the additional mechanisms will be needed), this spin is necessary because L<sub>1</sub> point is located on the Earth-Sun connecting line (that is towards the Sun if we look from the Earth) and when directing the rod from the Moon it will lay ''along'' this line while we need across. After this the rod should be slid to another side and then the next rod should be directed to the Lagrangian Space Catapult where it will be attached to the previous rod and etc. In other words, the extra-long rod will be assembled from one side and its length will “grow” from this side to other one, this is necessary because the distance between Moon (the rod should be manufactured exactly there and not on the Earth due to our planet’s relatively more gravity, atmosphere and problematic space debris belt around it) and L<sub>1</sub> point is constant and rod’s parts cannot be more. Due to whole rod’s and its parts’ lengths (400 million and 1.5 million km correspondingly) we think that about 260-270 such operations will be needed to finish assembling the rod (400/1.5). The process of assembling the Lagrangian Space Catapult is shown on the image below:<br />
<br />
[[File: Lagrangian-point-assemble.jpg]]<br />
<br />
=Conclusion=<br />
<br />
As we have seen, for leaving the Solar system and reaching the remote celestial bodies (stars, nebulas) there is no need to develop advanced and complicated technologies that mostly are not capable for gaining extra high velocities nevertheless. In any case, until the Space Elevator is really built (scheduled for construction by 2031) we have got much time for developing the idea of Space Catapult in technical aspect, like finding appropriate materials for the rod, perfect the ways how the Space Catapult can be assembled in space and etc. The concept of Space Catapult itself is the easiest one, does not need developing neither complex and sophisticated technologies, nor some exotic methods (such as ''Gravitoelectromagnetic toroidal launchers'', ''Antimatter rocket'' and etc.) and can be easily implemented in near future; in other words the Space Catapult is not some sophisticated structure that would need profound science research and the fact that it will enable us to gain whatever high speed will justify its developing and building by the humankind. As for other technologies like Ion Drive, they could be used by the spacecraft during flight for other purposes, for example for correcting/changing the flight direction.<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Space_Elevator<br />
<br />
2. http://www.isec.info/index.php?option=com_content&view=article&id=14&Itemid=9<br />
<br />
3. http://www.space-track.org/perl/geo_report.pl (provided data updates regularly, registering is needed) <br />
<br />
4. http://www.oosa.unvienna.org/pdf/reports/ac105/AC105_720E.pdf page 24 (data as at 21 August, 1997) <br />
<br />
5. http://www.amostech.com/ssw/presentations/Session7/S7-1Molotov.pdf page 16<br />
<br />
6. http://www.esa.int/SPECIALS/ESOC/SEMN2VM5NDF_mg_1_s_b.html <br />
<br />
7. http://eetd.lbl.gov/ecs/aerogels/sa-physical.html<br />
<br />
8. http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant<br />
<br />
9. http://www.you.com.au/news/2005.htm, http://www.spacedaily.com/news/ssp-03b.html<br />
<br />
10. http://www.efunda.com/formulae/solid_mechanics/beams/casestudy_display.cfm?case=simple_uniformload<br />
<br />
11. http://en.wikipedia.org/wiki/Young%27s_modulus<br />
<br />
<br />
'''Appendix''': <br />
<br />
Animation illustrating the payload’s departure from the Lagrangian Space Catapult:<br />
[[File: Lagrangian-point-animation.gif]]</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_5&diff=3666OpenSpace 52013-09-21T12:55:20Z<p>Eagle9: </p>
<hr />
<div><div style="float:right; border:#CCCCCC solid 1px; background-color: #F7F7F7"><br />
<table cellspacing=0 cellpadding=0 width=550><br />
<br />
<tr><td colspan="3" align="center" style="background-color:#CCCCCC"><b>Title:</b> Place Title Here</td></tr><br />
<br />
<br />
<br />
<br />
<br />
<br />
== '''Space Catapult''' ==<br />
<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
=INTRODUCTION=<br />
<br />
<br />
The new method for sending the spacecrafts in deep space is presented here. The paper describes the long rod rotated by electro motor placed at the Space Elevator’s counterweight and at Lagrangian points. This simple structure will enable the rod to gain high velocity and carry the payload with it. After reaching the desired speed the rod will release the payload that will fly in space along the imaginary circle’s tangent. This structure we called Space Catapult and it should work with the assist of Space Elevator. This latter should be used for carrying the payload from the Earth to Space Catapult’s rod.<br />
<br />
For exploring the outer space the humankind generally uses the rocket engines, mostly chemical-propelled ones. They enable us the explore near-Earth celestial bodies and other planets in the solar system. They even enabled us to send several deep space missions beyond the solar system such as '''Pioneer-10''', '''Pioneer-11''', '''Voyager-1''', '''Voyager-2''', however by means of this technology the flight lasts undesirably long and it seems to be impossible to reach remote celestial bodies in space such as stars, so new technologies are necessary for this purpose. However new technologies do not necessary imply new kind of rocket engines, such as ''Ion Drives'' because they are capable for gaining several ten times higher speeds only, but for remote celestial bodies even they are not suitable. Besides, they need a huge amount of energy to be stored onboard the spacecraft and this will make additional problems. So, high speed should be achieved with absolutely different approach. How this can be done?<br />
<br />
High speed can be easily achieved by means of fast-rotating rod around the electric motor. The motor’s rotational speed can be very high; the rod also can be quite long, hence the rod’s end’s linear speed can be extremely high, absolutely unachievable for any other technologies nowadays. The payload should be fastened at the rod’s end where the linear speed generally reaches maximal value. After reaching the necessary speed the rod will release the payload that will fly along the tangent from the current position. Thus the electric energy can be turned into payload’s speed and its velocity could be as high as we wish (except the ''speed of light'' of course). In principle the '''Space Catapult''' (thus we call this structure) would be the simplest, the most convenient and direct way for converting the energy/electricity into speed and conveying it to payload. <br />
<br />
As we see the Space Catapult is quite uncomplicated structure, however if we wish to gain high speeds we should deploy it in space, not on the Earth. Indeed, our planet is surrounded with dense atmosphere that impedes any quick motion, so if we rotate the rod quickly the atmospheric drag and generated heat would burn it very soon, therefore the Space Catapult should be built and deployed in space only, and as we suppose-at the Space Elevator’s counterweight. In other words, the Space Elevator’s counterweight will operate as Space Catapult. See image below:<br />
[[File:Space-catapult.jpg]]<br />
Generally, what is the Space Elevator <sup>1</sup> <sup>2</sup>? According to modern concepts it will be the tall vertical structure built on equator and will have height of several ten thousand kilometers with its thin cable fastened to the base station on the Earth and with counterweight placed higher geostationary orbit. Because of balance between centrifugal force and gravity this structure will be stretched and the cabin will move along its cable carrying the goods into high orbit. After delivering the payload, the cabin will descend and carry the next one.<br />
In Space Elevator’s concepts several solutions have been proposed to act as a counterweight: <br />
<br />
1. Heavy, captured asteroid <br />
<br />
2. Space dock, space station or spaceport positioned past geostationary orbit <br />
<br />
3. Extension of the cable itself far beyond geostationary orbit. <br />
<br />
The third idea has gained more support in recent years due to the relative simplicity of the task and the fact that a payload that went to the end of the counterweight-cable would acquire considerable velocity relative to the Earth, allowing it to be launched into interplanetary space. However this idea cannot be completely shared by us due to following reason: <br />
<br />
It is well-known that the values of both '''Orbital''' and '''Escape Velocities''' decreases with increasing the altitude while the '''tangential velocity''' of Space Elevator’s cable increases. We can see the differences between them from the chart presented below:<br />
[[Image: Cxrili.gif]]<br />
<br />
As we see from this chart the ''tangential velocity'' of the Space Elevator even at its end (144 000 or 200 000 km altitude) is not very high to decrease the necessary time for covering the distance from the Earth to remote celestial bodies significantly. To achieve this, even the longer Space Elevator would be needed (its ''tangential velocity'' is directly proportional to its length) and this circumstance would complicate the technical task for building such Space Elevator. Because of this, there is no necessity to extend the cable itself far beyond geostationary orbit as proposed in the third variant. In any case, we have already seen that by means of Space Catapult it is possible to gain such huge velocities that are absolutely unachievable with other technologies, for example with Space Elevator. Therefore, using the counterweight and placing the Space Catapult there definitely has got some technical sense. <br />
<br />
However, we think that the question where the Space Catapult should be placed needs further discussion. Theoretically, the Space Catapult with its payload and nuclear reactor/solar panel needed for rotating the rod may be mounted not only at the counterweight, but on the Space Elevator’s cabin also that can carry all these goods to space in a usual way, as it should do it according to Space Elevator’s modern concepts. This option is quite possible, however for realizing this we need to know the mass of the payload, nuclear reactor/solar panels’ mass plus Space Catapult’s mass from one hand and Space Elevator’s lifting capacity (this ''must'' be more) from other hand, but these data are not available nowadays, therefore we think that the Space Catapult should be still mounted at the Space Elevator’s counterweight where it will be possible to send the payloads into deep space in ''continuous mode'' at high velocities.<br />
<br />
As we saw the Space Catapult is capable to gain very high velocities; however there is being developed other technologies and they in future will enable the spacecraft to fly at high speeds in space. These are Ion Drive systems, more precisely the most perspective one-''Variable Specific Impulse Magnetoplasma Rocket'' (VASIMR) which still under development can be used in future for deep space missions. Can these engines and Space Catapult be the rivals in space? Since none of them have been built and used in space yet we cannot give a persuasive answer to this question; however still it is possible to underline Space Catapult’s one significant advantage: if the future spacecraft uses the VASIMR (or any other kind of Ion Drive) engine it will definitely need to be equipped with nuclear reactor, otherwise the spacecraft will not be able to gain high speeds, also it will need to carry fuel tanks for this purpose. As for the Space Catapult, it can give much higher speed to spacecraft, besides it will have ''stationery'' power plant (see ''Energy source placed on the Space Elevator’s counterweight'') at the Space Elevator’s counterweight, so the payload will ''not'' have to carry the nuclear reactor onboard and this circumstance will lighten the work for deep space spacecraft. Besides, we should not forget that unlike the spacecrafts equipped with ion drive engines the Space Catapult will need no fuel for gaining high velocities. <br />
<br />
Briefly, Space Catapult’s advantages over any kind of propulsion systems are: <br />
<br />
1. Ability to gain any speed that is absolutely unachievable by means of other kinds of engines. <br />
<br />
2. No need by spacecraft to carry energy source that would make it too heavy and impracticable.<br />
<br />
=The Space Catapult needs long rod=<br />
<br />
When building the Space Catapult at Space Elevator’s counterweight we should install quite long rod there, the shorter the rod is, the easier would be installing it, however we should note that rod cannot be extremely short, let’s say 1 km length or so due to following reason:<br />
<br />
When we are going to send some payload into space, we need not only high velocity, but one certain direction also. The little inaccuracy in direction, inclination in several arcminutes is actually acceptable since the spacecraft would easily balance it with its engines; however great inclination from the initial direction would send the spacecraft into the completely different direction and in such case the whole mission will fail.<br />
<br />
If two Space Catapult’s rods have the length of let’s say 1 kilometer and 10 kilometers, then for giving to payload some certain linear speed (for instance 100 km/sec) these rods should rotate at different angular velocity. It is easy to ascertain that the shorter rod should rotate 10 times faster to gain the same linear speed than the rod with more length. But the faster the rod rotates, the more difficult will be to “catch” the needed moment for releasing the payload from the rod for sending it towards some certain direction. If the rod is too short, then it has to rotate very quickly for gaining some certain linear speed and therefore it will be extremely difficult catching the needed moment for releasing the payload. Hence, too short rod can make problem for sending the payload to some certain direction in space especially at high velocities. So, based on payload’s needed velocity we should find rod’s desired, minimal length that will enable us to send the payload in space to necessary direction without fear that it may yaw from the course. <br />
<br />
However, rod’s length will be crucial for payload’s abilities for withstanding the acceleration also. As an example, we can try to calculate its value which the payload will have to withstand during rod’s rotation. The acceleration of the body rotating at the circle with some constant velocity is calculated by the following formula:<br />
<br />
[[File: Acceleration - Copy.jpg]] <br />
<br />
Where a is acceleration in ''m/sec''<sup>2</sup>, ''v'' is payload’s linear velocity on the circle in ''m/sec'' and ''r'' is radius of the circle in ''meters'', in our case it is equal to rod’s length. Let’s assume that the rod is 100 km length and the electromotor rotates it so that payload’s speed is equal to 50 km/sec, in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design and manufacture the spacecraft’s subsystems (avionic and etc.) capable to withstand such acceleration. This circumstance somehow restricts the speeds that we can achieve, in any case their values actually depends on spacecrafts’ abilities for withstanding g-loads. But what can we do if much higher speeds are needed? The answer directly derives from that formula: the radius should be more; by the way note that this is additional reason why the longer rod is more useful. If we are able to make the extra long rod, then this will enable us to gain much higher velocities. <br />
<br />
What material should be used for manufacturing the rod? It is obvious that if very high speeds are needed the rod should be long and even in this case the acceleration at its end will be quite high, therefore ''sufficiently strong and light materials'' are needed for this purpose and making them is as similar challenge as in case of Space Elevator where the same requirements arises for the cable’s material. The lightness is needed because in case of heavy rod a lot of energy will be needed to rotate it; the strength is needed because in case of lack this property the rod will be destroyed due to great acceleration.<br />
<br />
=The mechanism for holding and releasing the payload=<br />
<br />
How the payload can be held by Space Catapult’s rod during rotation and how it can be released from the rod? We think that using ''electromagnet plus mechanical holding devices'' would be a good solution. More precisely, after the payload is attached to the rod it must be held by means of both methods until the rod accelerates and reaches necessary velocity (it may take even several days), but with approaching the desired speed the mechanical device should release the payload however the electromagnet(s) should still hold it. The explanation of such approach is following: generally the mechanical devices are much slower/sluggish in performance than electronic ones. We have already said that when releasing the payload the extreme accuracy is needed and mechanical devices cannot guarantee ''the exact time of releasing'' the payload unlike electronic ones. That is, it’s unlikely that mechanical devices can release the payload at some certain moment when needed while in case of electromagnet it would be enough to cease electric current there, it would lead to immediate vanishing of the magnetic field and sending the payload along the tangent from the point where the payload would be at the current moment. <br />
<br />
<br />
We think that the ''fastest control system'' would enable to release the payload to certain direction. This system (extremely fast-operating computer plus measuring equipments) should know the current position of the rod’s end, the current speed, the needed direction and be capable for computing the necessary moment for giving the order for diminishing the voltage for electromagnets and hence releasing the payload to desired direction and velocity.<br />
<br />
=Rod’s plane of rotation towards the Earth=<br />
<br />
The Space Catapult’s rod when rotating makes the circular plane/flatness in space and this plane may be horizontal/parallel to Earth surface, that is making the right angle to Space Elevator’s cable or it may be placed along the cable; see the both possible situations here:<br />
<br />
[[File: Planes-of-rotation - Copy.jpg]] <br />
<br />
Both approaches have got their advantages/disadvantages and here we will discuss this question, first of all from the point of view of safety.<br />
<br />
For gaining extremely high velocities quite long rod would be needed, maybe with the length of several thousand kilometers or even more. If such rod is placed ''along'' the Space Elevator’s cable then the rod during rotation will cross many orbits from the ''Medium Earth Orbit'' to ''High'' ones. When rotating, the rod may actually hit any satellite and/or space debris object and such collision can lead to rod’s complete destruction; therefore we should choose such plane which would be much more free from any artificial objects; hence if the rod rotates ''horizontally/parallel'' to Earth’s surface at high enough altitude where the satellites’ population is relatively low then this measurement would justify itself because under such circumstance the rod will not cross satellites’ orbits (rod’s plane of rotation will simply coincide to ''one'' orbit’s path). However, we should also note that this altitude actually depends on the Space Elevator’s proposed length. Indeed, the Space Catapult’s rod should be mounted at the Space Elevator’s counterweight; this counterweight from its side should be placed at the end of the Space Elevator at such altitude where the satellites’ population is as low as possible. This means that Space Elevator’s proposed height should be agreed with mounting Space Catapult on its counterweight. According to various databases the number of man-made objects at high orbits, more precisely beyond geostationary orbit is much less than on the lower orbits <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup>, therefore the Space Catapult with its rod should be located at the altitude of 50 000-60 000 km above the sea level. At such altitude the space is almost free and nothing will impede rod’s rapid rotation. Besides, the satellites at high orbits are orbiting around the Earth slower than on the lower orbits (as known any satellite orbits around its primary body slower in apogee than in perigee), therefore if some tracking system is mounted at Space Elevator’s counterweight then it will enable the Space Catapult to avoid undesired collision with satellites during Space Catapult’s performance. In other words, the Space Catapult should operate only when the there are no satellites near its vicinities.<br />
<br />
Now we will try to discuss this question from other side.<br />
<br />
How the payload can be transferred from the Space Elevator’s cabin to the Space Catapult’s rod? One way is following: cabin reaches the counterweight where the payload will be released, then payload will be mechanically conveyed to rod, continues its way ''on the rod'' (like the train rides on the rails) and after reaching rod’s end it stops, the rod begins rotating and after gaining necessary linear speed it releases the payload to needed direction. This method is generally realizable; however it seems to be too complicated and unpromising compare to the second one: the Space Catapult’s rod is stopped in space so that it to be directed downwards to the Earth and be parallel to Space Elevator’s cable. The Space Elevator’s cabin moving along the cable with payload stops at the cable ''near'' the end of the Space Catapult’s rod and releases the payload that will fly to the rod, attaches itself to the rod’s end (here the electromagnets would be useful), the rod begins rotating and after gaining needed linear speed will release the payload to necessary direction.<br />
<br />
This second way seems to be more promising because the first one is much more complicated as we have already said: first of all there would be needed some mechanical devices for transferring the payload from the Space Elevator’s cabin to counterweight, the counterweight should have the hole for the payload to move through it from below (we should not forget that the Space Catapult should be mounted ''at'' the counterweight, not ''beneath'' it), besides the rod should be made so that it to have some conveying surface (rails for instance) the payload to move on it. As we see it would be much more convenient if it is possible to convey the payload from the cabin to the rod directly and this would be feasible under the second method which is depicted below:<br />
<br />
[[File: Convey.jpg]] <br />
<br />
One more aspect regarding Space Catapult’s position. This structure, its rod, its electro motor and etc should be mounted at Space Elevator’s counterweight so that the rod to be placed westwards from the cable. The reason of it is following: when the Space Elevator’s cabin stops and releases the payload (which should fly to Space Catapult’s rod) the current speed of which will/should be more than the value of the ''Orbital/Escape Velocity'' at the current altitude. After releasing the payload will fly westwards and upwards because its orbit will be ellipse, under ellipse the payload will fly higher to apogee and at the speed less than Space Elevator’s current speed at the given altitude, in other words the released payload will “lag behind” the Space Elevator’s cable; therefore payloads’ ''stopping points'' at the cable and Space Catapult’s rod’s length should be calculated and chosen so that the payload to fly directly towards rod’s end. This process would be feasible in both cases-if the rod’s plane of rotation is parallel to Earth’s surface and if it is placed along the cable-but still this would be easier for the payload to achieve the rod’s end if the rod is placed along the cable because at least the distance that the payload should cover in space will be less.<br />
<br />
The length of the Space Catapult’s rod placed at the Space Elevator’s counterweight might vary since for various spaceflight purposes different initial speed will be needed and relatively low speed could be achieved by means of shorter rod. Because of this reason it might be necessary to change Space Catapult’s rod’s length, therefore it would be useful if the rod consists of two parts where the first part would be perpetually attached to electro motor and the second one will be attached to the first part if necessary. For this operation Space Catapult’s rod should be placed along the cable since the relative nearness would make this operation quite easy and it could be accomplished by the crew directly from the Space Elevator’s cabin stopped at the needed altitude. <br />
<br />
For deciding the question how the Space Catapult’s rod should be placed towards the Space Elevator’s cable we should take into consideration one substantial circumstance-to which direction do we plan to send the payload in space by means of Space Catapult? This circumstance will influence deciding this problem due to following reason:<br />
<br />
In case ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and if rod’s plane of rotation is parallel to Earth equator, then this plane will be orthogonal to Earth’s rotation axis. This axis from its side is tilted to ''ecliptic plane'' by 66° 34'. This means that Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 23°26'. Here follows very important consequence: under above-mentioned conditions the rod when rotating will be capable for covering only the part of the ''celestial sphere'' from 0° to 23°26' (counted from ''ecliptic plane'' northwards and southwards to ''Ecliptic poles''). This is about one fourth of the ''celestial sphere'' (23°/90°), this will not make problems if we intend to use the Space Catapult for exploring the solar system’s planets because their orbits’ tilts towards ''ecliptic plane'' do not exceed 7° (for planet Mercury, for other planets this tilt is even less); however we will not be able to send the payload for example to the nearest star ''Alpha Centaurs'' because this star is located at -42 degree according to ''ecliptic coordinate system'' in the celestial sphere.<br />
<br />
The situation will drastically change ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and ''if'' rod’s plane of rotation is orthogonal to Earth’s equator and therefore parallel to Earth’s axis of rotation. We have already discussed this option when we mentioned that the rod should be placed westwards from the cable and explained why it would be useful-for delivering the payload from Space Elevator’s cabin to Space Catapult’s rod. Under such conditions the Space Catapult will be capable to aim to any point on the ''celestial sphere''. Indeed, the Earth with the Space Elevator rotates around its axis and Space Elevator’s counterweight draws an imaginary circle in space. This circle is tilted to ''ecliptic plane'' at 23°26' and crosses this plane in two point called ''ascending'' and ''descending nodes''. The other points that are 90° away from these nodes we call point(s) of ''maximum elevation/depression'' (relative to ''ecliptic plane''). When the Space Elevator is at a''scending/descending node'' its rod and hence the payload can be directed to any point from 0º to 66º on the celestial sphere northwards and southwards from ecliptic plane. This makes about 75 % of celestial sphere. See the image depicting this situation:<br />
<br />
[[File: Node.jpg]]<br />
<br />
But when the space Elevator reaches the points of ''maximum elevation/depression'' then its rod during rapid rotation may be directed to any point from southern ''Ecliptic pole'' to ''Northern pole'' at the celestial sphere because at these points rod’s ''plane of rotation'' is orthogonal to ''ecliptic plane'' and thus the rotating rod can aim to ecliptic poles as well as other points. See this situation below:<br />
<br />
[[File: Elevation.jpg]] <br />
<br />
The situation will be similar if the Space Catapult’s rod is orthogonally placed towards cable. Under such approach Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 66° 34' and the Space Catapult will be capable to cover ''three fourths'' (66°/90°) of the ''celestial'' ''sphere'' when the Space Elevator is at the points of ''maximum elevation/depression'' and the whole celestial sphere when the Space Elevator is at ascending/descending nodes. For aiming the needed point on the celestial sphere the Earth should occupy the appropriate attitude towards the stars during the revolution around its axis, the same thing should be done under previous case described in the paragraph above. <br />
<br />
In conclusion, thinking about rod’s plane of rotation towards the Earth, we should note one important difference between above-mentioned approaches: if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, then in case of emergency during Space Catapult’s performance (for example if the Space Catapult’s rod is cut by sudden meteorite bombardment) the rod’s part with the payload may simply crash to the Earth at huge velocity if the rod at this moment is directed to the Earth. This cannot happen if Space Catapult’s rod’s plane of rotation is orthogonal to Space Elevator’s cable because payload’s rotational path will not be directed towards the Earth and hence its flying trajectory will never cross the Earth.<br />
<br />
=Braking the Space Catapult’s rod=<br />
<br />
After releasing the payload at necessary speed and direction, the Space Catapult’s rod will have a huge angular velocity that needs to be decreased to zero in order the Space Catapult’s rod to get another payload in motionless position and then to send it to space. <br />
What methods can we use to reduce Space Catapult’s rod’s rotation to zero? There are several possible ways: <br />
<br />
1. The electromotor designed for accelerating the rod may actually play a role of brakes, more precisely after releasing the payload to space the electromotor should operate/rotate in the opposite direction, hence rod’s rotational speed will be diminished to zero after that electromotor will stop operating. Under such method a bit less energy will be spent for decelerating the rod than in case of accelerating because when decelerating the rod is free from payload. <br />
<br />
2. An ordinary mechanical brakes, however due to electro motor’s and rod’s sizes a huge brake(s) would be needed to be installed on the Space Elevator’s counterweight and this circumstance would make additional problems from the engineering point of view. Nevertheless, we should admit that under such method we would not need as much energy as during accelerating; on the contrary, in this process the heat will be emitted as it generally happens during braking. <br />
<br />
3. For decelerating the rod we can use the well-known phenomenon in physics-''electromagnetic induction'': when the c''onductor/ closed circuit'' moves into the magnetic field the electric current is generated there. In case of Space Catapult we can use this phenomenon in the following manner: the conductor should be wrapped around the whole length of the rod like a helix and there should be possibility that this conductor to be turned into the ''closed circuit'' by means of mechanically connecting its ends (see the image below). After releasing the payload at necessary speed and direction this circuit should be closed, then according to ''electromagnetic induction'' the electric current will be generated in the conductor and the energy of this electric current will come from rod’s kinetic energy. Therefore, inducted electric current in the enclosed circuit will force this circuit and rod to lose kinetic energy and speed. The part of the generated electric current will be spent in prevailing conductor’s electric resistance:<br />
<br />
[[File: Helix.jpg]] <br />
<br />
The advantage of this method is that for decelerating the rod no energy will be required, as for drawback-much time will be required for this purpose because at the altitude of several ten thousand kilometers the Earth’s magnetic field is quite weak and the effect described in the paragraph above will need much time to operate and give necessary result. <br />
<br />
4. The above-described third method could be realized in a bit different way: if the conductor wrapped around the rod is a closed circuit and if we conduct the electricity there then the electric current will generate its own magnetic field that will counteract with Earth’s one. More precisely, according to ''Lenz's law'' induced current’s magnetic field will be in such a direction as to oppose the motion or change causing it, in other words induced current’s magnetic field will counteract outer magnetic field’s any change and this will cause decelerating rod’s rotation and finally its stopping. <br />
<br />
5. The obvious disadvantage of the third and fourth method described above is weakness of the Earth’s magnetic field because of which decelerating the rod may be delayed in time. For solving this problem we can create artificial magnetic field by means of electromagnets. Particularly, one electromagnet should be placed at the Space Elevator’s counterweight, very close to Space Catapult’s rod. The second electromagnet should be placed directly on the Space Catapult’s rod close to first electromagnet (actually, instead of this second electromagnet there could be used the conductor wrapped around the rod as we described above in previous methods). The reason of this nearness is that magnetic field generally weakens directly proportional to distance’s third power and much time will be needed for decelerating Space Catapult’s rod if two electromagnets are far from each other.<br />
<br />
This method probably will consume the most amount of energy but at the same time it will be the most effective because it does not depend on outer factors such as Earth’s magnetic field which is quite weak at the altitude of several ten thousand kilometers above the sea level. <br />
<br />
Eventually, which methods for decelerating the Space Catapult’s rod would be the best? As we see each one of them have got their advantages and disadvantages. We can state that we should choose one of them according to spaceflight’s profile and goal. Particularly, if we decide to send the spacecraft into the deep space mission where especially high speed is necessary then in this case ''longer/more massive'' rod would be needed rotating at very high speed. Under such circumstance much energy will be needed for accelerating/decelerating the rod. We should also take into consideration the fact how frequently the Space Catapult will operate, in other words how mane payloads it will have to send into space per some certain amount of time, week/month and etc. If time interval between two following missions is relatively high then we should choose the method that will consume less energy and more time for decelerating the rod. On the contrary, if the Space Catapult has to send payloads very often then we should choose the method that will consume more energy and enable the rod to decelerate faster. In other words, we should find ''golden mean'' between consuming time and energy. We should also take into account how much energy supply will be produced at the Space Elevator’s counterweight (see ''Energy source placed on the Space Elevator’s counterweight'') and what part of this energy can we spend for accelerating/decelerating the rod.<br />
<br />
The rod’s rotations can be decelerated much faster than accelerated; the reason of it is that when accelerating the rod has got some sophisticated device as payload and generally unmanned spacecrafts are capable to high g-loads, but still for them some restrictions exist. After the payload is released at needed direction and speed, the rod can decelerate much faster because the rod itself is quite simple device without any complex and sophisticated details. <br />
<br />
We can actually use several methods, such as the third one and then the first/fifth ones. This would be justified because of following reason: as we have already said when decelerating with the third/forth method the problem of weakness of the Earth’s magnetic field would occur, therefore much time would be necessary for described method(s) to perform and give us result. However, we should note that in the beginning when the rod rotates very quickly this method would still operate strong enough. This derives from Faraday's law of induction stating that “the electromotive force generated is proportional ''to the rate of change of the magnetic flux''”. Therefore, in the beginning when the rod is rotating very quickly we can use the third/forth method(s) and when the rod significantly brakes we can apply to the first/fifth ones-they do not depend on Earth magnetic field. In other words, such approach would greatly help us in finding the golden mean between spending energy and time necessary for decelerating the rod. <br />
<br />
And finally: after releasing the payload the Space Catapult’s rod can actually give us energy. More precisely, the electro motor itself can serve as electric generator also since we know that the same machine can operate as electric motor if it is fed with electricity and as generator for electricity if its rotor is rotated by other machines. Therefore after releasing the payload when the electro motor’s rotor is rotating very quickly it can give us energy, in result of which the rod will lose its kinetic energy and speed, as for generated energy it can be sent downwards to the Earth for our terrestrial needs (see the next section in this paper) or stored onboard the Space Elevator’s counterweight. This approach has got one substantial advantage: it does not imply additional mass (wrapped wire) that will cause problems because rotating heavier rod would consume more energy.<br />
<br />
=Energy source placed on the Space Elevator’s counterweight=<br />
<br />
As well-known, the Space Elevator’s cabin needs energy when moving along the cable and it can get it from the Earth by means of various ways, such as: laser beam, microwaves, through the cable itself and etc. On the other hand, Space Catapult also needs much energy for rotating the rod and for this purpose some energy source should be placed on the Space Elevator’s counterweight, presumably solar panels array. Doing this would demand additional funding and engineering work and this undertaking should be justified, so how can we prove that placing energy source on the counterweight would be necessary and useful? We should not forget that the energy generally could be simply transmitted from the Earth without carrying any material for energy source on counterweight; so we can justify this undertaking if we declare/prove that: <br />
<br />
1. Energy source should be designed for ''both'' Space Elevator’s cabin and Space Catapult’s rod. We can imagine it as array of numerous solar panels producing enough energy for both above-mentioned constructions. For this purpose solar panels would be better solution than nuclear reactor because they do not need nuclear fuel to be carried from the Earth to counterweight, also they are capable for producing energy in a continuous mode. By the way this circumstance will enable us to send the payload to space by Space Catapult whenever we want without depending existence nuclear fuel at the counterweight. <br />
<br />
2. Transmitting energy from the counterweight (“from above”) is better and advantageous than doing the same thing from Earth (“from below”). Indeed, when we try to transmit energy (laser or microwave beam) from the Earth to ascending cabin, the part of energy is inevitably lost and dispersed in the Earth’s atmosphere and (this is point of the question) this continues during the whole process of ascent. On the contrary, when transmitting the energy from counterweight to cabin the energy will be lost only on the little part of this voyage, more specifically until the cabin leaves the atmosphere (100 km in height) and when cabin leaves it the energy will be transmitted in vacuum without loss. <br />
<br />
3. For receiving the energy from the Earth the huge solar panels (in case of laser beam) or antennas (in case of microwaves) will be needed to be mounted on the counterweight and this is additional mass and additional engineering work.<br />
<br />
We think that these arguments given above are enough for shoving that placing energy source on the Space Elevator’s counterweight have advantages over transmitting energy from the Earth and as conclusion we can state that energy source on counterweight would serve both space transportation systems-Space Elevator and Space catapult. <br />
<br />
As addition, we could use the energy produced on the counterweight for terrestrial needs also. Indeed, there have been developed numerous projects for receiving energy from space since 60-ies implying producing it by means of solar panels and then transmitting to the Earth. Combining all these three goals we can conclude that placing solar power plant on the Space Elevator’s counterweight would be triply useful and advantageous. In other words, when the Space Catapult and Space Elevator do not function, the energy produced on the counterweight should be directly transmitted to the Earth for our terrestrial needs and thus the idea of Space Elevator, Space Catapult and space power plant will be combined in one project.<br />
<br />
=Assembling the Space Catapult=<br />
<br />
Assembling in space such a huge structure as Space Catapult will not be an easy task from the technical point of view and definitely needs special engineering approach. Besides, we think that Space Catapult’s rod should be mounted at the Space Elevator’s counterweight separately from every other parts of the Space Catapult (e.g. electro motor and etc.); this circumstance is caused by rod’s gigantic sizes. More precisely, electric motor and plus any other equipments necessary for Space Catapult’s performance should be delivered to space by means of Space Elevator in a usual way; as for Space Catapult’s rod, it is a different matter and it should be delivered and mounted separately in the end. <br />
<br />
Eventually, Space Catapult’s rod will be quite long, perhaps much more than 100 kilometers. It is obvious that delivering such a long rod as ''one single unit'' would be quite difficult task; also it is possible that due to its total mass the Space Elevator’s cabin will not be able to deliver such rod at all, but we have already mentioned that the Space Catapult may have the rod with various length; more precisely the rod may consist of two/more parts. In such case these parts should be delivered towards the counterweight separately and then assembled. <br />
<br />
But the Space Elevator’s cabin can actually deliver the Space Catapult’s rod as ''one single unit'' in space. We think that this would depend only on rod’s mass. The Space Elevator’s lifting capacity is not well-known yet; however apparently it will not exceed one hundred metric tons and if Space Catapult’s rod is made of extra light material then cabin will be able to deliver it in space and in such case the following question will arise: how the cabin will deliver such a huge object in space without any damage?<br />
<br />
This can be done by means of two cabins. Generally, Space Elevator’s conception implies only one cabin moving along the cable, but for some special purpose (like delivering Space Catapult’s rod in space) we can use the second cabin also that will descend downwards after finishing its job and will not participate in Space Elevator’s further performance. As for the process of delivering the rod, we can imagine it in a following manner: at first the rod will be placed horizontally on the Earth (thus it must be manufactured and then transported to the Space Elevator’s base station), then the Space Elevator’s first cabin will carry rod’s one end along the cable while the rod’s second end will be moved on the Earth so that the rod to take more and more vertical position. When the rod is in vertical position the second cabin will capture rod’s second end and will carry it in space. We think that without the second cabin it would be quite difficult for one cabin only to carry long/heavy rod because the rod may actually shake and crash to the Space Elevator’s cable and this is absolutely undesirable. <br />
<br />
So, as we see in principle it looks to be quite easy, however the assembling may complicate due to rod’s length. In this case it would be better to carry not the rod as ''one single unit'' but its parts and then to assemble them in space in the following manner: ''two'' cabins will carry the first part as described above, when this part is delivered to space and temporarily hung at the cable the next two cabins will carry the second part that will be attached to the first one from below; the other parts will be delivered to space and assembled into the rod in the same way. <br />
<br />
The obvious disadvantage of the above-described method is that each part needs two cabins on the Space Elevator’s cable, besides the humans will be needed for assembling the rod from these parts in the atmosphere’s upper layers; therefore we think that the first way-delivering the rod into space as one single unit still would be easier and more realistic; besides we should take into consideration the fact that if the rod is assembled the additional devices will be needed ''on the rod itself'' for joining these parts and this circumstance would lead to increasing the rod’s total mass and this is undesirable. See the image showing assembling process:<br />
<br />
[[File: Assembling.jpg]] <br />
<br />
Whatever design/structure the rod has-assembled from several parts or as one single unit, it must be delivered to its destination-Space Elevator’s counterweight and must be fastened to electro motor’s own axis. But the problem is that the rod will be quite long and also the fact that Space Catapult’s electro motor will be placed at counterweight’s upper side (or at the ''lateral'' side if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), so it will be necessary the rod coming from below to be moved to counterweight’s upper/lateral side, besides the rod should be docked with electro motor’s axis as accurately as possible. How is it possible to realize such complex engineering operation? Here we can indicate one possible theoretical way: <br />
<br />
The rod will be parallel to Space Elevator’s cable when carried by cabin, but later the cabin’s mechanisms should rotate it so that the rod to be orthogonal to Space Elevator’s cable (this will not be necessary if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), exactly in this position the rod should be delivered to counterweight, besides the rod when moving along the cable should be shifted a bit upwards (relative to the Earth) than the cabin itself. Under such conditions we will easily achieve docking the rod to electro motor’s own axis which from its side should have some trapping device (magnetic for example) to “catch” the rod and thus guarantee docking the rod to electro motor and finishing assembling the Space Catapult as a whole. But if the rod’s plane of rotation is parallel to cable then assembling process will be much easier because the ascending rod may directly dock to electro motor’s own axis. See the image showing this process:<br />
<br />
[[File: Deliver - Copy.jpg]] <br />
<br />
We think that it would be useful if one Space Elevator is built specially for Space Catapult with its base station located on the land, not the ocean. This would be justified because transporting Space Catapult’s rod from its place of manufacture to Space Elevator’s base station should occur on the land by means of several transports simultaneously (due to rod’s great length), this will enable us to deliver the rod to its destination without any damage while this kind of operation is hardly possible on the water.<br />
<br />
=The technical aspects regarding the Space Catapult=<br />
<br />
As an example, we can try to calculate/ascertain all possible kinds of aspects regarding the rod with some certain mass and sizes, for example we can assume the Space Catapult has got 100 km length rod. <br />
<br />
The circumference of the circle that this rod’s end will draw in space will be equal to 2πr=628 km. As we have already mentioned payload’s abilities for withstanding the g-load is restricted, so if the electromotor rotates the rod so that payload’s speed is equal to 50 km/sec (this means that it will take 12.56 seconds for the rod to make one complete revolution), in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design the spacecraft that will withstand such acceleration, but what about the rod itself? Which material can be used for designing this rod, what will be its mass and how much energy and time will be needed for the rod to reach this velocity? <br />
<br />
For manufacturing the rod we should choose the material with very low density and highest value of strength. Currently, the ''Carbon nanotubes'' are the best candidates for this purpose. What will the mass of the rod made of this material? This depends on width also and it should be as less as possible (otherwise the rod will be too heavy and too wide for transporting from manufacture place to Space Elevator’s base station and for delivering it to space by means of Space Elevator) but from the other hand the ''applied load'' will not let us to design very narrow rod.<br />
<br />
Let’s assume that we intend to launch the payload with the mass of 10 000 kg (during calculation we will use ''SI system'' only). To clarify what kind of material will be able to withstand the acceleration we should calculate and then compare two values: the ''applied load'' and ''tensile strength''. For calculating the first one we should multiply g-load (which we already know-2 550 g) to its mass-10 000 kg, we will get 25 500 000. As for calculating tensile strength, we should take its values (for Carbon nanotubes it varies from 11 000 MPa to 63 000, we will take some medium value-40 000 MPa) and multiply it to cross-section’s area, in our case rod is cylinder with circular cross-section. If radius of cross-section is 1 meters then its area is 3.14 square meters, multiplying this value to value of tensile strength (40 GPa as said) we will get 125 600 000 000 and this is significantly more than value of applied load-25 500 000. Of course, we should also take into consideration ''factor of safety'' which is generally equal to 2 and this indicates us that for safety the payload’s actual mass should be twice less but in our case as we see the rod will be able to accelerate the payload to above-mentioned speed. By the way, note that if that g-load ''2 550 g'' is almost at the payload’s withstanding limit this is not serious problem for the rod itself (we have already seen that value of tensile strength is much more than value of applied load) and this is clear why: payload generally contains sophisticated equipments (electrical circuit, optics an etc.) that will not be able to withstand very high g-loads while the rod will be made of some continuous solid substance, Carbon nanotubes is this case and of course it will be able to withstand much higher g-loads.<br />
<br />
<br />
What will be the mass of such rod? Knowing its volume (for this purpose its cross-section’s area 3.14 square meters should be multiplied to rod’s length-100 000 meters, we get 314 000 cubic meters) and taking the value of density (this also varies for Carbon nanotubes from 0.037 to 1.34 g/cm<sup>3</sup>, let’s take 0.1 g/cm<sup>3</sup>) we get rod’s mass as 31 400 000 kilograms. This is too heavy for Space Elevator’s modern concepts and for improving this situation we should either use many cabins for raising the rod as single unit or use nuclear energy for feeding the cabins instead of laser/microwave beams or deliver the rod’s parts separately in space and then assemble them (see ''Assembling the Space Catapult''). But if some advanced substances are chosen for this purpose (for example ''Silica aerogel'' the density of which is about 1.9 mg/cm<sup>3</sup>, this is 50 times less than the density of the Carbon nanotubes taken above-0.1 g/cm<sup>3</sup>) than problem may be lightened in spite of the fact that their current tensile strength is quite low-16 kPa for the density of 0.1 g/cm<sup>3</sup> <sup>7</sup>. So, we can conclude that we need the material with the density of ''Aerogels'' and tensile strength of Carbon nanotubes.<br />
<br />
How much energy and time will be needed for the rod to accelerate from zero to desired speed-50 km/sec? The amount of rotational energy of the rotating rod can be calculated by the following formula:<br />
Kinetic Energy<sub>rotational</sub>= (1/2)*I*ω2 <br />
<br />
Where:<br />
<br />
'''I'''=moment of inertia <br />
<br />
'''ω'''=angular velocity<br />
<br />
"I" depends on the shape of the mass under rotation. In the case of a uniform rod rotating from its end (axis of rotation is at the end of the rod) I = (m*L2)/3<br />
<br />
<br />
“ω” = V/R, where V = tangential velocity and R = radius<br />
<br />
In our case ''moment of inertia'' is equal to (31 400 000 kg*100 000 m2)/3=104 666 666 666 666 666<br />
ω is equal to (50 000 m/sec)/100 000 m=0.5<br />
<br />
So, Kinetic Energy<sub>rotational</sub>=(1/2)*104 666 666 666 666 666*(0.52)= 13 083 333 333 333 333.25 Joules<br />
<br />
Now, how much time and what amount of solar panels will be needed for accelerating this rod? The amount of Solar constant near the Earth is approximately equal to 1300 W/m2 [<sup>8</sup>], with assuming that ''coefficient of efficiency'' of solar panels is roughly 20 % we get 260 Watts per square meters and we can easily link amount energy (that we have already calculated) and power with the time needed. Particularly, ''Energy'' is equal to ''Power''’s multiplication to ''Time'':<br />
<br />
[[File: Formula - Copy.jpg]] <br />
<br />
So, Time is equal to 13 083 333 333 333 333.25 Joules/260 Watts=50320512820512.8 seconds, or 1 595 652 years. If we take much more area for solar panels, for example 10 millions square meters then 0.1595652 years or approximately 58 days will be needed and we think that this is acceptable time span.<br />
<br />
Actually, the time and energy will be needed a bit more for overcoming static friction in electro motor, for overcoming the rarified atmosphere’s resistance (we know that there no absolute vacuum in space), also we should take into consideration electric motors’ coefficient of efficiency that generally reaches 90-95 %, so some energy loss will occur here also. <br />
<br />
Now, what will be the total mass of solar panels producing the energy for Space Catapult? This depends on mass/power ratio, in near future it is expected that very lightweight designs could likely achieve 1 kg/kW [<sup>8</sup>] or 0.260 kg/ 260 W (per 1 square meter), so if for rotating the Space Catapult 10 millions square meters of solar panels are used then their total mass would be equal to 2 600 000 kg. We think that it is too heavy for Space Elevator the mass of which is expected to be equal around several hundred metric tons. If so, we will have to use fewer amounts of solar panels and therefore increase the time needed for accelerating the payload’s speed from zero to designed one. This will not make problems if the rod is accelerated only once and then keeps its constant rotation-for this purpose less energy will be needed and the payload will have to reach the rod’s end by first method as described earlier in this paper (see ''Rod’s plane of rotation towards the Earth'').<br />
<br />
We also need to take into consideration the value of deflection when the rod will be delivered to space by means of Space Elevator (see ''Assembling the Space Catapult''), in this case the thin and long rod will be bent due to its own weight and here we will try to calculate its value. This is quite complex problem that apparently cannot have an unambiguous solution because of many reasons, for example due to various temperatures in atmosphere’s different layers, various humidity and possible wind, but still we will try to calculate the value of ''Deflection'' that will occur in case when the rod’s one end is fastened to Space Elevator’s ascending cabin and the second end is fastened to the transport moving on the land, we discussed this option in above-mentioned section of our paper (see ''Assembling the Space Catapult''). The inclination angle for the rod will vary from 0º (rod is transported horizontally on the ground) to 90º (Space Elevator’s cabins are carrying the rod to space) and here we will discuss some medium case when the rod is semi-elevated in the air, when the angle between rod and ground/cable is equal to 45º. On the engineers’ ''eFunda'' web-site there is online calculator that enables to receive the value of ''Deflection'' (actually that site gives different term for this-''Displacement'') [10]:<br />
<br />
Here we need to enter the relevant values:<br />
<br />
''Length of beam'', ''L'': 100 000 meters<br />
<br />
''Line pressure load on beam'', p: In our case this is the weight per meter length. As we have already mentioned the radius of the rod’s cross-section is 1 meter, so the volume of rod’s 1 meter-length part will be 3.14 cubic meter. In case of using Carbon nanotubes with above-mentioned density-0.1 g/cm<sup>3</sup> the weight will be equal to 314 kg or 3 079 Newton. Since we have got the inclination of 45º we should multiply this value to cos45º- 0.707, so we get 2176 N/m.<br />
<br />
''Young's Modulus'', ''E'': This is equal to 1 000 GPa for Carbon nanotubes [11] <br />
<br />
''Distance from neutral axis to extreme fibers'', ''c'': In our case it is equal to the radius of the rod-1 meter<br />
<br />
''Moment of Inertia'', ''I'': It is equal to (pi*r<sup>4</sup>)/4, so it is equal to 0.785<br />
<br />
According to these initial data the calculator returns extremely high value of Deflection, much higher than the length of the rod itself: -3.61 × 10<sup>9</sup> meters. This result shows us that with the current materials (Carbon nanotubes in our case) it is impossible to raise the rod as ''one single unit'' to space by means of Space Elevator and we need other materials with less density and more ''Young's Modulus'' (or the rod should be much thicker but this will lead to increasing its mass). Therefore, we have got two options: either we should deliver the parts of that rod and then assemble them in space (we have already discussed this option) or completely different technologies for manufacturing the rod should be developed. Particularly, it would be very good if it was possible to manufacture the rod ''in continuous mode'' in vertical position and then uninterruptedly directly to carry it to space by means of Space Elevator’s cabins. Under such approach there will be no ''Deflection'' and several cabins will be able to deliver the rod in space. <br />
<br />
One note about transporting the rod from its place of manufacture to Space Elevator’s base station. We think that this process should be executed by many transports, in other words we are convinced that if the rod is carried by two trains only (or any other kind of transport) then the rod will continuously touch the ground since the ''Deflection'' occurs in any position-horizontal, inclined or vertical and this circumstance will lead to its damage, that’s why several transports will be needed to hold the rod at as many places as possible.<br />
<br />
=Stabilizing the counterweight=<br />
Stabilizing the Space Elevator’s counterweight is very important question during Space Catapult’s performance. Indeed, when the rod rotates it makes the imaginary circles in space and due to rod’s and payload’s masses the Space Catapult’s ''center of mass'' will be continuously shifted and if the counterweight is not somehow stabilized then it will make problems for accurate aiming to certain point at the celestial sphere. Also, if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable then there will be the danger that the rod may actually hit the cable and cut it. To avoid these problems we need to apply to serious measurements. <br />
<br />
First of all, the electro motor’s own axis can be quite long and this will diminish the chance to failure of the whole system. Actually, we are convinced that counterweight’s (where the electric motor will be placed) size will be quite large, mainly due to solar panels’ sizes and amount (this issue was discussed above), also the electromotor should be quite large and powerful to rotate the rod, and hence there will be enough distance between the rod and Space Elevator’s cable. <br />
<br />
The second serious problem is that the center of gravity of the system is not at the center of rotation, therefore it will be necessary to balance the rotating system when the payload is attached and when it is released.<br />
<br />
We think that the Space Catapult’s rod should not be deployed/directed to one side only but some counterweight of it should also exist. This is necessary since the unilaterally loaded (we mean the rod itself plus payload) rod will cause the counterweight to somersault. In other words, the rod should extend to other side and the ''moments of inertia'' of both sides should be the same as during rotating the rod as after releasing the payload when the rod still rotates. This is easily achievable if some additional, second payload is placed on the rod’s second end. Therefore, the Space Catapult will launch two payloads at the same time to the ''opposite'' directions but at various speeds if the second part/side of the rod is shorter.<br />
<br />
How the second payload should be placed on the rod and should we really send two payloads? Until we have got balanced rod this problem does not arise but as soon as the Space Catapult releases the payload this balance will be violated, how it can be restored? There are two theoretical ways for achieving this: reducing the ''mass'' or reducing the ''length''-with diminishing either one of them the ''moment of inertia'' will be decreased. We think that reducing the mass will be less practicable since this would require placing the second payload (spacecraft or anything else) on the rod’s second part and this cannot be done from the Space Elevator’s cabin-this is the easiest way for delivering the payload from Earth to Space Catapult’s rod; so we would have to (see ''Rod’s plane of rotation towards the Earth'') put the second payload on the electro motor and then send it rod’s second part’s end. This is quite complicated task; therefore we can apply to second approach-put some sliding object that will immediately move to electromotor as soon as the spacecraft is released.<br />
<br />
[[File: MOI.jpg]] <br />
<br />
The next problem that may occur is that when the electro motor rotates the rod this motion will make the Space Elevator to rotate to the opposite direction. The same problem arises when helicopter’s primary blade’s rotation forces the helicopter to rotate to opposite direction and this possible rotation is annulled by ''tail rotor''. We think that for balancing the counterweight the additional motor and rod should be installed and this rod should rotate to opposite direction and if their ''angular momentums'' are equal to each other, then their rotations will cancel each other. More precisely, the following equation should be fulfilled:<br />
<br />
[[File: Angular momentum.png]] <br />
<br />
Where ''m'' is mass of the rod, ''v'' is angular speed and ''L'' is rod’s length, the numbers ''1'' and ''2'' refer to first and second rods correspondingly. For balancing both rods’ rotation the multiplication at both sides of the counterweight should be equal, by the way this circumstance enables us to use the second rod with shorter length and even with less mass but rotating at more angular velocity.<br />
<br />
Such approach will effectively deal with other problem which will arise when the Space Catapult releases the payload(s), at this moment the second motor should instantly diminish its angular velocity to some certain level (an ordinary mechanical brakes could be used for this purpose), in this case ''angular momentums'' for both motors/rods will be equal again and Space Elevator’s counterweight will maintain its attitude in space. See the image below depicting the Space Catapult with two electro motors and rods:<br />
<br />
[[File: Two-rods.jpg]] <br />
<br />
Such approach will justify itself if rod’s plane of rotation is parallel to Space Elevator’s cable, but if this plane is orthogonal to cable (see ''Rod’s plane of rotation towards the Earth'') then the second/balancing electromotor cannot be placed under the counterweight because the cable will be cut when rod touches it. Therefore a bit different approach should used and we need to install two/four/eight electro motors with their own relatively shorter rods rotating to opposite direction. They should be placed at the counterweight’s lower side and on its edge (as we suppose the counterweight should be disc) so that their rods not to touch and cut Space Elevator’s cable. Also, total a''ngular momentums'' from these motors should be equal to the ''angular momentum'' from upper motor and thus the counterweight will not rotate and the Space Elevator’s cable will not be twisted. This situation is presented below:<br />
<br />
[[File: Modified-2.jpg]] <br />
<br />
We think that the array of gyroscopes would be also very useful to be installed at the counterweight since they can maintain the attitude of the whole system and this is important for precise aiming to certain point at the celestial sphere. As for the energy required for gyroscopes’ performance it could be received from the array of solar panels which as a result will generally serve Space Catapult’s precise performance.<br />
<br />
=Space Catapult placed at Lagrangian points-the way for gaining subluminal speeds=<br />
<br />
In our paper we discussed the Space Catapult based on the Space Elevator’s counterweight and concluded that this would be convenient when we intend to deliver the payload to space from the Earth. However, such Space Catapult cannot gain very high speeds and therefore we need to choose other way. It is obvious that we need to keep rod’s plane of rotation orthogonally relative to the ''Earth-Sun connecting line'' and hence we should place the rod on the celestial body which will be in synchronous rotation with the Sun but since there is no such body in the solar system we conclude that the Space Catapult for subluminal speeds (the speeds close to speed of light are in mind) should be placed at such point near the Earth where it will be easy to reach it from our planet and where the rotating rod will not hit the Earth and will be always at the same distance from the Sun to avoid the influence of its tidal forces. The examples of such places are '''Lagrangian''' L<sub>1</sub> and/or L<sub>2</sub> points at 1.5 million km away from the Earth. If the Space Catapult is placed at one of these points then its rod can be always orthogonal to the Sun in principle, at the same time it will never collide with the Earth and also it will be quite close to the Earth since 1.5 million km distance is very negligible in space.<br />
<br />
We have got several notes regarding such approach. First, when we mentioned that the rod’s various parts can be at the same distance from the Sun this strictly speaking is not very true because the Sun can be referred as little point where its gravity “comes out” from while the rod is quite long and its initial part (placed at one of the Lagrangian points) will be attracted stronger than the utmost one (for equal attracting the rod should the arc ''with the same curviness as Sun’s surface'' and not straight line); but still this is better than to direct the rod exactly towards the Sun where the tidal forces will try to tear the rod. Second, the Space Catapult should be placed at Lagrangian L1 point which is closer to the Sun than L2 one and therefore receives by 4 % more energy per area from the Sun. Third, the rod should be in constant rotation, this requires much less energy than accelerating it from zero, then stopping it and accelerating it again. Fourth, the existence of the asteroid belt in the solar system between Mars and Jupiter will somehow restrict the actual length of the rod. Indeed, the Space Catapult should be placed at one of the Lagrangian points at 1 AU distance from the Sun while asteroid belt approximately lays at 2.7 AU, from the simple geometry it is obvious that the length of the rod ''almost reaching'' the asteroid belt can be approximately equal to 390 million km, and if the rod is longer then it may simply hit any asteroid within that belt. For 390 million km length rod and for 100 000 m/sec2 acceleration at rod’s end (where the payload will be attached) the maximal speed that the spacecraft can gain will be approximately equal to 200 000 km/sec (two thirds of the speed of light) and this can be considered as enough for practical interstellar spaceflight. Fifth, the spacecraft should be directly put on the rotating rod’s initial end (near electromotor) and then slide towards the other end with its own rocket engines. To achieve this, the spacecraft will have to cover relatively less distance on the rod and then rod’s circular motion will accelerate the spacecraft further-we have already mentioned this in this paper when speaking about deploying the Lunar Space Catapult. This action-putting the spacecraft on the rod will not be difficult since rod’s angular velocity will be quite low due to rod’s huge length, particularly for 400 million km length rod and for 200 000 km/sec linear speed the rod’s angular velocity will be 0.0000796 revolutions/sec.<br />
<br />
[[File: Lagrangian-point.jpg]] <br />
<br />
We have already mentioned that to avoid the destructive influence of the Sun’s tidal forces the rod’s plane of rotation should be orthogonal to the Earth-Sun connecting line. By the way, note that under such approach we may have to wait one year until the Lagrangian Space Catapult occupies the relevant position towards the certain point at the celestial sphere where the spacecraft should be sent to. But from the other hand it would be useful if it is feasible to rotate this whole structure around the imaginary axis directed towards the ''ecliptic poles'' (depicted as faint green dash line on the image above), the reason if this is the possible danger when the rotating rod may hit Mars or asteroids that orbit around the Sun closer than 2.7 AU distance (for example ''433 Eros'' or ''1036 Ganymed''), hence for avoiding such undesired collision the Lagrangian Space Catapult should be slightly rotated by several degrees clockwise/counterclockwise so that the rod not to collide with any celestial object. We are convinced that rotation by several degrees will be absolutely enough measurement due to rod’s gigantic length and relatively less sizes of the celestial objects in the solar system.<br />
<br />
The next issue that we should discuss refers to stability of the Lagrangian Space Catapult placed at L<sub>1</sub> point. As we see this structure will have enormously gigantic size while the Lagrangian point is relatively little mathematical one in space, so what can be done to be convinced that this structure will remain at that point and do not shift aside? The body placed at one of the Lagrangian points is affected by other celestial objects’ gravity and therefore for achieving the balance the rod needs to have the counterweight with more mass if it (counterweight) is shorter. As we clearly see the rod needs the counterweight for two reasons: not to let the Space Catapult somersault and for maintaining it at the L1 point. We think that it would be very useful if the arrays of solar panels act as counterweight since exactly they can give us energy for rotating the rod. Also, we need the second, shorter, perhaps less massive but faster-rotating rod (again-solar panel arrays) the opposite rotation of which would cancel first rod’s rotation, this issue was discussed in this paper. These arrays of solar panels are depicted on the image shown above. <br />
<br />
How such a gigantic structure as Lagrangian Space Catapult can be assembled in space? In our paper we discussed the possible ways for delivering the rod from the Earth to the Space Elevator’s counterweight, now we will try to show that it is possible ''in principle'' to assemble the extra-long rod in space. <br />
<br />
If it is possible from the technical point of view to manufacture extra-long rod then we can use this approach and make 1.5 million km length rod (this is the distance between the Earth and Lagrangian L<sub>1</sub>/L<sub>2</sub> point) that will be mechanically directed to the base station at L<sub>1</sub> point. The capturing devices there will catch the rod and attach it to the electro motor’s shaft after which the rod should be spun by 90º so that it to be orthogonal to Earth-Sun connecting line (for this purpose the additional mechanisms will be needed), this spin is necessary because L<sub>1</sub> point is located on the Earth-Sun connecting line (that is towards the Sun if we look from the Earth) and when directing the rod from the Moon it will lay ''along'' this line while we need across. After this the rod should be slid to another side and then the next rod should be directed to the Lagrangian Space Catapult where it will be attached to the previous rod and etc. In other words, the extra-long rod will be assembled from one side and its length will “grow” from this side to other one, this is necessary because the distance between Moon (the rod should be manufactured exactly there and not on the Earth due to our planet’s relatively more gravity, atmosphere and problematic space debris belt around it) and L<sub>1</sub> point is constant and rod’s parts cannot be more. Due to whole rod’s and its parts’ lengths (400 million and 1.5 million km correspondingly) we think that about 260-270 such operations will be needed to finish assembling the rod (400/1.5). The process of assembling the Lagrangian Space Catapult is shown on the image below:<br />
<br />
[[File: Lagrangian-point-assemble.jpg]]<br />
<br />
=Conclusion=<br />
<br />
As we have seen, for leaving the Solar system and reaching the remote celestial bodies (stars, nebulas) there is no need to develop advanced and complicated technologies that mostly are not capable for gaining extra high velocities nevertheless. In any case, until the Space Elevator is really built (scheduled for construction by 2031) we have got much time for developing the idea of Space Catapult in technical aspect, like finding appropriate materials for the rod, perfect the ways how the Space Catapult can be assembled in space and etc. The concept of Space Catapult itself is the easiest one, does not need developing neither complex and sophisticated technologies, nor some exotic methods (such as ''Gravitoelectromagnetic toroidal launchers'', ''Antimatter rocket'' and etc.) and can be easily implemented in near future; in other words the Space Catapult is not some sophisticated structure that would need profound science research and the fact that it will enable us to gain whatever high speed will justify its developing and building by the humankind. As for other technologies like Ion Drive, they could be used by the spacecraft during flight for other purposes, for example for correcting/changing the flight direction.<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Space_Elevator<br />
<br />
2. http://www.isec.info/index.php?option=com_content&view=article&id=14&Itemid=9<br />
<br />
3. http://www.space-track.org/perl/geo_report.pl (provided data updates regularly, registering is needed) <br />
<br />
4. http://www.oosa.unvienna.org/pdf/reports/ac105/AC105_720E.pdf page 24 (data as at 21 August, 1997) <br />
<br />
5. http://www.amostech.com/ssw/presentations/Session7/S7-1Molotov.pdf page 16<br />
<br />
6. http://www.esa.int/SPECIALS/ESOC/SEMN2VM5NDF_mg_1_s_b.html <br />
<br />
7. http://eetd.lbl.gov/ecs/aerogels/sa-physical.html<br />
<br />
8. http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant<br />
<br />
9. http://www.you.com.au/news/2005.htm, http://www.spacedaily.com/news/ssp-03b.html<br />
<br />
10. http://www.efunda.com/formulae/solid_mechanics/beams/casestudy_display.cfm?case=simple_uniformload<br />
<br />
11. http://en.wikipedia.org/wiki/Young%27s_modulus<br />
<br />
<br />
'''Appendix''': <br />
<br />
Animation illustrating the payload’s departure from the Lagrangian Space Catapult:<br />
[[File: Lagrangian-point-animation.gif]]</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_5&diff=3665OpenSpace 52013-09-21T12:54:13Z<p>Eagle9: </p>
<hr />
<div><div style="float:right; border:#CCCCCC solid 1px; background-color: #F7F7F7"><br />
<table cellspacing=0 cellpadding=0 width=550><br />
<br />
<tr><td colspan="3" align="center" style="background-color:#CCCCCC"><b>Title:</b> Place Title Here</td></tr><br />
<br />
<tr><br />
<td align="center" valign="middle" height=125 width=100 style='padding:10px'><br />
<div style="background-color:#CCCCFF; height:110px; width:90px"><br />
[Cover Img]<br />
</div><br />
</td><br />
<br />
<br />
<br />
<br />
<br />
== '''Space Catapult''' ==<br />
<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
=INTRODUCTION=<br />
<br />
<br />
The new method for sending the spacecrafts in deep space is presented here. The paper describes the long rod rotated by electro motor placed at the Space Elevator’s counterweight and at Lagrangian points. This simple structure will enable the rod to gain high velocity and carry the payload with it. After reaching the desired speed the rod will release the payload that will fly in space along the imaginary circle’s tangent. This structure we called Space Catapult and it should work with the assist of Space Elevator. This latter should be used for carrying the payload from the Earth to Space Catapult’s rod.<br />
<br />
For exploring the outer space the humankind generally uses the rocket engines, mostly chemical-propelled ones. They enable us the explore near-Earth celestial bodies and other planets in the solar system. They even enabled us to send several deep space missions beyond the solar system such as '''Pioneer-10''', '''Pioneer-11''', '''Voyager-1''', '''Voyager-2''', however by means of this technology the flight lasts undesirably long and it seems to be impossible to reach remote celestial bodies in space such as stars, so new technologies are necessary for this purpose. However new technologies do not necessary imply new kind of rocket engines, such as ''Ion Drives'' because they are capable for gaining several ten times higher speeds only, but for remote celestial bodies even they are not suitable. Besides, they need a huge amount of energy to be stored onboard the spacecraft and this will make additional problems. So, high speed should be achieved with absolutely different approach. How this can be done?<br />
<br />
High speed can be easily achieved by means of fast-rotating rod around the electric motor. The motor’s rotational speed can be very high; the rod also can be quite long, hence the rod’s end’s linear speed can be extremely high, absolutely unachievable for any other technologies nowadays. The payload should be fastened at the rod’s end where the linear speed generally reaches maximal value. After reaching the necessary speed the rod will release the payload that will fly along the tangent from the current position. Thus the electric energy can be turned into payload’s speed and its velocity could be as high as we wish (except the ''speed of light'' of course). In principle the '''Space Catapult''' (thus we call this structure) would be the simplest, the most convenient and direct way for converting the energy/electricity into speed and conveying it to payload. <br />
<br />
As we see the Space Catapult is quite uncomplicated structure, however if we wish to gain high speeds we should deploy it in space, not on the Earth. Indeed, our planet is surrounded with dense atmosphere that impedes any quick motion, so if we rotate the rod quickly the atmospheric drag and generated heat would burn it very soon, therefore the Space Catapult should be built and deployed in space only, and as we suppose-at the Space Elevator’s counterweight. In other words, the Space Elevator’s counterweight will operate as Space Catapult. See image below:<br />
[[File:Space-catapult.jpg]]<br />
Generally, what is the Space Elevator <sup>1</sup> <sup>2</sup>? According to modern concepts it will be the tall vertical structure built on equator and will have height of several ten thousand kilometers with its thin cable fastened to the base station on the Earth and with counterweight placed higher geostationary orbit. Because of balance between centrifugal force and gravity this structure will be stretched and the cabin will move along its cable carrying the goods into high orbit. After delivering the payload, the cabin will descend and carry the next one.<br />
In Space Elevator’s concepts several solutions have been proposed to act as a counterweight: <br />
<br />
1. Heavy, captured asteroid <br />
<br />
2. Space dock, space station or spaceport positioned past geostationary orbit <br />
<br />
3. Extension of the cable itself far beyond geostationary orbit. <br />
<br />
The third idea has gained more support in recent years due to the relative simplicity of the task and the fact that a payload that went to the end of the counterweight-cable would acquire considerable velocity relative to the Earth, allowing it to be launched into interplanetary space. However this idea cannot be completely shared by us due to following reason: <br />
<br />
It is well-known that the values of both '''Orbital''' and '''Escape Velocities''' decreases with increasing the altitude while the '''tangential velocity''' of Space Elevator’s cable increases. We can see the differences between them from the chart presented below:<br />
[[Image: Cxrili.gif]]<br />
<br />
As we see from this chart the ''tangential velocity'' of the Space Elevator even at its end (144 000 or 200 000 km altitude) is not very high to decrease the necessary time for covering the distance from the Earth to remote celestial bodies significantly. To achieve this, even the longer Space Elevator would be needed (its ''tangential velocity'' is directly proportional to its length) and this circumstance would complicate the technical task for building such Space Elevator. Because of this, there is no necessity to extend the cable itself far beyond geostationary orbit as proposed in the third variant. In any case, we have already seen that by means of Space Catapult it is possible to gain such huge velocities that are absolutely unachievable with other technologies, for example with Space Elevator. Therefore, using the counterweight and placing the Space Catapult there definitely has got some technical sense. <br />
<br />
However, we think that the question where the Space Catapult should be placed needs further discussion. Theoretically, the Space Catapult with its payload and nuclear reactor/solar panel needed for rotating the rod may be mounted not only at the counterweight, but on the Space Elevator’s cabin also that can carry all these goods to space in a usual way, as it should do it according to Space Elevator’s modern concepts. This option is quite possible, however for realizing this we need to know the mass of the payload, nuclear reactor/solar panels’ mass plus Space Catapult’s mass from one hand and Space Elevator’s lifting capacity (this ''must'' be more) from other hand, but these data are not available nowadays, therefore we think that the Space Catapult should be still mounted at the Space Elevator’s counterweight where it will be possible to send the payloads into deep space in ''continuous mode'' at high velocities.<br />
<br />
As we saw the Space Catapult is capable to gain very high velocities; however there is being developed other technologies and they in future will enable the spacecraft to fly at high speeds in space. These are Ion Drive systems, more precisely the most perspective one-''Variable Specific Impulse Magnetoplasma Rocket'' (VASIMR) which still under development can be used in future for deep space missions. Can these engines and Space Catapult be the rivals in space? Since none of them have been built and used in space yet we cannot give a persuasive answer to this question; however still it is possible to underline Space Catapult’s one significant advantage: if the future spacecraft uses the VASIMR (or any other kind of Ion Drive) engine it will definitely need to be equipped with nuclear reactor, otherwise the spacecraft will not be able to gain high speeds, also it will need to carry fuel tanks for this purpose. As for the Space Catapult, it can give much higher speed to spacecraft, besides it will have ''stationery'' power plant (see ''Energy source placed on the Space Elevator’s counterweight'') at the Space Elevator’s counterweight, so the payload will ''not'' have to carry the nuclear reactor onboard and this circumstance will lighten the work for deep space spacecraft. Besides, we should not forget that unlike the spacecrafts equipped with ion drive engines the Space Catapult will need no fuel for gaining high velocities. <br />
<br />
Briefly, Space Catapult’s advantages over any kind of propulsion systems are: <br />
<br />
1. Ability to gain any speed that is absolutely unachievable by means of other kinds of engines. <br />
<br />
2. No need by spacecraft to carry energy source that would make it too heavy and impracticable.<br />
<br />
=The Space Catapult needs long rod=<br />
<br />
When building the Space Catapult at Space Elevator’s counterweight we should install quite long rod there, the shorter the rod is, the easier would be installing it, however we should note that rod cannot be extremely short, let’s say 1 km length or so due to following reason:<br />
<br />
When we are going to send some payload into space, we need not only high velocity, but one certain direction also. The little inaccuracy in direction, inclination in several arcminutes is actually acceptable since the spacecraft would easily balance it with its engines; however great inclination from the initial direction would send the spacecraft into the completely different direction and in such case the whole mission will fail.<br />
<br />
If two Space Catapult’s rods have the length of let’s say 1 kilometer and 10 kilometers, then for giving to payload some certain linear speed (for instance 100 km/sec) these rods should rotate at different angular velocity. It is easy to ascertain that the shorter rod should rotate 10 times faster to gain the same linear speed than the rod with more length. But the faster the rod rotates, the more difficult will be to “catch” the needed moment for releasing the payload from the rod for sending it towards some certain direction. If the rod is too short, then it has to rotate very quickly for gaining some certain linear speed and therefore it will be extremely difficult catching the needed moment for releasing the payload. Hence, too short rod can make problem for sending the payload to some certain direction in space especially at high velocities. So, based on payload’s needed velocity we should find rod’s desired, minimal length that will enable us to send the payload in space to necessary direction without fear that it may yaw from the course. <br />
<br />
However, rod’s length will be crucial for payload’s abilities for withstanding the acceleration also. As an example, we can try to calculate its value which the payload will have to withstand during rod’s rotation. The acceleration of the body rotating at the circle with some constant velocity is calculated by the following formula:<br />
<br />
[[File: Acceleration - Copy.jpg]] <br />
<br />
Where a is acceleration in ''m/sec''<sup>2</sup>, ''v'' is payload’s linear velocity on the circle in ''m/sec'' and ''r'' is radius of the circle in ''meters'', in our case it is equal to rod’s length. Let’s assume that the rod is 100 km length and the electromotor rotates it so that payload’s speed is equal to 50 km/sec, in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design and manufacture the spacecraft’s subsystems (avionic and etc.) capable to withstand such acceleration. This circumstance somehow restricts the speeds that we can achieve, in any case their values actually depends on spacecrafts’ abilities for withstanding g-loads. But what can we do if much higher speeds are needed? The answer directly derives from that formula: the radius should be more; by the way note that this is additional reason why the longer rod is more useful. If we are able to make the extra long rod, then this will enable us to gain much higher velocities. <br />
<br />
What material should be used for manufacturing the rod? It is obvious that if very high speeds are needed the rod should be long and even in this case the acceleration at its end will be quite high, therefore ''sufficiently strong and light materials'' are needed for this purpose and making them is as similar challenge as in case of Space Elevator where the same requirements arises for the cable’s material. The lightness is needed because in case of heavy rod a lot of energy will be needed to rotate it; the strength is needed because in case of lack this property the rod will be destroyed due to great acceleration.<br />
<br />
=The mechanism for holding and releasing the payload=<br />
<br />
How the payload can be held by Space Catapult’s rod during rotation and how it can be released from the rod? We think that using ''electromagnet plus mechanical holding devices'' would be a good solution. More precisely, after the payload is attached to the rod it must be held by means of both methods until the rod accelerates and reaches necessary velocity (it may take even several days), but with approaching the desired speed the mechanical device should release the payload however the electromagnet(s) should still hold it. The explanation of such approach is following: generally the mechanical devices are much slower/sluggish in performance than electronic ones. We have already said that when releasing the payload the extreme accuracy is needed and mechanical devices cannot guarantee ''the exact time of releasing'' the payload unlike electronic ones. That is, it’s unlikely that mechanical devices can release the payload at some certain moment when needed while in case of electromagnet it would be enough to cease electric current there, it would lead to immediate vanishing of the magnetic field and sending the payload along the tangent from the point where the payload would be at the current moment. <br />
<br />
<br />
We think that the ''fastest control system'' would enable to release the payload to certain direction. This system (extremely fast-operating computer plus measuring equipments) should know the current position of the rod’s end, the current speed, the needed direction and be capable for computing the necessary moment for giving the order for diminishing the voltage for electromagnets and hence releasing the payload to desired direction and velocity.<br />
<br />
=Rod’s plane of rotation towards the Earth=<br />
<br />
The Space Catapult’s rod when rotating makes the circular plane/flatness in space and this plane may be horizontal/parallel to Earth surface, that is making the right angle to Space Elevator’s cable or it may be placed along the cable; see the both possible situations here:<br />
<br />
[[File: Planes-of-rotation - Copy.jpg]] <br />
<br />
Both approaches have got their advantages/disadvantages and here we will discuss this question, first of all from the point of view of safety.<br />
<br />
For gaining extremely high velocities quite long rod would be needed, maybe with the length of several thousand kilometers or even more. If such rod is placed ''along'' the Space Elevator’s cable then the rod during rotation will cross many orbits from the ''Medium Earth Orbit'' to ''High'' ones. When rotating, the rod may actually hit any satellite and/or space debris object and such collision can lead to rod’s complete destruction; therefore we should choose such plane which would be much more free from any artificial objects; hence if the rod rotates ''horizontally/parallel'' to Earth’s surface at high enough altitude where the satellites’ population is relatively low then this measurement would justify itself because under such circumstance the rod will not cross satellites’ orbits (rod’s plane of rotation will simply coincide to ''one'' orbit’s path). However, we should also note that this altitude actually depends on the Space Elevator’s proposed length. Indeed, the Space Catapult’s rod should be mounted at the Space Elevator’s counterweight; this counterweight from its side should be placed at the end of the Space Elevator at such altitude where the satellites’ population is as low as possible. This means that Space Elevator’s proposed height should be agreed with mounting Space Catapult on its counterweight. According to various databases the number of man-made objects at high orbits, more precisely beyond geostationary orbit is much less than on the lower orbits <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup>, therefore the Space Catapult with its rod should be located at the altitude of 50 000-60 000 km above the sea level. At such altitude the space is almost free and nothing will impede rod’s rapid rotation. Besides, the satellites at high orbits are orbiting around the Earth slower than on the lower orbits (as known any satellite orbits around its primary body slower in apogee than in perigee), therefore if some tracking system is mounted at Space Elevator’s counterweight then it will enable the Space Catapult to avoid undesired collision with satellites during Space Catapult’s performance. In other words, the Space Catapult should operate only when the there are no satellites near its vicinities.<br />
<br />
Now we will try to discuss this question from other side.<br />
<br />
How the payload can be transferred from the Space Elevator’s cabin to the Space Catapult’s rod? One way is following: cabin reaches the counterweight where the payload will be released, then payload will be mechanically conveyed to rod, continues its way ''on the rod'' (like the train rides on the rails) and after reaching rod’s end it stops, the rod begins rotating and after gaining necessary linear speed it releases the payload to needed direction. This method is generally realizable; however it seems to be too complicated and unpromising compare to the second one: the Space Catapult’s rod is stopped in space so that it to be directed downwards to the Earth and be parallel to Space Elevator’s cable. The Space Elevator’s cabin moving along the cable with payload stops at the cable ''near'' the end of the Space Catapult’s rod and releases the payload that will fly to the rod, attaches itself to the rod’s end (here the electromagnets would be useful), the rod begins rotating and after gaining needed linear speed will release the payload to necessary direction.<br />
<br />
This second way seems to be more promising because the first one is much more complicated as we have already said: first of all there would be needed some mechanical devices for transferring the payload from the Space Elevator’s cabin to counterweight, the counterweight should have the hole for the payload to move through it from below (we should not forget that the Space Catapult should be mounted ''at'' the counterweight, not ''beneath'' it), besides the rod should be made so that it to have some conveying surface (rails for instance) the payload to move on it. As we see it would be much more convenient if it is possible to convey the payload from the cabin to the rod directly and this would be feasible under the second method which is depicted below:<br />
<br />
[[File: Convey.jpg]] <br />
<br />
One more aspect regarding Space Catapult’s position. This structure, its rod, its electro motor and etc should be mounted at Space Elevator’s counterweight so that the rod to be placed westwards from the cable. The reason of it is following: when the Space Elevator’s cabin stops and releases the payload (which should fly to Space Catapult’s rod) the current speed of which will/should be more than the value of the ''Orbital/Escape Velocity'' at the current altitude. After releasing the payload will fly westwards and upwards because its orbit will be ellipse, under ellipse the payload will fly higher to apogee and at the speed less than Space Elevator’s current speed at the given altitude, in other words the released payload will “lag behind” the Space Elevator’s cable; therefore payloads’ ''stopping points'' at the cable and Space Catapult’s rod’s length should be calculated and chosen so that the payload to fly directly towards rod’s end. This process would be feasible in both cases-if the rod’s plane of rotation is parallel to Earth’s surface and if it is placed along the cable-but still this would be easier for the payload to achieve the rod’s end if the rod is placed along the cable because at least the distance that the payload should cover in space will be less.<br />
<br />
The length of the Space Catapult’s rod placed at the Space Elevator’s counterweight might vary since for various spaceflight purposes different initial speed will be needed and relatively low speed could be achieved by means of shorter rod. Because of this reason it might be necessary to change Space Catapult’s rod’s length, therefore it would be useful if the rod consists of two parts where the first part would be perpetually attached to electro motor and the second one will be attached to the first part if necessary. For this operation Space Catapult’s rod should be placed along the cable since the relative nearness would make this operation quite easy and it could be accomplished by the crew directly from the Space Elevator’s cabin stopped at the needed altitude. <br />
<br />
For deciding the question how the Space Catapult’s rod should be placed towards the Space Elevator’s cable we should take into consideration one substantial circumstance-to which direction do we plan to send the payload in space by means of Space Catapult? This circumstance will influence deciding this problem due to following reason:<br />
<br />
In case ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and if rod’s plane of rotation is parallel to Earth equator, then this plane will be orthogonal to Earth’s rotation axis. This axis from its side is tilted to ''ecliptic plane'' by 66° 34'. This means that Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 23°26'. Here follows very important consequence: under above-mentioned conditions the rod when rotating will be capable for covering only the part of the ''celestial sphere'' from 0° to 23°26' (counted from ''ecliptic plane'' northwards and southwards to ''Ecliptic poles''). This is about one fourth of the ''celestial sphere'' (23°/90°), this will not make problems if we intend to use the Space Catapult for exploring the solar system’s planets because their orbits’ tilts towards ''ecliptic plane'' do not exceed 7° (for planet Mercury, for other planets this tilt is even less); however we will not be able to send the payload for example to the nearest star ''Alpha Centaurs'' because this star is located at -42 degree according to ''ecliptic coordinate system'' in the celestial sphere.<br />
<br />
The situation will drastically change ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and ''if'' rod’s plane of rotation is orthogonal to Earth’s equator and therefore parallel to Earth’s axis of rotation. We have already discussed this option when we mentioned that the rod should be placed westwards from the cable and explained why it would be useful-for delivering the payload from Space Elevator’s cabin to Space Catapult’s rod. Under such conditions the Space Catapult will be capable to aim to any point on the ''celestial sphere''. Indeed, the Earth with the Space Elevator rotates around its axis and Space Elevator’s counterweight draws an imaginary circle in space. This circle is tilted to ''ecliptic plane'' at 23°26' and crosses this plane in two point called ''ascending'' and ''descending nodes''. The other points that are 90° away from these nodes we call point(s) of ''maximum elevation/depression'' (relative to ''ecliptic plane''). When the Space Elevator is at a''scending/descending node'' its rod and hence the payload can be directed to any point from 0º to 66º on the celestial sphere northwards and southwards from ecliptic plane. This makes about 75 % of celestial sphere. See the image depicting this situation:<br />
<br />
[[File: Node.jpg]]<br />
<br />
But when the space Elevator reaches the points of ''maximum elevation/depression'' then its rod during rapid rotation may be directed to any point from southern ''Ecliptic pole'' to ''Northern pole'' at the celestial sphere because at these points rod’s ''plane of rotation'' is orthogonal to ''ecliptic plane'' and thus the rotating rod can aim to ecliptic poles as well as other points. See this situation below:<br />
<br />
[[File: Elevation.jpg]] <br />
<br />
The situation will be similar if the Space Catapult’s rod is orthogonally placed towards cable. Under such approach Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 66° 34' and the Space Catapult will be capable to cover ''three fourths'' (66°/90°) of the ''celestial'' ''sphere'' when the Space Elevator is at the points of ''maximum elevation/depression'' and the whole celestial sphere when the Space Elevator is at ascending/descending nodes. For aiming the needed point on the celestial sphere the Earth should occupy the appropriate attitude towards the stars during the revolution around its axis, the same thing should be done under previous case described in the paragraph above. <br />
<br />
In conclusion, thinking about rod’s plane of rotation towards the Earth, we should note one important difference between above-mentioned approaches: if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, then in case of emergency during Space Catapult’s performance (for example if the Space Catapult’s rod is cut by sudden meteorite bombardment) the rod’s part with the payload may simply crash to the Earth at huge velocity if the rod at this moment is directed to the Earth. This cannot happen if Space Catapult’s rod’s plane of rotation is orthogonal to Space Elevator’s cable because payload’s rotational path will not be directed towards the Earth and hence its flying trajectory will never cross the Earth.<br />
<br />
=Braking the Space Catapult’s rod=<br />
<br />
After releasing the payload at necessary speed and direction, the Space Catapult’s rod will have a huge angular velocity that needs to be decreased to zero in order the Space Catapult’s rod to get another payload in motionless position and then to send it to space. <br />
What methods can we use to reduce Space Catapult’s rod’s rotation to zero? There are several possible ways: <br />
<br />
1. The electromotor designed for accelerating the rod may actually play a role of brakes, more precisely after releasing the payload to space the electromotor should operate/rotate in the opposite direction, hence rod’s rotational speed will be diminished to zero after that electromotor will stop operating. Under such method a bit less energy will be spent for decelerating the rod than in case of accelerating because when decelerating the rod is free from payload. <br />
<br />
2. An ordinary mechanical brakes, however due to electro motor’s and rod’s sizes a huge brake(s) would be needed to be installed on the Space Elevator’s counterweight and this circumstance would make additional problems from the engineering point of view. Nevertheless, we should admit that under such method we would not need as much energy as during accelerating; on the contrary, in this process the heat will be emitted as it generally happens during braking. <br />
<br />
3. For decelerating the rod we can use the well-known phenomenon in physics-''electromagnetic induction'': when the c''onductor/ closed circuit'' moves into the magnetic field the electric current is generated there. In case of Space Catapult we can use this phenomenon in the following manner: the conductor should be wrapped around the whole length of the rod like a helix and there should be possibility that this conductor to be turned into the ''closed circuit'' by means of mechanically connecting its ends (see the image below). After releasing the payload at necessary speed and direction this circuit should be closed, then according to ''electromagnetic induction'' the electric current will be generated in the conductor and the energy of this electric current will come from rod’s kinetic energy. Therefore, inducted electric current in the enclosed circuit will force this circuit and rod to lose kinetic energy and speed. The part of the generated electric current will be spent in prevailing conductor’s electric resistance:<br />
<br />
[[File: Helix.jpg]] <br />
<br />
The advantage of this method is that for decelerating the rod no energy will be required, as for drawback-much time will be required for this purpose because at the altitude of several ten thousand kilometers the Earth’s magnetic field is quite weak and the effect described in the paragraph above will need much time to operate and give necessary result. <br />
<br />
4. The above-described third method could be realized in a bit different way: if the conductor wrapped around the rod is a closed circuit and if we conduct the electricity there then the electric current will generate its own magnetic field that will counteract with Earth’s one. More precisely, according to ''Lenz's law'' induced current’s magnetic field will be in such a direction as to oppose the motion or change causing it, in other words induced current’s magnetic field will counteract outer magnetic field’s any change and this will cause decelerating rod’s rotation and finally its stopping. <br />
<br />
5. The obvious disadvantage of the third and fourth method described above is weakness of the Earth’s magnetic field because of which decelerating the rod may be delayed in time. For solving this problem we can create artificial magnetic field by means of electromagnets. Particularly, one electromagnet should be placed at the Space Elevator’s counterweight, very close to Space Catapult’s rod. The second electromagnet should be placed directly on the Space Catapult’s rod close to first electromagnet (actually, instead of this second electromagnet there could be used the conductor wrapped around the rod as we described above in previous methods). The reason of this nearness is that magnetic field generally weakens directly proportional to distance’s third power and much time will be needed for decelerating Space Catapult’s rod if two electromagnets are far from each other.<br />
<br />
This method probably will consume the most amount of energy but at the same time it will be the most effective because it does not depend on outer factors such as Earth’s magnetic field which is quite weak at the altitude of several ten thousand kilometers above the sea level. <br />
<br />
Eventually, which methods for decelerating the Space Catapult’s rod would be the best? As we see each one of them have got their advantages and disadvantages. We can state that we should choose one of them according to spaceflight’s profile and goal. Particularly, if we decide to send the spacecraft into the deep space mission where especially high speed is necessary then in this case ''longer/more massive'' rod would be needed rotating at very high speed. Under such circumstance much energy will be needed for accelerating/decelerating the rod. We should also take into consideration the fact how frequently the Space Catapult will operate, in other words how mane payloads it will have to send into space per some certain amount of time, week/month and etc. If time interval between two following missions is relatively high then we should choose the method that will consume less energy and more time for decelerating the rod. On the contrary, if the Space Catapult has to send payloads very often then we should choose the method that will consume more energy and enable the rod to decelerate faster. In other words, we should find ''golden mean'' between consuming time and energy. We should also take into account how much energy supply will be produced at the Space Elevator’s counterweight (see ''Energy source placed on the Space Elevator’s counterweight'') and what part of this energy can we spend for accelerating/decelerating the rod.<br />
<br />
The rod’s rotations can be decelerated much faster than accelerated; the reason of it is that when accelerating the rod has got some sophisticated device as payload and generally unmanned spacecrafts are capable to high g-loads, but still for them some restrictions exist. After the payload is released at needed direction and speed, the rod can decelerate much faster because the rod itself is quite simple device without any complex and sophisticated details. <br />
<br />
We can actually use several methods, such as the third one and then the first/fifth ones. This would be justified because of following reason: as we have already said when decelerating with the third/forth method the problem of weakness of the Earth’s magnetic field would occur, therefore much time would be necessary for described method(s) to perform and give us result. However, we should note that in the beginning when the rod rotates very quickly this method would still operate strong enough. This derives from Faraday's law of induction stating that “the electromotive force generated is proportional ''to the rate of change of the magnetic flux''”. Therefore, in the beginning when the rod is rotating very quickly we can use the third/forth method(s) and when the rod significantly brakes we can apply to the first/fifth ones-they do not depend on Earth magnetic field. In other words, such approach would greatly help us in finding the golden mean between spending energy and time necessary for decelerating the rod. <br />
<br />
And finally: after releasing the payload the Space Catapult’s rod can actually give us energy. More precisely, the electro motor itself can serve as electric generator also since we know that the same machine can operate as electric motor if it is fed with electricity and as generator for electricity if its rotor is rotated by other machines. Therefore after releasing the payload when the electro motor’s rotor is rotating very quickly it can give us energy, in result of which the rod will lose its kinetic energy and speed, as for generated energy it can be sent downwards to the Earth for our terrestrial needs (see the next section in this paper) or stored onboard the Space Elevator’s counterweight. This approach has got one substantial advantage: it does not imply additional mass (wrapped wire) that will cause problems because rotating heavier rod would consume more energy.<br />
<br />
=Energy source placed on the Space Elevator’s counterweight=<br />
<br />
As well-known, the Space Elevator’s cabin needs energy when moving along the cable and it can get it from the Earth by means of various ways, such as: laser beam, microwaves, through the cable itself and etc. On the other hand, Space Catapult also needs much energy for rotating the rod and for this purpose some energy source should be placed on the Space Elevator’s counterweight, presumably solar panels array. Doing this would demand additional funding and engineering work and this undertaking should be justified, so how can we prove that placing energy source on the counterweight would be necessary and useful? We should not forget that the energy generally could be simply transmitted from the Earth without carrying any material for energy source on counterweight; so we can justify this undertaking if we declare/prove that: <br />
<br />
1. Energy source should be designed for ''both'' Space Elevator’s cabin and Space Catapult’s rod. We can imagine it as array of numerous solar panels producing enough energy for both above-mentioned constructions. For this purpose solar panels would be better solution than nuclear reactor because they do not need nuclear fuel to be carried from the Earth to counterweight, also they are capable for producing energy in a continuous mode. By the way this circumstance will enable us to send the payload to space by Space Catapult whenever we want without depending existence nuclear fuel at the counterweight. <br />
<br />
2. Transmitting energy from the counterweight (“from above”) is better and advantageous than doing the same thing from Earth (“from below”). Indeed, when we try to transmit energy (laser or microwave beam) from the Earth to ascending cabin, the part of energy is inevitably lost and dispersed in the Earth’s atmosphere and (this is point of the question) this continues during the whole process of ascent. On the contrary, when transmitting the energy from counterweight to cabin the energy will be lost only on the little part of this voyage, more specifically until the cabin leaves the atmosphere (100 km in height) and when cabin leaves it the energy will be transmitted in vacuum without loss. <br />
<br />
3. For receiving the energy from the Earth the huge solar panels (in case of laser beam) or antennas (in case of microwaves) will be needed to be mounted on the counterweight and this is additional mass and additional engineering work.<br />
<br />
We think that these arguments given above are enough for shoving that placing energy source on the Space Elevator’s counterweight have advantages over transmitting energy from the Earth and as conclusion we can state that energy source on counterweight would serve both space transportation systems-Space Elevator and Space catapult. <br />
<br />
As addition, we could use the energy produced on the counterweight for terrestrial needs also. Indeed, there have been developed numerous projects for receiving energy from space since 60-ies implying producing it by means of solar panels and then transmitting to the Earth. Combining all these three goals we can conclude that placing solar power plant on the Space Elevator’s counterweight would be triply useful and advantageous. In other words, when the Space Catapult and Space Elevator do not function, the energy produced on the counterweight should be directly transmitted to the Earth for our terrestrial needs and thus the idea of Space Elevator, Space Catapult and space power plant will be combined in one project.<br />
<br />
=Assembling the Space Catapult=<br />
<br />
Assembling in space such a huge structure as Space Catapult will not be an easy task from the technical point of view and definitely needs special engineering approach. Besides, we think that Space Catapult’s rod should be mounted at the Space Elevator’s counterweight separately from every other parts of the Space Catapult (e.g. electro motor and etc.); this circumstance is caused by rod’s gigantic sizes. More precisely, electric motor and plus any other equipments necessary for Space Catapult’s performance should be delivered to space by means of Space Elevator in a usual way; as for Space Catapult’s rod, it is a different matter and it should be delivered and mounted separately in the end. <br />
<br />
Eventually, Space Catapult’s rod will be quite long, perhaps much more than 100 kilometers. It is obvious that delivering such a long rod as ''one single unit'' would be quite difficult task; also it is possible that due to its total mass the Space Elevator’s cabin will not be able to deliver such rod at all, but we have already mentioned that the Space Catapult may have the rod with various length; more precisely the rod may consist of two/more parts. In such case these parts should be delivered towards the counterweight separately and then assembled. <br />
<br />
But the Space Elevator’s cabin can actually deliver the Space Catapult’s rod as ''one single unit'' in space. We think that this would depend only on rod’s mass. The Space Elevator’s lifting capacity is not well-known yet; however apparently it will not exceed one hundred metric tons and if Space Catapult’s rod is made of extra light material then cabin will be able to deliver it in space and in such case the following question will arise: how the cabin will deliver such a huge object in space without any damage?<br />
<br />
This can be done by means of two cabins. Generally, Space Elevator’s conception implies only one cabin moving along the cable, but for some special purpose (like delivering Space Catapult’s rod in space) we can use the second cabin also that will descend downwards after finishing its job and will not participate in Space Elevator’s further performance. As for the process of delivering the rod, we can imagine it in a following manner: at first the rod will be placed horizontally on the Earth (thus it must be manufactured and then transported to the Space Elevator’s base station), then the Space Elevator’s first cabin will carry rod’s one end along the cable while the rod’s second end will be moved on the Earth so that the rod to take more and more vertical position. When the rod is in vertical position the second cabin will capture rod’s second end and will carry it in space. We think that without the second cabin it would be quite difficult for one cabin only to carry long/heavy rod because the rod may actually shake and crash to the Space Elevator’s cable and this is absolutely undesirable. <br />
<br />
So, as we see in principle it looks to be quite easy, however the assembling may complicate due to rod’s length. In this case it would be better to carry not the rod as ''one single unit'' but its parts and then to assemble them in space in the following manner: ''two'' cabins will carry the first part as described above, when this part is delivered to space and temporarily hung at the cable the next two cabins will carry the second part that will be attached to the first one from below; the other parts will be delivered to space and assembled into the rod in the same way. <br />
<br />
The obvious disadvantage of the above-described method is that each part needs two cabins on the Space Elevator’s cable, besides the humans will be needed for assembling the rod from these parts in the atmosphere’s upper layers; therefore we think that the first way-delivering the rod into space as one single unit still would be easier and more realistic; besides we should take into consideration the fact that if the rod is assembled the additional devices will be needed ''on the rod itself'' for joining these parts and this circumstance would lead to increasing the rod’s total mass and this is undesirable. See the image showing assembling process:<br />
<br />
[[File: Assembling.jpg]] <br />
<br />
Whatever design/structure the rod has-assembled from several parts or as one single unit, it must be delivered to its destination-Space Elevator’s counterweight and must be fastened to electro motor’s own axis. But the problem is that the rod will be quite long and also the fact that Space Catapult’s electro motor will be placed at counterweight’s upper side (or at the ''lateral'' side if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), so it will be necessary the rod coming from below to be moved to counterweight’s upper/lateral side, besides the rod should be docked with electro motor’s axis as accurately as possible. How is it possible to realize such complex engineering operation? Here we can indicate one possible theoretical way: <br />
<br />
The rod will be parallel to Space Elevator’s cable when carried by cabin, but later the cabin’s mechanisms should rotate it so that the rod to be orthogonal to Space Elevator’s cable (this will not be necessary if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), exactly in this position the rod should be delivered to counterweight, besides the rod when moving along the cable should be shifted a bit upwards (relative to the Earth) than the cabin itself. Under such conditions we will easily achieve docking the rod to electro motor’s own axis which from its side should have some trapping device (magnetic for example) to “catch” the rod and thus guarantee docking the rod to electro motor and finishing assembling the Space Catapult as a whole. But if the rod’s plane of rotation is parallel to cable then assembling process will be much easier because the ascending rod may directly dock to electro motor’s own axis. See the image showing this process:<br />
<br />
[[File: Deliver - Copy.jpg]] <br />
<br />
We think that it would be useful if one Space Elevator is built specially for Space Catapult with its base station located on the land, not the ocean. This would be justified because transporting Space Catapult’s rod from its place of manufacture to Space Elevator’s base station should occur on the land by means of several transports simultaneously (due to rod’s great length), this will enable us to deliver the rod to its destination without any damage while this kind of operation is hardly possible on the water.<br />
<br />
=The technical aspects regarding the Space Catapult=<br />
<br />
As an example, we can try to calculate/ascertain all possible kinds of aspects regarding the rod with some certain mass and sizes, for example we can assume the Space Catapult has got 100 km length rod. <br />
<br />
The circumference of the circle that this rod’s end will draw in space will be equal to 2πr=628 km. As we have already mentioned payload’s abilities for withstanding the g-load is restricted, so if the electromotor rotates the rod so that payload’s speed is equal to 50 km/sec (this means that it will take 12.56 seconds for the rod to make one complete revolution), in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design the spacecraft that will withstand such acceleration, but what about the rod itself? Which material can be used for designing this rod, what will be its mass and how much energy and time will be needed for the rod to reach this velocity? <br />
<br />
For manufacturing the rod we should choose the material with very low density and highest value of strength. Currently, the ''Carbon nanotubes'' are the best candidates for this purpose. What will the mass of the rod made of this material? This depends on width also and it should be as less as possible (otherwise the rod will be too heavy and too wide for transporting from manufacture place to Space Elevator’s base station and for delivering it to space by means of Space Elevator) but from the other hand the ''applied load'' will not let us to design very narrow rod.<br />
<br />
Let’s assume that we intend to launch the payload with the mass of 10 000 kg (during calculation we will use ''SI system'' only). To clarify what kind of material will be able to withstand the acceleration we should calculate and then compare two values: the ''applied load'' and ''tensile strength''. For calculating the first one we should multiply g-load (which we already know-2 550 g) to its mass-10 000 kg, we will get 25 500 000. As for calculating tensile strength, we should take its values (for Carbon nanotubes it varies from 11 000 MPa to 63 000, we will take some medium value-40 000 MPa) and multiply it to cross-section’s area, in our case rod is cylinder with circular cross-section. If radius of cross-section is 1 meters then its area is 3.14 square meters, multiplying this value to value of tensile strength (40 GPa as said) we will get 125 600 000 000 and this is significantly more than value of applied load-25 500 000. Of course, we should also take into consideration ''factor of safety'' which is generally equal to 2 and this indicates us that for safety the payload’s actual mass should be twice less but in our case as we see the rod will be able to accelerate the payload to above-mentioned speed. By the way, note that if that g-load ''2 550 g'' is almost at the payload’s withstanding limit this is not serious problem for the rod itself (we have already seen that value of tensile strength is much more than value of applied load) and this is clear why: payload generally contains sophisticated equipments (electrical circuit, optics an etc.) that will not be able to withstand very high g-loads while the rod will be made of some continuous solid substance, Carbon nanotubes is this case and of course it will be able to withstand much higher g-loads.<br />
<br />
<br />
What will be the mass of such rod? Knowing its volume (for this purpose its cross-section’s area 3.14 square meters should be multiplied to rod’s length-100 000 meters, we get 314 000 cubic meters) and taking the value of density (this also varies for Carbon nanotubes from 0.037 to 1.34 g/cm<sup>3</sup>, let’s take 0.1 g/cm<sup>3</sup>) we get rod’s mass as 31 400 000 kilograms. This is too heavy for Space Elevator’s modern concepts and for improving this situation we should either use many cabins for raising the rod as single unit or use nuclear energy for feeding the cabins instead of laser/microwave beams or deliver the rod’s parts separately in space and then assemble them (see ''Assembling the Space Catapult''). But if some advanced substances are chosen for this purpose (for example ''Silica aerogel'' the density of which is about 1.9 mg/cm<sup>3</sup>, this is 50 times less than the density of the Carbon nanotubes taken above-0.1 g/cm<sup>3</sup>) than problem may be lightened in spite of the fact that their current tensile strength is quite low-16 kPa for the density of 0.1 g/cm<sup>3</sup> <sup>7</sup>. So, we can conclude that we need the material with the density of ''Aerogels'' and tensile strength of Carbon nanotubes.<br />
<br />
How much energy and time will be needed for the rod to accelerate from zero to desired speed-50 km/sec? The amount of rotational energy of the rotating rod can be calculated by the following formula:<br />
Kinetic Energy<sub>rotational</sub>= (1/2)*I*ω2 <br />
<br />
Where:<br />
<br />
'''I'''=moment of inertia <br />
<br />
'''ω'''=angular velocity<br />
<br />
"I" depends on the shape of the mass under rotation. In the case of a uniform rod rotating from its end (axis of rotation is at the end of the rod) I = (m*L2)/3<br />
<br />
<br />
“ω” = V/R, where V = tangential velocity and R = radius<br />
<br />
In our case ''moment of inertia'' is equal to (31 400 000 kg*100 000 m2)/3=104 666 666 666 666 666<br />
ω is equal to (50 000 m/sec)/100 000 m=0.5<br />
<br />
So, Kinetic Energy<sub>rotational</sub>=(1/2)*104 666 666 666 666 666*(0.52)= 13 083 333 333 333 333.25 Joules<br />
<br />
Now, how much time and what amount of solar panels will be needed for accelerating this rod? The amount of Solar constant near the Earth is approximately equal to 1300 W/m2 [<sup>8</sup>], with assuming that ''coefficient of efficiency'' of solar panels is roughly 20 % we get 260 Watts per square meters and we can easily link amount energy (that we have already calculated) and power with the time needed. Particularly, ''Energy'' is equal to ''Power''’s multiplication to ''Time'':<br />
<br />
[[File: Formula - Copy.jpg]] <br />
<br />
So, Time is equal to 13 083 333 333 333 333.25 Joules/260 Watts=50320512820512.8 seconds, or 1 595 652 years. If we take much more area for solar panels, for example 10 millions square meters then 0.1595652 years or approximately 58 days will be needed and we think that this is acceptable time span.<br />
<br />
Actually, the time and energy will be needed a bit more for overcoming static friction in electro motor, for overcoming the rarified atmosphere’s resistance (we know that there no absolute vacuum in space), also we should take into consideration electric motors’ coefficient of efficiency that generally reaches 90-95 %, so some energy loss will occur here also. <br />
<br />
Now, what will be the total mass of solar panels producing the energy for Space Catapult? This depends on mass/power ratio, in near future it is expected that very lightweight designs could likely achieve 1 kg/kW [<sup>8</sup>] or 0.260 kg/ 260 W (per 1 square meter), so if for rotating the Space Catapult 10 millions square meters of solar panels are used then their total mass would be equal to 2 600 000 kg. We think that it is too heavy for Space Elevator the mass of which is expected to be equal around several hundred metric tons. If so, we will have to use fewer amounts of solar panels and therefore increase the time needed for accelerating the payload’s speed from zero to designed one. This will not make problems if the rod is accelerated only once and then keeps its constant rotation-for this purpose less energy will be needed and the payload will have to reach the rod’s end by first method as described earlier in this paper (see ''Rod’s plane of rotation towards the Earth'').<br />
<br />
We also need to take into consideration the value of deflection when the rod will be delivered to space by means of Space Elevator (see ''Assembling the Space Catapult''), in this case the thin and long rod will be bent due to its own weight and here we will try to calculate its value. This is quite complex problem that apparently cannot have an unambiguous solution because of many reasons, for example due to various temperatures in atmosphere’s different layers, various humidity and possible wind, but still we will try to calculate the value of ''Deflection'' that will occur in case when the rod’s one end is fastened to Space Elevator’s ascending cabin and the second end is fastened to the transport moving on the land, we discussed this option in above-mentioned section of our paper (see ''Assembling the Space Catapult''). The inclination angle for the rod will vary from 0º (rod is transported horizontally on the ground) to 90º (Space Elevator’s cabins are carrying the rod to space) and here we will discuss some medium case when the rod is semi-elevated in the air, when the angle between rod and ground/cable is equal to 45º. On the engineers’ ''eFunda'' web-site there is online calculator that enables to receive the value of ''Deflection'' (actually that site gives different term for this-''Displacement'') [10]:<br />
<br />
Here we need to enter the relevant values:<br />
<br />
''Length of beam'', ''L'': 100 000 meters<br />
<br />
''Line pressure load on beam'', p: In our case this is the weight per meter length. As we have already mentioned the radius of the rod’s cross-section is 1 meter, so the volume of rod’s 1 meter-length part will be 3.14 cubic meter. In case of using Carbon nanotubes with above-mentioned density-0.1 g/cm<sup>3</sup> the weight will be equal to 314 kg or 3 079 Newton. Since we have got the inclination of 45º we should multiply this value to cos45º- 0.707, so we get 2176 N/m.<br />
<br />
''Young's Modulus'', ''E'': This is equal to 1 000 GPa for Carbon nanotubes [11] <br />
<br />
''Distance from neutral axis to extreme fibers'', ''c'': In our case it is equal to the radius of the rod-1 meter<br />
<br />
''Moment of Inertia'', ''I'': It is equal to (pi*r<sup>4</sup>)/4, so it is equal to 0.785<br />
<br />
According to these initial data the calculator returns extremely high value of Deflection, much higher than the length of the rod itself: -3.61 × 10<sup>9</sup> meters. This result shows us that with the current materials (Carbon nanotubes in our case) it is impossible to raise the rod as ''one single unit'' to space by means of Space Elevator and we need other materials with less density and more ''Young's Modulus'' (or the rod should be much thicker but this will lead to increasing its mass). Therefore, we have got two options: either we should deliver the parts of that rod and then assemble them in space (we have already discussed this option) or completely different technologies for manufacturing the rod should be developed. Particularly, it would be very good if it was possible to manufacture the rod ''in continuous mode'' in vertical position and then uninterruptedly directly to carry it to space by means of Space Elevator’s cabins. Under such approach there will be no ''Deflection'' and several cabins will be able to deliver the rod in space. <br />
<br />
One note about transporting the rod from its place of manufacture to Space Elevator’s base station. We think that this process should be executed by many transports, in other words we are convinced that if the rod is carried by two trains only (or any other kind of transport) then the rod will continuously touch the ground since the ''Deflection'' occurs in any position-horizontal, inclined or vertical and this circumstance will lead to its damage, that’s why several transports will be needed to hold the rod at as many places as possible.<br />
<br />
=Stabilizing the counterweight=<br />
Stabilizing the Space Elevator’s counterweight is very important question during Space Catapult’s performance. Indeed, when the rod rotates it makes the imaginary circles in space and due to rod’s and payload’s masses the Space Catapult’s ''center of mass'' will be continuously shifted and if the counterweight is not somehow stabilized then it will make problems for accurate aiming to certain point at the celestial sphere. Also, if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable then there will be the danger that the rod may actually hit the cable and cut it. To avoid these problems we need to apply to serious measurements. <br />
<br />
First of all, the electro motor’s own axis can be quite long and this will diminish the chance to failure of the whole system. Actually, we are convinced that counterweight’s (where the electric motor will be placed) size will be quite large, mainly due to solar panels’ sizes and amount (this issue was discussed above), also the electromotor should be quite large and powerful to rotate the rod, and hence there will be enough distance between the rod and Space Elevator’s cable. <br />
<br />
The second serious problem is that the center of gravity of the system is not at the center of rotation, therefore it will be necessary to balance the rotating system when the payload is attached and when it is released.<br />
<br />
We think that the Space Catapult’s rod should not be deployed/directed to one side only but some counterweight of it should also exist. This is necessary since the unilaterally loaded (we mean the rod itself plus payload) rod will cause the counterweight to somersault. In other words, the rod should extend to other side and the ''moments of inertia'' of both sides should be the same as during rotating the rod as after releasing the payload when the rod still rotates. This is easily achievable if some additional, second payload is placed on the rod’s second end. Therefore, the Space Catapult will launch two payloads at the same time to the ''opposite'' directions but at various speeds if the second part/side of the rod is shorter.<br />
<br />
How the second payload should be placed on the rod and should we really send two payloads? Until we have got balanced rod this problem does not arise but as soon as the Space Catapult releases the payload this balance will be violated, how it can be restored? There are two theoretical ways for achieving this: reducing the ''mass'' or reducing the ''length''-with diminishing either one of them the ''moment of inertia'' will be decreased. We think that reducing the mass will be less practicable since this would require placing the second payload (spacecraft or anything else) on the rod’s second part and this cannot be done from the Space Elevator’s cabin-this is the easiest way for delivering the payload from Earth to Space Catapult’s rod; so we would have to (see ''Rod’s plane of rotation towards the Earth'') put the second payload on the electro motor and then send it rod’s second part’s end. This is quite complicated task; therefore we can apply to second approach-put some sliding object that will immediately move to electromotor as soon as the spacecraft is released.<br />
<br />
[[File: MOI.jpg]] <br />
<br />
The next problem that may occur is that when the electro motor rotates the rod this motion will make the Space Elevator to rotate to the opposite direction. The same problem arises when helicopter’s primary blade’s rotation forces the helicopter to rotate to opposite direction and this possible rotation is annulled by ''tail rotor''. We think that for balancing the counterweight the additional motor and rod should be installed and this rod should rotate to opposite direction and if their ''angular momentums'' are equal to each other, then their rotations will cancel each other. More precisely, the following equation should be fulfilled:<br />
<br />
[[File: Angular momentum.png]] <br />
<br />
Where ''m'' is mass of the rod, ''v'' is angular speed and ''L'' is rod’s length, the numbers ''1'' and ''2'' refer to first and second rods correspondingly. For balancing both rods’ rotation the multiplication at both sides of the counterweight should be equal, by the way this circumstance enables us to use the second rod with shorter length and even with less mass but rotating at more angular velocity.<br />
<br />
Such approach will effectively deal with other problem which will arise when the Space Catapult releases the payload(s), at this moment the second motor should instantly diminish its angular velocity to some certain level (an ordinary mechanical brakes could be used for this purpose), in this case ''angular momentums'' for both motors/rods will be equal again and Space Elevator’s counterweight will maintain its attitude in space. See the image below depicting the Space Catapult with two electro motors and rods:<br />
<br />
[[File: Two-rods.jpg]] <br />
<br />
Such approach will justify itself if rod’s plane of rotation is parallel to Space Elevator’s cable, but if this plane is orthogonal to cable (see ''Rod’s plane of rotation towards the Earth'') then the second/balancing electromotor cannot be placed under the counterweight because the cable will be cut when rod touches it. Therefore a bit different approach should used and we need to install two/four/eight electro motors with their own relatively shorter rods rotating to opposite direction. They should be placed at the counterweight’s lower side and on its edge (as we suppose the counterweight should be disc) so that their rods not to touch and cut Space Elevator’s cable. Also, total a''ngular momentums'' from these motors should be equal to the ''angular momentum'' from upper motor and thus the counterweight will not rotate and the Space Elevator’s cable will not be twisted. This situation is presented below:<br />
<br />
[[File: Modified-2.jpg]] <br />
<br />
We think that the array of gyroscopes would be also very useful to be installed at the counterweight since they can maintain the attitude of the whole system and this is important for precise aiming to certain point at the celestial sphere. As for the energy required for gyroscopes’ performance it could be received from the array of solar panels which as a result will generally serve Space Catapult’s precise performance.<br />
<br />
=Space Catapult placed at Lagrangian points-the way for gaining subluminal speeds=<br />
<br />
In our paper we discussed the Space Catapult based on the Space Elevator’s counterweight and concluded that this would be convenient when we intend to deliver the payload to space from the Earth. However, such Space Catapult cannot gain very high speeds and therefore we need to choose other way. It is obvious that we need to keep rod’s plane of rotation orthogonally relative to the ''Earth-Sun connecting line'' and hence we should place the rod on the celestial body which will be in synchronous rotation with the Sun but since there is no such body in the solar system we conclude that the Space Catapult for subluminal speeds (the speeds close to speed of light are in mind) should be placed at such point near the Earth where it will be easy to reach it from our planet and where the rotating rod will not hit the Earth and will be always at the same distance from the Sun to avoid the influence of its tidal forces. The examples of such places are '''Lagrangian''' L<sub>1</sub> and/or L<sub>2</sub> points at 1.5 million km away from the Earth. If the Space Catapult is placed at one of these points then its rod can be always orthogonal to the Sun in principle, at the same time it will never collide with the Earth and also it will be quite close to the Earth since 1.5 million km distance is very negligible in space.<br />
<br />
We have got several notes regarding such approach. First, when we mentioned that the rod’s various parts can be at the same distance from the Sun this strictly speaking is not very true because the Sun can be referred as little point where its gravity “comes out” from while the rod is quite long and its initial part (placed at one of the Lagrangian points) will be attracted stronger than the utmost one (for equal attracting the rod should the arc ''with the same curviness as Sun’s surface'' and not straight line); but still this is better than to direct the rod exactly towards the Sun where the tidal forces will try to tear the rod. Second, the Space Catapult should be placed at Lagrangian L1 point which is closer to the Sun than L2 one and therefore receives by 4 % more energy per area from the Sun. Third, the rod should be in constant rotation, this requires much less energy than accelerating it from zero, then stopping it and accelerating it again. Fourth, the existence of the asteroid belt in the solar system between Mars and Jupiter will somehow restrict the actual length of the rod. Indeed, the Space Catapult should be placed at one of the Lagrangian points at 1 AU distance from the Sun while asteroid belt approximately lays at 2.7 AU, from the simple geometry it is obvious that the length of the rod ''almost reaching'' the asteroid belt can be approximately equal to 390 million km, and if the rod is longer then it may simply hit any asteroid within that belt. For 390 million km length rod and for 100 000 m/sec2 acceleration at rod’s end (where the payload will be attached) the maximal speed that the spacecraft can gain will be approximately equal to 200 000 km/sec (two thirds of the speed of light) and this can be considered as enough for practical interstellar spaceflight. Fifth, the spacecraft should be directly put on the rotating rod’s initial end (near electromotor) and then slide towards the other end with its own rocket engines. To achieve this, the spacecraft will have to cover relatively less distance on the rod and then rod’s circular motion will accelerate the spacecraft further-we have already mentioned this in this paper when speaking about deploying the Lunar Space Catapult. This action-putting the spacecraft on the rod will not be difficult since rod’s angular velocity will be quite low due to rod’s huge length, particularly for 400 million km length rod and for 200 000 km/sec linear speed the rod’s angular velocity will be 0.0000796 revolutions/sec.<br />
<br />
[[File: Lagrangian-point.jpg]] <br />
<br />
We have already mentioned that to avoid the destructive influence of the Sun’s tidal forces the rod’s plane of rotation should be orthogonal to the Earth-Sun connecting line. By the way, note that under such approach we may have to wait one year until the Lagrangian Space Catapult occupies the relevant position towards the certain point at the celestial sphere where the spacecraft should be sent to. But from the other hand it would be useful if it is feasible to rotate this whole structure around the imaginary axis directed towards the ''ecliptic poles'' (depicted as faint green dash line on the image above), the reason if this is the possible danger when the rotating rod may hit Mars or asteroids that orbit around the Sun closer than 2.7 AU distance (for example ''433 Eros'' or ''1036 Ganymed''), hence for avoiding such undesired collision the Lagrangian Space Catapult should be slightly rotated by several degrees clockwise/counterclockwise so that the rod not to collide with any celestial object. We are convinced that rotation by several degrees will be absolutely enough measurement due to rod’s gigantic length and relatively less sizes of the celestial objects in the solar system.<br />
<br />
The next issue that we should discuss refers to stability of the Lagrangian Space Catapult placed at L<sub>1</sub> point. As we see this structure will have enormously gigantic size while the Lagrangian point is relatively little mathematical one in space, so what can be done to be convinced that this structure will remain at that point and do not shift aside? The body placed at one of the Lagrangian points is affected by other celestial objects’ gravity and therefore for achieving the balance the rod needs to have the counterweight with more mass if it (counterweight) is shorter. As we clearly see the rod needs the counterweight for two reasons: not to let the Space Catapult somersault and for maintaining it at the L1 point. We think that it would be very useful if the arrays of solar panels act as counterweight since exactly they can give us energy for rotating the rod. Also, we need the second, shorter, perhaps less massive but faster-rotating rod (again-solar panel arrays) the opposite rotation of which would cancel first rod’s rotation, this issue was discussed in this paper. These arrays of solar panels are depicted on the image shown above. <br />
<br />
How such a gigantic structure as Lagrangian Space Catapult can be assembled in space? In our paper we discussed the possible ways for delivering the rod from the Earth to the Space Elevator’s counterweight, now we will try to show that it is possible ''in principle'' to assemble the extra-long rod in space. <br />
<br />
If it is possible from the technical point of view to manufacture extra-long rod then we can use this approach and make 1.5 million km length rod (this is the distance between the Earth and Lagrangian L<sub>1</sub>/L<sub>2</sub> point) that will be mechanically directed to the base station at L<sub>1</sub> point. The capturing devices there will catch the rod and attach it to the electro motor’s shaft after which the rod should be spun by 90º so that it to be orthogonal to Earth-Sun connecting line (for this purpose the additional mechanisms will be needed), this spin is necessary because L<sub>1</sub> point is located on the Earth-Sun connecting line (that is towards the Sun if we look from the Earth) and when directing the rod from the Moon it will lay ''along'' this line while we need across. After this the rod should be slid to another side and then the next rod should be directed to the Lagrangian Space Catapult where it will be attached to the previous rod and etc. In other words, the extra-long rod will be assembled from one side and its length will “grow” from this side to other one, this is necessary because the distance between Moon (the rod should be manufactured exactly there and not on the Earth due to our planet’s relatively more gravity, atmosphere and problematic space debris belt around it) and L<sub>1</sub> point is constant and rod’s parts cannot be more. Due to whole rod’s and its parts’ lengths (400 million and 1.5 million km correspondingly) we think that about 260-270 such operations will be needed to finish assembling the rod (400/1.5). The process of assembling the Lagrangian Space Catapult is shown on the image below:<br />
<br />
[[File: Lagrangian-point-assemble.jpg]]<br />
<br />
=Conclusion=<br />
<br />
As we have seen, for leaving the Solar system and reaching the remote celestial bodies (stars, nebulas) there is no need to develop advanced and complicated technologies that mostly are not capable for gaining extra high velocities nevertheless. In any case, until the Space Elevator is really built (scheduled for construction by 2031) we have got much time for developing the idea of Space Catapult in technical aspect, like finding appropriate materials for the rod, perfect the ways how the Space Catapult can be assembled in space and etc. The concept of Space Catapult itself is the easiest one, does not need developing neither complex and sophisticated technologies, nor some exotic methods (such as ''Gravitoelectromagnetic toroidal launchers'', ''Antimatter rocket'' and etc.) and can be easily implemented in near future; in other words the Space Catapult is not some sophisticated structure that would need profound science research and the fact that it will enable us to gain whatever high speed will justify its developing and building by the humankind. As for other technologies like Ion Drive, they could be used by the spacecraft during flight for other purposes, for example for correcting/changing the flight direction.<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Space_Elevator<br />
<br />
2. http://www.isec.info/index.php?option=com_content&view=article&id=14&Itemid=9<br />
<br />
3. http://www.space-track.org/perl/geo_report.pl (provided data updates regularly, registering is needed) <br />
<br />
4. http://www.oosa.unvienna.org/pdf/reports/ac105/AC105_720E.pdf page 24 (data as at 21 August, 1997) <br />
<br />
5. http://www.amostech.com/ssw/presentations/Session7/S7-1Molotov.pdf page 16<br />
<br />
6. http://www.esa.int/SPECIALS/ESOC/SEMN2VM5NDF_mg_1_s_b.html <br />
<br />
7. http://eetd.lbl.gov/ecs/aerogels/sa-physical.html<br />
<br />
8. http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant<br />
<br />
9. http://www.you.com.au/news/2005.htm, http://www.spacedaily.com/news/ssp-03b.html<br />
<br />
10. http://www.efunda.com/formulae/solid_mechanics/beams/casestudy_display.cfm?case=simple_uniformload<br />
<br />
11. http://en.wikipedia.org/wiki/Young%27s_modulus<br />
<br />
<br />
'''Appendix''': <br />
<br />
Animation illustrating the payload’s departure from the Lagrangian Space Catapult:<br />
[[File: Lagrangian-point-animation.gif]]</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_5&diff=3664OpenSpace 52013-09-21T12:52:50Z<p>Eagle9: </p>
<hr />
<div><div style="float:right; border:#CCCCCC solid 1px; background-color: #F7F7F7"><br />
<table cellspacing=0 cellpadding=0 width=550><br />
<br />
<tr><td colspan="3" align="center" style="background-color:#CCCCCC"><b>Title:</b> Place Title Here</td></tr><br />
<br />
<tr><br />
<td align="center" valign="middle" height=125 width=100 style='padding:10px'><br />
<div style="background-color:#CCCCFF; height:110px; width:90px"><br />
[Cover Img]<br />
</div><br />
</td><br />
<br />
<br />
<br />
<td align="left" valign="top"><br />
<div><br />
'''[[Article Tags|Tags]]''':<br /><br />
* This is open space for development<br />
</div><br />
</td><br />
</tr><br />
<br />
</table></div><br />
<br />
<br />
== '''Space Catapult''' ==<br />
<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
=INTRODUCTION=<br />
<br />
<br />
The new method for sending the spacecrafts in deep space is presented here. The paper describes the long rod rotated by electro motor placed at the Space Elevator’s counterweight and at Lagrangian points. This simple structure will enable the rod to gain high velocity and carry the payload with it. After reaching the desired speed the rod will release the payload that will fly in space along the imaginary circle’s tangent. This structure we called Space Catapult and it should work with the assist of Space Elevator. This latter should be used for carrying the payload from the Earth to Space Catapult’s rod.<br />
<br />
For exploring the outer space the humankind generally uses the rocket engines, mostly chemical-propelled ones. They enable us the explore near-Earth celestial bodies and other planets in the solar system. They even enabled us to send several deep space missions beyond the solar system such as '''Pioneer-10''', '''Pioneer-11''', '''Voyager-1''', '''Voyager-2''', however by means of this technology the flight lasts undesirably long and it seems to be impossible to reach remote celestial bodies in space such as stars, so new technologies are necessary for this purpose. However new technologies do not necessary imply new kind of rocket engines, such as ''Ion Drives'' because they are capable for gaining several ten times higher speeds only, but for remote celestial bodies even they are not suitable. Besides, they need a huge amount of energy to be stored onboard the spacecraft and this will make additional problems. So, high speed should be achieved with absolutely different approach. How this can be done?<br />
<br />
High speed can be easily achieved by means of fast-rotating rod around the electric motor. The motor’s rotational speed can be very high; the rod also can be quite long, hence the rod’s end’s linear speed can be extremely high, absolutely unachievable for any other technologies nowadays. The payload should be fastened at the rod’s end where the linear speed generally reaches maximal value. After reaching the necessary speed the rod will release the payload that will fly along the tangent from the current position. Thus the electric energy can be turned into payload’s speed and its velocity could be as high as we wish (except the ''speed of light'' of course). In principle the '''Space Catapult''' (thus we call this structure) would be the simplest, the most convenient and direct way for converting the energy/electricity into speed and conveying it to payload. <br />
<br />
As we see the Space Catapult is quite uncomplicated structure, however if we wish to gain high speeds we should deploy it in space, not on the Earth. Indeed, our planet is surrounded with dense atmosphere that impedes any quick motion, so if we rotate the rod quickly the atmospheric drag and generated heat would burn it very soon, therefore the Space Catapult should be built and deployed in space only, and as we suppose-at the Space Elevator’s counterweight. In other words, the Space Elevator’s counterweight will operate as Space Catapult. See image below:<br />
[[File:Space-catapult.jpg]]<br />
Generally, what is the Space Elevator <sup>1</sup> <sup>2</sup>? According to modern concepts it will be the tall vertical structure built on equator and will have height of several ten thousand kilometers with its thin cable fastened to the base station on the Earth and with counterweight placed higher geostationary orbit. Because of balance between centrifugal force and gravity this structure will be stretched and the cabin will move along its cable carrying the goods into high orbit. After delivering the payload, the cabin will descend and carry the next one.<br />
In Space Elevator’s concepts several solutions have been proposed to act as a counterweight: <br />
<br />
1. Heavy, captured asteroid <br />
<br />
2. Space dock, space station or spaceport positioned past geostationary orbit <br />
<br />
3. Extension of the cable itself far beyond geostationary orbit. <br />
<br />
The third idea has gained more support in recent years due to the relative simplicity of the task and the fact that a payload that went to the end of the counterweight-cable would acquire considerable velocity relative to the Earth, allowing it to be launched into interplanetary space. However this idea cannot be completely shared by us due to following reason: <br />
<br />
It is well-known that the values of both '''Orbital''' and '''Escape Velocities''' decreases with increasing the altitude while the '''tangential velocity''' of Space Elevator’s cable increases. We can see the differences between them from the chart presented below:<br />
[[Image: Cxrili.gif]]<br />
<br />
As we see from this chart the ''tangential velocity'' of the Space Elevator even at its end (144 000 or 200 000 km altitude) is not very high to decrease the necessary time for covering the distance from the Earth to remote celestial bodies significantly. To achieve this, even the longer Space Elevator would be needed (its ''tangential velocity'' is directly proportional to its length) and this circumstance would complicate the technical task for building such Space Elevator. Because of this, there is no necessity to extend the cable itself far beyond geostationary orbit as proposed in the third variant. In any case, we have already seen that by means of Space Catapult it is possible to gain such huge velocities that are absolutely unachievable with other technologies, for example with Space Elevator. Therefore, using the counterweight and placing the Space Catapult there definitely has got some technical sense. <br />
<br />
However, we think that the question where the Space Catapult should be placed needs further discussion. Theoretically, the Space Catapult with its payload and nuclear reactor/solar panel needed for rotating the rod may be mounted not only at the counterweight, but on the Space Elevator’s cabin also that can carry all these goods to space in a usual way, as it should do it according to Space Elevator’s modern concepts. This option is quite possible, however for realizing this we need to know the mass of the payload, nuclear reactor/solar panels’ mass plus Space Catapult’s mass from one hand and Space Elevator’s lifting capacity (this ''must'' be more) from other hand, but these data are not available nowadays, therefore we think that the Space Catapult should be still mounted at the Space Elevator’s counterweight where it will be possible to send the payloads into deep space in ''continuous mode'' at high velocities.<br />
<br />
As we saw the Space Catapult is capable to gain very high velocities; however there is being developed other technologies and they in future will enable the spacecraft to fly at high speeds in space. These are Ion Drive systems, more precisely the most perspective one-''Variable Specific Impulse Magnetoplasma Rocket'' (VASIMR) which still under development can be used in future for deep space missions. Can these engines and Space Catapult be the rivals in space? Since none of them have been built and used in space yet we cannot give a persuasive answer to this question; however still it is possible to underline Space Catapult’s one significant advantage: if the future spacecraft uses the VASIMR (or any other kind of Ion Drive) engine it will definitely need to be equipped with nuclear reactor, otherwise the spacecraft will not be able to gain high speeds, also it will need to carry fuel tanks for this purpose. As for the Space Catapult, it can give much higher speed to spacecraft, besides it will have ''stationery'' power plant (see ''Energy source placed on the Space Elevator’s counterweight'') at the Space Elevator’s counterweight, so the payload will ''not'' have to carry the nuclear reactor onboard and this circumstance will lighten the work for deep space spacecraft. Besides, we should not forget that unlike the spacecrafts equipped with ion drive engines the Space Catapult will need no fuel for gaining high velocities. <br />
<br />
Briefly, Space Catapult’s advantages over any kind of propulsion systems are: <br />
<br />
1. Ability to gain any speed that is absolutely unachievable by means of other kinds of engines. <br />
<br />
2. No need by spacecraft to carry energy source that would make it too heavy and impracticable.<br />
<br />
=The Space Catapult needs long rod=<br />
<br />
When building the Space Catapult at Space Elevator’s counterweight we should install quite long rod there, the shorter the rod is, the easier would be installing it, however we should note that rod cannot be extremely short, let’s say 1 km length or so due to following reason:<br />
<br />
When we are going to send some payload into space, we need not only high velocity, but one certain direction also. The little inaccuracy in direction, inclination in several arcminutes is actually acceptable since the spacecraft would easily balance it with its engines; however great inclination from the initial direction would send the spacecraft into the completely different direction and in such case the whole mission will fail.<br />
<br />
If two Space Catapult’s rods have the length of let’s say 1 kilometer and 10 kilometers, then for giving to payload some certain linear speed (for instance 100 km/sec) these rods should rotate at different angular velocity. It is easy to ascertain that the shorter rod should rotate 10 times faster to gain the same linear speed than the rod with more length. But the faster the rod rotates, the more difficult will be to “catch” the needed moment for releasing the payload from the rod for sending it towards some certain direction. If the rod is too short, then it has to rotate very quickly for gaining some certain linear speed and therefore it will be extremely difficult catching the needed moment for releasing the payload. Hence, too short rod can make problem for sending the payload to some certain direction in space especially at high velocities. So, based on payload’s needed velocity we should find rod’s desired, minimal length that will enable us to send the payload in space to necessary direction without fear that it may yaw from the course. <br />
<br />
However, rod’s length will be crucial for payload’s abilities for withstanding the acceleration also. As an example, we can try to calculate its value which the payload will have to withstand during rod’s rotation. The acceleration of the body rotating at the circle with some constant velocity is calculated by the following formula:<br />
<br />
[[File: Acceleration - Copy.jpg]] <br />
<br />
Where a is acceleration in ''m/sec''<sup>2</sup>, ''v'' is payload’s linear velocity on the circle in ''m/sec'' and ''r'' is radius of the circle in ''meters'', in our case it is equal to rod’s length. Let’s assume that the rod is 100 km length and the electromotor rotates it so that payload’s speed is equal to 50 km/sec, in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design and manufacture the spacecraft’s subsystems (avionic and etc.) capable to withstand such acceleration. This circumstance somehow restricts the speeds that we can achieve, in any case their values actually depends on spacecrafts’ abilities for withstanding g-loads. But what can we do if much higher speeds are needed? The answer directly derives from that formula: the radius should be more; by the way note that this is additional reason why the longer rod is more useful. If we are able to make the extra long rod, then this will enable us to gain much higher velocities. <br />
<br />
What material should be used for manufacturing the rod? It is obvious that if very high speeds are needed the rod should be long and even in this case the acceleration at its end will be quite high, therefore ''sufficiently strong and light materials'' are needed for this purpose and making them is as similar challenge as in case of Space Elevator where the same requirements arises for the cable’s material. The lightness is needed because in case of heavy rod a lot of energy will be needed to rotate it; the strength is needed because in case of lack this property the rod will be destroyed due to great acceleration.<br />
<br />
=The mechanism for holding and releasing the payload=<br />
<br />
How the payload can be held by Space Catapult’s rod during rotation and how it can be released from the rod? We think that using ''electromagnet plus mechanical holding devices'' would be a good solution. More precisely, after the payload is attached to the rod it must be held by means of both methods until the rod accelerates and reaches necessary velocity (it may take even several days), but with approaching the desired speed the mechanical device should release the payload however the electromagnet(s) should still hold it. The explanation of such approach is following: generally the mechanical devices are much slower/sluggish in performance than electronic ones. We have already said that when releasing the payload the extreme accuracy is needed and mechanical devices cannot guarantee ''the exact time of releasing'' the payload unlike electronic ones. That is, it’s unlikely that mechanical devices can release the payload at some certain moment when needed while in case of electromagnet it would be enough to cease electric current there, it would lead to immediate vanishing of the magnetic field and sending the payload along the tangent from the point where the payload would be at the current moment. <br />
<br />
<br />
We think that the ''fastest control system'' would enable to release the payload to certain direction. This system (extremely fast-operating computer plus measuring equipments) should know the current position of the rod’s end, the current speed, the needed direction and be capable for computing the necessary moment for giving the order for diminishing the voltage for electromagnets and hence releasing the payload to desired direction and velocity.<br />
<br />
=Rod’s plane of rotation towards the Earth=<br />
<br />
The Space Catapult’s rod when rotating makes the circular plane/flatness in space and this plane may be horizontal/parallel to Earth surface, that is making the right angle to Space Elevator’s cable or it may be placed along the cable; see the both possible situations here:<br />
<br />
[[File: Planes-of-rotation - Copy.jpg]] <br />
<br />
Both approaches have got their advantages/disadvantages and here we will discuss this question, first of all from the point of view of safety.<br />
<br />
For gaining extremely high velocities quite long rod would be needed, maybe with the length of several thousand kilometers or even more. If such rod is placed ''along'' the Space Elevator’s cable then the rod during rotation will cross many orbits from the ''Medium Earth Orbit'' to ''High'' ones. When rotating, the rod may actually hit any satellite and/or space debris object and such collision can lead to rod’s complete destruction; therefore we should choose such plane which would be much more free from any artificial objects; hence if the rod rotates ''horizontally/parallel'' to Earth’s surface at high enough altitude where the satellites’ population is relatively low then this measurement would justify itself because under such circumstance the rod will not cross satellites’ orbits (rod’s plane of rotation will simply coincide to ''one'' orbit’s path). However, we should also note that this altitude actually depends on the Space Elevator’s proposed length. Indeed, the Space Catapult’s rod should be mounted at the Space Elevator’s counterweight; this counterweight from its side should be placed at the end of the Space Elevator at such altitude where the satellites’ population is as low as possible. This means that Space Elevator’s proposed height should be agreed with mounting Space Catapult on its counterweight. According to various databases the number of man-made objects at high orbits, more precisely beyond geostationary orbit is much less than on the lower orbits <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup>, therefore the Space Catapult with its rod should be located at the altitude of 50 000-60 000 km above the sea level. At such altitude the space is almost free and nothing will impede rod’s rapid rotation. Besides, the satellites at high orbits are orbiting around the Earth slower than on the lower orbits (as known any satellite orbits around its primary body slower in apogee than in perigee), therefore if some tracking system is mounted at Space Elevator’s counterweight then it will enable the Space Catapult to avoid undesired collision with satellites during Space Catapult’s performance. In other words, the Space Catapult should operate only when the there are no satellites near its vicinities.<br />
<br />
Now we will try to discuss this question from other side.<br />
<br />
How the payload can be transferred from the Space Elevator’s cabin to the Space Catapult’s rod? One way is following: cabin reaches the counterweight where the payload will be released, then payload will be mechanically conveyed to rod, continues its way ''on the rod'' (like the train rides on the rails) and after reaching rod’s end it stops, the rod begins rotating and after gaining necessary linear speed it releases the payload to needed direction. This method is generally realizable; however it seems to be too complicated and unpromising compare to the second one: the Space Catapult’s rod is stopped in space so that it to be directed downwards to the Earth and be parallel to Space Elevator’s cable. The Space Elevator’s cabin moving along the cable with payload stops at the cable ''near'' the end of the Space Catapult’s rod and releases the payload that will fly to the rod, attaches itself to the rod’s end (here the electromagnets would be useful), the rod begins rotating and after gaining needed linear speed will release the payload to necessary direction.<br />
<br />
This second way seems to be more promising because the first one is much more complicated as we have already said: first of all there would be needed some mechanical devices for transferring the payload from the Space Elevator’s cabin to counterweight, the counterweight should have the hole for the payload to move through it from below (we should not forget that the Space Catapult should be mounted ''at'' the counterweight, not ''beneath'' it), besides the rod should be made so that it to have some conveying surface (rails for instance) the payload to move on it. As we see it would be much more convenient if it is possible to convey the payload from the cabin to the rod directly and this would be feasible under the second method which is depicted below:<br />
<br />
[[File: Convey.jpg]] <br />
<br />
One more aspect regarding Space Catapult’s position. This structure, its rod, its electro motor and etc should be mounted at Space Elevator’s counterweight so that the rod to be placed westwards from the cable. The reason of it is following: when the Space Elevator’s cabin stops and releases the payload (which should fly to Space Catapult’s rod) the current speed of which will/should be more than the value of the ''Orbital/Escape Velocity'' at the current altitude. After releasing the payload will fly westwards and upwards because its orbit will be ellipse, under ellipse the payload will fly higher to apogee and at the speed less than Space Elevator’s current speed at the given altitude, in other words the released payload will “lag behind” the Space Elevator’s cable; therefore payloads’ ''stopping points'' at the cable and Space Catapult’s rod’s length should be calculated and chosen so that the payload to fly directly towards rod’s end. This process would be feasible in both cases-if the rod’s plane of rotation is parallel to Earth’s surface and if it is placed along the cable-but still this would be easier for the payload to achieve the rod’s end if the rod is placed along the cable because at least the distance that the payload should cover in space will be less.<br />
<br />
The length of the Space Catapult’s rod placed at the Space Elevator’s counterweight might vary since for various spaceflight purposes different initial speed will be needed and relatively low speed could be achieved by means of shorter rod. Because of this reason it might be necessary to change Space Catapult’s rod’s length, therefore it would be useful if the rod consists of two parts where the first part would be perpetually attached to electro motor and the second one will be attached to the first part if necessary. For this operation Space Catapult’s rod should be placed along the cable since the relative nearness would make this operation quite easy and it could be accomplished by the crew directly from the Space Elevator’s cabin stopped at the needed altitude. <br />
<br />
For deciding the question how the Space Catapult’s rod should be placed towards the Space Elevator’s cable we should take into consideration one substantial circumstance-to which direction do we plan to send the payload in space by means of Space Catapult? This circumstance will influence deciding this problem due to following reason:<br />
<br />
In case ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and if rod’s plane of rotation is parallel to Earth equator, then this plane will be orthogonal to Earth’s rotation axis. This axis from its side is tilted to ''ecliptic plane'' by 66° 34'. This means that Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 23°26'. Here follows very important consequence: under above-mentioned conditions the rod when rotating will be capable for covering only the part of the ''celestial sphere'' from 0° to 23°26' (counted from ''ecliptic plane'' northwards and southwards to ''Ecliptic poles''). This is about one fourth of the ''celestial sphere'' (23°/90°), this will not make problems if we intend to use the Space Catapult for exploring the solar system’s planets because their orbits’ tilts towards ''ecliptic plane'' do not exceed 7° (for planet Mercury, for other planets this tilt is even less); however we will not be able to send the payload for example to the nearest star ''Alpha Centaurs'' because this star is located at -42 degree according to ''ecliptic coordinate system'' in the celestial sphere.<br />
<br />
The situation will drastically change ''if'' Space Catapult’s rod is parallel to Space Elevator’s cable and ''if'' rod’s plane of rotation is orthogonal to Earth’s equator and therefore parallel to Earth’s axis of rotation. We have already discussed this option when we mentioned that the rod should be placed westwards from the cable and explained why it would be useful-for delivering the payload from Space Elevator’s cabin to Space Catapult’s rod. Under such conditions the Space Catapult will be capable to aim to any point on the ''celestial sphere''. Indeed, the Earth with the Space Elevator rotates around its axis and Space Elevator’s counterweight draws an imaginary circle in space. This circle is tilted to ''ecliptic plane'' at 23°26' and crosses this plane in two point called ''ascending'' and ''descending nodes''. The other points that are 90° away from these nodes we call point(s) of ''maximum elevation/depression'' (relative to ''ecliptic plane''). When the Space Elevator is at a''scending/descending node'' its rod and hence the payload can be directed to any point from 0º to 66º on the celestial sphere northwards and southwards from ecliptic plane. This makes about 75 % of celestial sphere. See the image depicting this situation:<br />
<br />
[[File: Node.jpg]]<br />
<br />
But when the space Elevator reaches the points of ''maximum elevation/depression'' then its rod during rapid rotation may be directed to any point from southern ''Ecliptic pole'' to ''Northern pole'' at the celestial sphere because at these points rod’s ''plane of rotation'' is orthogonal to ''ecliptic plane'' and thus the rotating rod can aim to ecliptic poles as well as other points. See this situation below:<br />
<br />
[[File: Elevation.jpg]] <br />
<br />
The situation will be similar if the Space Catapult’s rod is orthogonally placed towards cable. Under such approach Space Catapult’s rod’s plane of rotation will be tilted to ecliptic plane by 66° 34' and the Space Catapult will be capable to cover ''three fourths'' (66°/90°) of the ''celestial'' ''sphere'' when the Space Elevator is at the points of ''maximum elevation/depression'' and the whole celestial sphere when the Space Elevator is at ascending/descending nodes. For aiming the needed point on the celestial sphere the Earth should occupy the appropriate attitude towards the stars during the revolution around its axis, the same thing should be done under previous case described in the paragraph above. <br />
<br />
In conclusion, thinking about rod’s plane of rotation towards the Earth, we should note one important difference between above-mentioned approaches: if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, then in case of emergency during Space Catapult’s performance (for example if the Space Catapult’s rod is cut by sudden meteorite bombardment) the rod’s part with the payload may simply crash to the Earth at huge velocity if the rod at this moment is directed to the Earth. This cannot happen if Space Catapult’s rod’s plane of rotation is orthogonal to Space Elevator’s cable because payload’s rotational path will not be directed towards the Earth and hence its flying trajectory will never cross the Earth.<br />
<br />
=Braking the Space Catapult’s rod=<br />
<br />
After releasing the payload at necessary speed and direction, the Space Catapult’s rod will have a huge angular velocity that needs to be decreased to zero in order the Space Catapult’s rod to get another payload in motionless position and then to send it to space. <br />
What methods can we use to reduce Space Catapult’s rod’s rotation to zero? There are several possible ways: <br />
<br />
1. The electromotor designed for accelerating the rod may actually play a role of brakes, more precisely after releasing the payload to space the electromotor should operate/rotate in the opposite direction, hence rod’s rotational speed will be diminished to zero after that electromotor will stop operating. Under such method a bit less energy will be spent for decelerating the rod than in case of accelerating because when decelerating the rod is free from payload. <br />
<br />
2. An ordinary mechanical brakes, however due to electro motor’s and rod’s sizes a huge brake(s) would be needed to be installed on the Space Elevator’s counterweight and this circumstance would make additional problems from the engineering point of view. Nevertheless, we should admit that under such method we would not need as much energy as during accelerating; on the contrary, in this process the heat will be emitted as it generally happens during braking. <br />
<br />
3. For decelerating the rod we can use the well-known phenomenon in physics-''electromagnetic induction'': when the c''onductor/ closed circuit'' moves into the magnetic field the electric current is generated there. In case of Space Catapult we can use this phenomenon in the following manner: the conductor should be wrapped around the whole length of the rod like a helix and there should be possibility that this conductor to be turned into the ''closed circuit'' by means of mechanically connecting its ends (see the image below). After releasing the payload at necessary speed and direction this circuit should be closed, then according to ''electromagnetic induction'' the electric current will be generated in the conductor and the energy of this electric current will come from rod’s kinetic energy. Therefore, inducted electric current in the enclosed circuit will force this circuit and rod to lose kinetic energy and speed. The part of the generated electric current will be spent in prevailing conductor’s electric resistance:<br />
<br />
[[File: Helix.jpg]] <br />
<br />
The advantage of this method is that for decelerating the rod no energy will be required, as for drawback-much time will be required for this purpose because at the altitude of several ten thousand kilometers the Earth’s magnetic field is quite weak and the effect described in the paragraph above will need much time to operate and give necessary result. <br />
<br />
4. The above-described third method could be realized in a bit different way: if the conductor wrapped around the rod is a closed circuit and if we conduct the electricity there then the electric current will generate its own magnetic field that will counteract with Earth’s one. More precisely, according to ''Lenz's law'' induced current’s magnetic field will be in such a direction as to oppose the motion or change causing it, in other words induced current’s magnetic field will counteract outer magnetic field’s any change and this will cause decelerating rod’s rotation and finally its stopping. <br />
<br />
5. The obvious disadvantage of the third and fourth method described above is weakness of the Earth’s magnetic field because of which decelerating the rod may be delayed in time. For solving this problem we can create artificial magnetic field by means of electromagnets. Particularly, one electromagnet should be placed at the Space Elevator’s counterweight, very close to Space Catapult’s rod. The second electromagnet should be placed directly on the Space Catapult’s rod close to first electromagnet (actually, instead of this second electromagnet there could be used the conductor wrapped around the rod as we described above in previous methods). The reason of this nearness is that magnetic field generally weakens directly proportional to distance’s third power and much time will be needed for decelerating Space Catapult’s rod if two electromagnets are far from each other.<br />
<br />
This method probably will consume the most amount of energy but at the same time it will be the most effective because it does not depend on outer factors such as Earth’s magnetic field which is quite weak at the altitude of several ten thousand kilometers above the sea level. <br />
<br />
Eventually, which methods for decelerating the Space Catapult’s rod would be the best? As we see each one of them have got their advantages and disadvantages. We can state that we should choose one of them according to spaceflight’s profile and goal. Particularly, if we decide to send the spacecraft into the deep space mission where especially high speed is necessary then in this case ''longer/more massive'' rod would be needed rotating at very high speed. Under such circumstance much energy will be needed for accelerating/decelerating the rod. We should also take into consideration the fact how frequently the Space Catapult will operate, in other words how mane payloads it will have to send into space per some certain amount of time, week/month and etc. If time interval between two following missions is relatively high then we should choose the method that will consume less energy and more time for decelerating the rod. On the contrary, if the Space Catapult has to send payloads very often then we should choose the method that will consume more energy and enable the rod to decelerate faster. In other words, we should find ''golden mean'' between consuming time and energy. We should also take into account how much energy supply will be produced at the Space Elevator’s counterweight (see ''Energy source placed on the Space Elevator’s counterweight'') and what part of this energy can we spend for accelerating/decelerating the rod.<br />
<br />
The rod’s rotations can be decelerated much faster than accelerated; the reason of it is that when accelerating the rod has got some sophisticated device as payload and generally unmanned spacecrafts are capable to high g-loads, but still for them some restrictions exist. After the payload is released at needed direction and speed, the rod can decelerate much faster because the rod itself is quite simple device without any complex and sophisticated details. <br />
<br />
We can actually use several methods, such as the third one and then the first/fifth ones. This would be justified because of following reason: as we have already said when decelerating with the third/forth method the problem of weakness of the Earth’s magnetic field would occur, therefore much time would be necessary for described method(s) to perform and give us result. However, we should note that in the beginning when the rod rotates very quickly this method would still operate strong enough. This derives from Faraday's law of induction stating that “the electromotive force generated is proportional ''to the rate of change of the magnetic flux''”. Therefore, in the beginning when the rod is rotating very quickly we can use the third/forth method(s) and when the rod significantly brakes we can apply to the first/fifth ones-they do not depend on Earth magnetic field. In other words, such approach would greatly help us in finding the golden mean between spending energy and time necessary for decelerating the rod. <br />
<br />
And finally: after releasing the payload the Space Catapult’s rod can actually give us energy. More precisely, the electro motor itself can serve as electric generator also since we know that the same machine can operate as electric motor if it is fed with electricity and as generator for electricity if its rotor is rotated by other machines. Therefore after releasing the payload when the electro motor’s rotor is rotating very quickly it can give us energy, in result of which the rod will lose its kinetic energy and speed, as for generated energy it can be sent downwards to the Earth for our terrestrial needs (see the next section in this paper) or stored onboard the Space Elevator’s counterweight. This approach has got one substantial advantage: it does not imply additional mass (wrapped wire) that will cause problems because rotating heavier rod would consume more energy.<br />
<br />
=Energy source placed on the Space Elevator’s counterweight=<br />
<br />
As well-known, the Space Elevator’s cabin needs energy when moving along the cable and it can get it from the Earth by means of various ways, such as: laser beam, microwaves, through the cable itself and etc. On the other hand, Space Catapult also needs much energy for rotating the rod and for this purpose some energy source should be placed on the Space Elevator’s counterweight, presumably solar panels array. Doing this would demand additional funding and engineering work and this undertaking should be justified, so how can we prove that placing energy source on the counterweight would be necessary and useful? We should not forget that the energy generally could be simply transmitted from the Earth without carrying any material for energy source on counterweight; so we can justify this undertaking if we declare/prove that: <br />
<br />
1. Energy source should be designed for ''both'' Space Elevator’s cabin and Space Catapult’s rod. We can imagine it as array of numerous solar panels producing enough energy for both above-mentioned constructions. For this purpose solar panels would be better solution than nuclear reactor because they do not need nuclear fuel to be carried from the Earth to counterweight, also they are capable for producing energy in a continuous mode. By the way this circumstance will enable us to send the payload to space by Space Catapult whenever we want without depending existence nuclear fuel at the counterweight. <br />
<br />
2. Transmitting energy from the counterweight (“from above”) is better and advantageous than doing the same thing from Earth (“from below”). Indeed, when we try to transmit energy (laser or microwave beam) from the Earth to ascending cabin, the part of energy is inevitably lost and dispersed in the Earth’s atmosphere and (this is point of the question) this continues during the whole process of ascent. On the contrary, when transmitting the energy from counterweight to cabin the energy will be lost only on the little part of this voyage, more specifically until the cabin leaves the atmosphere (100 km in height) and when cabin leaves it the energy will be transmitted in vacuum without loss. <br />
<br />
3. For receiving the energy from the Earth the huge solar panels (in case of laser beam) or antennas (in case of microwaves) will be needed to be mounted on the counterweight and this is additional mass and additional engineering work.<br />
<br />
We think that these arguments given above are enough for shoving that placing energy source on the Space Elevator’s counterweight have advantages over transmitting energy from the Earth and as conclusion we can state that energy source on counterweight would serve both space transportation systems-Space Elevator and Space catapult. <br />
<br />
As addition, we could use the energy produced on the counterweight for terrestrial needs also. Indeed, there have been developed numerous projects for receiving energy from space since 60-ies implying producing it by means of solar panels and then transmitting to the Earth. Combining all these three goals we can conclude that placing solar power plant on the Space Elevator’s counterweight would be triply useful and advantageous. In other words, when the Space Catapult and Space Elevator do not function, the energy produced on the counterweight should be directly transmitted to the Earth for our terrestrial needs and thus the idea of Space Elevator, Space Catapult and space power plant will be combined in one project.<br />
<br />
=Assembling the Space Catapult=<br />
<br />
Assembling in space such a huge structure as Space Catapult will not be an easy task from the technical point of view and definitely needs special engineering approach. Besides, we think that Space Catapult’s rod should be mounted at the Space Elevator’s counterweight separately from every other parts of the Space Catapult (e.g. electro motor and etc.); this circumstance is caused by rod’s gigantic sizes. More precisely, electric motor and plus any other equipments necessary for Space Catapult’s performance should be delivered to space by means of Space Elevator in a usual way; as for Space Catapult’s rod, it is a different matter and it should be delivered and mounted separately in the end. <br />
<br />
Eventually, Space Catapult’s rod will be quite long, perhaps much more than 100 kilometers. It is obvious that delivering such a long rod as ''one single unit'' would be quite difficult task; also it is possible that due to its total mass the Space Elevator’s cabin will not be able to deliver such rod at all, but we have already mentioned that the Space Catapult may have the rod with various length; more precisely the rod may consist of two/more parts. In such case these parts should be delivered towards the counterweight separately and then assembled. <br />
<br />
But the Space Elevator’s cabin can actually deliver the Space Catapult’s rod as ''one single unit'' in space. We think that this would depend only on rod’s mass. The Space Elevator’s lifting capacity is not well-known yet; however apparently it will not exceed one hundred metric tons and if Space Catapult’s rod is made of extra light material then cabin will be able to deliver it in space and in such case the following question will arise: how the cabin will deliver such a huge object in space without any damage?<br />
<br />
This can be done by means of two cabins. Generally, Space Elevator’s conception implies only one cabin moving along the cable, but for some special purpose (like delivering Space Catapult’s rod in space) we can use the second cabin also that will descend downwards after finishing its job and will not participate in Space Elevator’s further performance. As for the process of delivering the rod, we can imagine it in a following manner: at first the rod will be placed horizontally on the Earth (thus it must be manufactured and then transported to the Space Elevator’s base station), then the Space Elevator’s first cabin will carry rod’s one end along the cable while the rod’s second end will be moved on the Earth so that the rod to take more and more vertical position. When the rod is in vertical position the second cabin will capture rod’s second end and will carry it in space. We think that without the second cabin it would be quite difficult for one cabin only to carry long/heavy rod because the rod may actually shake and crash to the Space Elevator’s cable and this is absolutely undesirable. <br />
<br />
So, as we see in principle it looks to be quite easy, however the assembling may complicate due to rod’s length. In this case it would be better to carry not the rod as ''one single unit'' but its parts and then to assemble them in space in the following manner: ''two'' cabins will carry the first part as described above, when this part is delivered to space and temporarily hung at the cable the next two cabins will carry the second part that will be attached to the first one from below; the other parts will be delivered to space and assembled into the rod in the same way. <br />
<br />
The obvious disadvantage of the above-described method is that each part needs two cabins on the Space Elevator’s cable, besides the humans will be needed for assembling the rod from these parts in the atmosphere’s upper layers; therefore we think that the first way-delivering the rod into space as one single unit still would be easier and more realistic; besides we should take into consideration the fact that if the rod is assembled the additional devices will be needed ''on the rod itself'' for joining these parts and this circumstance would lead to increasing the rod’s total mass and this is undesirable. See the image showing assembling process:<br />
<br />
[[File: Assembling.jpg]] <br />
<br />
Whatever design/structure the rod has-assembled from several parts or as one single unit, it must be delivered to its destination-Space Elevator’s counterweight and must be fastened to electro motor’s own axis. But the problem is that the rod will be quite long and also the fact that Space Catapult’s electro motor will be placed at counterweight’s upper side (or at the ''lateral'' side if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), so it will be necessary the rod coming from below to be moved to counterweight’s upper/lateral side, besides the rod should be docked with electro motor’s axis as accurately as possible. How is it possible to realize such complex engineering operation? Here we can indicate one possible theoretical way: <br />
<br />
The rod will be parallel to Space Elevator’s cable when carried by cabin, but later the cabin’s mechanisms should rotate it so that the rod to be orthogonal to Space Elevator’s cable (this will not be necessary if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable, see ''Rod’s plane of rotation towards the Earth''), exactly in this position the rod should be delivered to counterweight, besides the rod when moving along the cable should be shifted a bit upwards (relative to the Earth) than the cabin itself. Under such conditions we will easily achieve docking the rod to electro motor’s own axis which from its side should have some trapping device (magnetic for example) to “catch” the rod and thus guarantee docking the rod to electro motor and finishing assembling the Space Catapult as a whole. But if the rod’s plane of rotation is parallel to cable then assembling process will be much easier because the ascending rod may directly dock to electro motor’s own axis. See the image showing this process:<br />
<br />
[[File: Deliver - Copy.jpg]] <br />
<br />
We think that it would be useful if one Space Elevator is built specially for Space Catapult with its base station located on the land, not the ocean. This would be justified because transporting Space Catapult’s rod from its place of manufacture to Space Elevator’s base station should occur on the land by means of several transports simultaneously (due to rod’s great length), this will enable us to deliver the rod to its destination without any damage while this kind of operation is hardly possible on the water.<br />
<br />
=The technical aspects regarding the Space Catapult=<br />
<br />
As an example, we can try to calculate/ascertain all possible kinds of aspects regarding the rod with some certain mass and sizes, for example we can assume the Space Catapult has got 100 km length rod. <br />
<br />
The circumference of the circle that this rod’s end will draw in space will be equal to 2πr=628 km. As we have already mentioned payload’s abilities for withstanding the g-load is restricted, so if the electromotor rotates the rod so that payload’s speed is equal to 50 km/sec (this means that it will take 12.56 seconds for the rod to make one complete revolution), in this case acceleration will be equal to 25 000 m/sec2, which is about 2550 g. The modern technologies enable to design the spacecraft that will withstand such acceleration, but what about the rod itself? Which material can be used for designing this rod, what will be its mass and how much energy and time will be needed for the rod to reach this velocity? <br />
<br />
For manufacturing the rod we should choose the material with very low density and highest value of strength. Currently, the ''Carbon nanotubes'' are the best candidates for this purpose. What will the mass of the rod made of this material? This depends on width also and it should be as less as possible (otherwise the rod will be too heavy and too wide for transporting from manufacture place to Space Elevator’s base station and for delivering it to space by means of Space Elevator) but from the other hand the ''applied load'' will not let us to design very narrow rod.<br />
<br />
Let’s assume that we intend to launch the payload with the mass of 10 000 kg (during calculation we will use ''SI system'' only). To clarify what kind of material will be able to withstand the acceleration we should calculate and then compare two values: the ''applied load'' and ''tensile strength''. For calculating the first one we should multiply g-load (which we already know-2 550 g) to its mass-10 000 kg, we will get 25 500 000. As for calculating tensile strength, we should take its values (for Carbon nanotubes it varies from 11 000 MPa to 63 000, we will take some medium value-40 000 MPa) and multiply it to cross-section’s area, in our case rod is cylinder with circular cross-section. If radius of cross-section is 1 meters then its area is 3.14 square meters, multiplying this value to value of tensile strength (40 GPa as said) we will get 125 600 000 000 and this is significantly more than value of applied load-25 500 000. Of course, we should also take into consideration ''factor of safety'' which is generally equal to 2 and this indicates us that for safety the payload’s actual mass should be twice less but in our case as we see the rod will be able to accelerate the payload to above-mentioned speed. By the way, note that if that g-load ''2 550 g'' is almost at the payload’s withstanding limit this is not serious problem for the rod itself (we have already seen that value of tensile strength is much more than value of applied load) and this is clear why: payload generally contains sophisticated equipments (electrical circuit, optics an etc.) that will not be able to withstand very high g-loads while the rod will be made of some continuous solid substance, Carbon nanotubes is this case and of course it will be able to withstand much higher g-loads.<br />
<br />
<br />
What will be the mass of such rod? Knowing its volume (for this purpose its cross-section’s area 3.14 square meters should be multiplied to rod’s length-100 000 meters, we get 314 000 cubic meters) and taking the value of density (this also varies for Carbon nanotubes from 0.037 to 1.34 g/cm<sup>3</sup>, let’s take 0.1 g/cm<sup>3</sup>) we get rod’s mass as 31 400 000 kilograms. This is too heavy for Space Elevator’s modern concepts and for improving this situation we should either use many cabins for raising the rod as single unit or use nuclear energy for feeding the cabins instead of laser/microwave beams or deliver the rod’s parts separately in space and then assemble them (see ''Assembling the Space Catapult''). But if some advanced substances are chosen for this purpose (for example ''Silica aerogel'' the density of which is about 1.9 mg/cm<sup>3</sup>, this is 50 times less than the density of the Carbon nanotubes taken above-0.1 g/cm<sup>3</sup>) than problem may be lightened in spite of the fact that their current tensile strength is quite low-16 kPa for the density of 0.1 g/cm<sup>3</sup> <sup>7</sup>. So, we can conclude that we need the material with the density of ''Aerogels'' and tensile strength of Carbon nanotubes.<br />
<br />
How much energy and time will be needed for the rod to accelerate from zero to desired speed-50 km/sec? The amount of rotational energy of the rotating rod can be calculated by the following formula:<br />
Kinetic Energy<sub>rotational</sub>= (1/2)*I*ω2 <br />
<br />
Where:<br />
<br />
'''I'''=moment of inertia <br />
<br />
'''ω'''=angular velocity<br />
<br />
"I" depends on the shape of the mass under rotation. In the case of a uniform rod rotating from its end (axis of rotation is at the end of the rod) I = (m*L2)/3<br />
<br />
<br />
“ω” = V/R, where V = tangential velocity and R = radius<br />
<br />
In our case ''moment of inertia'' is equal to (31 400 000 kg*100 000 m2)/3=104 666 666 666 666 666<br />
ω is equal to (50 000 m/sec)/100 000 m=0.5<br />
<br />
So, Kinetic Energy<sub>rotational</sub>=(1/2)*104 666 666 666 666 666*(0.52)= 13 083 333 333 333 333.25 Joules<br />
<br />
Now, how much time and what amount of solar panels will be needed for accelerating this rod? The amount of Solar constant near the Earth is approximately equal to 1300 W/m2 [<sup>8</sup>], with assuming that ''coefficient of efficiency'' of solar panels is roughly 20 % we get 260 Watts per square meters and we can easily link amount energy (that we have already calculated) and power with the time needed. Particularly, ''Energy'' is equal to ''Power''’s multiplication to ''Time'':<br />
<br />
[[File: Formula - Copy.jpg]] <br />
<br />
So, Time is equal to 13 083 333 333 333 333.25 Joules/260 Watts=50320512820512.8 seconds, or 1 595 652 years. If we take much more area for solar panels, for example 10 millions square meters then 0.1595652 years or approximately 58 days will be needed and we think that this is acceptable time span.<br />
<br />
Actually, the time and energy will be needed a bit more for overcoming static friction in electro motor, for overcoming the rarified atmosphere’s resistance (we know that there no absolute vacuum in space), also we should take into consideration electric motors’ coefficient of efficiency that generally reaches 90-95 %, so some energy loss will occur here also. <br />
<br />
Now, what will be the total mass of solar panels producing the energy for Space Catapult? This depends on mass/power ratio, in near future it is expected that very lightweight designs could likely achieve 1 kg/kW [<sup>8</sup>] or 0.260 kg/ 260 W (per 1 square meter), so if for rotating the Space Catapult 10 millions square meters of solar panels are used then their total mass would be equal to 2 600 000 kg. We think that it is too heavy for Space Elevator the mass of which is expected to be equal around several hundred metric tons. If so, we will have to use fewer amounts of solar panels and therefore increase the time needed for accelerating the payload’s speed from zero to designed one. This will not make problems if the rod is accelerated only once and then keeps its constant rotation-for this purpose less energy will be needed and the payload will have to reach the rod’s end by first method as described earlier in this paper (see ''Rod’s plane of rotation towards the Earth'').<br />
<br />
We also need to take into consideration the value of deflection when the rod will be delivered to space by means of Space Elevator (see ''Assembling the Space Catapult''), in this case the thin and long rod will be bent due to its own weight and here we will try to calculate its value. This is quite complex problem that apparently cannot have an unambiguous solution because of many reasons, for example due to various temperatures in atmosphere’s different layers, various humidity and possible wind, but still we will try to calculate the value of ''Deflection'' that will occur in case when the rod’s one end is fastened to Space Elevator’s ascending cabin and the second end is fastened to the transport moving on the land, we discussed this option in above-mentioned section of our paper (see ''Assembling the Space Catapult''). The inclination angle for the rod will vary from 0º (rod is transported horizontally on the ground) to 90º (Space Elevator’s cabins are carrying the rod to space) and here we will discuss some medium case when the rod is semi-elevated in the air, when the angle between rod and ground/cable is equal to 45º. On the engineers’ ''eFunda'' web-site there is online calculator that enables to receive the value of ''Deflection'' (actually that site gives different term for this-''Displacement'') [10]:<br />
<br />
Here we need to enter the relevant values:<br />
<br />
''Length of beam'', ''L'': 100 000 meters<br />
<br />
''Line pressure load on beam'', p: In our case this is the weight per meter length. As we have already mentioned the radius of the rod’s cross-section is 1 meter, so the volume of rod’s 1 meter-length part will be 3.14 cubic meter. In case of using Carbon nanotubes with above-mentioned density-0.1 g/cm<sup>3</sup> the weight will be equal to 314 kg or 3 079 Newton. Since we have got the inclination of 45º we should multiply this value to cos45º- 0.707, so we get 2176 N/m.<br />
<br />
''Young's Modulus'', ''E'': This is equal to 1 000 GPa for Carbon nanotubes [11] <br />
<br />
''Distance from neutral axis to extreme fibers'', ''c'': In our case it is equal to the radius of the rod-1 meter<br />
<br />
''Moment of Inertia'', ''I'': It is equal to (pi*r<sup>4</sup>)/4, so it is equal to 0.785<br />
<br />
According to these initial data the calculator returns extremely high value of Deflection, much higher than the length of the rod itself: -3.61 × 10<sup>9</sup> meters. This result shows us that with the current materials (Carbon nanotubes in our case) it is impossible to raise the rod as ''one single unit'' to space by means of Space Elevator and we need other materials with less density and more ''Young's Modulus'' (or the rod should be much thicker but this will lead to increasing its mass). Therefore, we have got two options: either we should deliver the parts of that rod and then assemble them in space (we have already discussed this option) or completely different technologies for manufacturing the rod should be developed. Particularly, it would be very good if it was possible to manufacture the rod ''in continuous mode'' in vertical position and then uninterruptedly directly to carry it to space by means of Space Elevator’s cabins. Under such approach there will be no ''Deflection'' and several cabins will be able to deliver the rod in space. <br />
<br />
One note about transporting the rod from its place of manufacture to Space Elevator’s base station. We think that this process should be executed by many transports, in other words we are convinced that if the rod is carried by two trains only (or any other kind of transport) then the rod will continuously touch the ground since the ''Deflection'' occurs in any position-horizontal, inclined or vertical and this circumstance will lead to its damage, that’s why several transports will be needed to hold the rod at as many places as possible.<br />
<br />
=Stabilizing the counterweight=<br />
Stabilizing the Space Elevator’s counterweight is very important question during Space Catapult’s performance. Indeed, when the rod rotates it makes the imaginary circles in space and due to rod’s and payload’s masses the Space Catapult’s ''center of mass'' will be continuously shifted and if the counterweight is not somehow stabilized then it will make problems for accurate aiming to certain point at the celestial sphere. Also, if Space Catapult’s rod’s plane of rotation is parallel to Space Elevator’s cable then there will be the danger that the rod may actually hit the cable and cut it. To avoid these problems we need to apply to serious measurements. <br />
<br />
First of all, the electro motor’s own axis can be quite long and this will diminish the chance to failure of the whole system. Actually, we are convinced that counterweight’s (where the electric motor will be placed) size will be quite large, mainly due to solar panels’ sizes and amount (this issue was discussed above), also the electromotor should be quite large and powerful to rotate the rod, and hence there will be enough distance between the rod and Space Elevator’s cable. <br />
<br />
The second serious problem is that the center of gravity of the system is not at the center of rotation, therefore it will be necessary to balance the rotating system when the payload is attached and when it is released.<br />
<br />
We think that the Space Catapult’s rod should not be deployed/directed to one side only but some counterweight of it should also exist. This is necessary since the unilaterally loaded (we mean the rod itself plus payload) rod will cause the counterweight to somersault. In other words, the rod should extend to other side and the ''moments of inertia'' of both sides should be the same as during rotating the rod as after releasing the payload when the rod still rotates. This is easily achievable if some additional, second payload is placed on the rod’s second end. Therefore, the Space Catapult will launch two payloads at the same time to the ''opposite'' directions but at various speeds if the second part/side of the rod is shorter.<br />
<br />
How the second payload should be placed on the rod and should we really send two payloads? Until we have got balanced rod this problem does not arise but as soon as the Space Catapult releases the payload this balance will be violated, how it can be restored? There are two theoretical ways for achieving this: reducing the ''mass'' or reducing the ''length''-with diminishing either one of them the ''moment of inertia'' will be decreased. We think that reducing the mass will be less practicable since this would require placing the second payload (spacecraft or anything else) on the rod’s second part and this cannot be done from the Space Elevator’s cabin-this is the easiest way for delivering the payload from Earth to Space Catapult’s rod; so we would have to (see ''Rod’s plane of rotation towards the Earth'') put the second payload on the electro motor and then send it rod’s second part’s end. This is quite complicated task; therefore we can apply to second approach-put some sliding object that will immediately move to electromotor as soon as the spacecraft is released.<br />
<br />
[[File: MOI.jpg]] <br />
<br />
The next problem that may occur is that when the electro motor rotates the rod this motion will make the Space Elevator to rotate to the opposite direction. The same problem arises when helicopter’s primary blade’s rotation forces the helicopter to rotate to opposite direction and this possible rotation is annulled by ''tail rotor''. We think that for balancing the counterweight the additional motor and rod should be installed and this rod should rotate to opposite direction and if their ''angular momentums'' are equal to each other, then their rotations will cancel each other. More precisely, the following equation should be fulfilled:<br />
<br />
[[File: Angular momentum.png]] <br />
<br />
Where ''m'' is mass of the rod, ''v'' is angular speed and ''L'' is rod’s length, the numbers ''1'' and ''2'' refer to first and second rods correspondingly. For balancing both rods’ rotation the multiplication at both sides of the counterweight should be equal, by the way this circumstance enables us to use the second rod with shorter length and even with less mass but rotating at more angular velocity.<br />
<br />
Such approach will effectively deal with other problem which will arise when the Space Catapult releases the payload(s), at this moment the second motor should instantly diminish its angular velocity to some certain level (an ordinary mechanical brakes could be used for this purpose), in this case ''angular momentums'' for both motors/rods will be equal again and Space Elevator’s counterweight will maintain its attitude in space. See the image below depicting the Space Catapult with two electro motors and rods:<br />
<br />
[[File: Two-rods.jpg]] <br />
<br />
Such approach will justify itself if rod’s plane of rotation is parallel to Space Elevator’s cable, but if this plane is orthogonal to cable (see ''Rod’s plane of rotation towards the Earth'') then the second/balancing electromotor cannot be placed under the counterweight because the cable will be cut when rod touches it. Therefore a bit different approach should used and we need to install two/four/eight electro motors with their own relatively shorter rods rotating to opposite direction. They should be placed at the counterweight’s lower side and on its edge (as we suppose the counterweight should be disc) so that their rods not to touch and cut Space Elevator’s cable. Also, total a''ngular momentums'' from these motors should be equal to the ''angular momentum'' from upper motor and thus the counterweight will not rotate and the Space Elevator’s cable will not be twisted. This situation is presented below:<br />
<br />
[[File: Modified-2.jpg]] <br />
<br />
We think that the array of gyroscopes would be also very useful to be installed at the counterweight since they can maintain the attitude of the whole system and this is important for precise aiming to certain point at the celestial sphere. As for the energy required for gyroscopes’ performance it could be received from the array of solar panels which as a result will generally serve Space Catapult’s precise performance.<br />
<br />
=Space Catapult placed at Lagrangian points-the way for gaining subluminal speeds=<br />
<br />
In our paper we discussed the Space Catapult based on the Space Elevator’s counterweight and concluded that this would be convenient when we intend to deliver the payload to space from the Earth. However, such Space Catapult cannot gain very high speeds and therefore we need to choose other way. It is obvious that we need to keep rod’s plane of rotation orthogonally relative to the ''Earth-Sun connecting line'' and hence we should place the rod on the celestial body which will be in synchronous rotation with the Sun but since there is no such body in the solar system we conclude that the Space Catapult for subluminal speeds (the speeds close to speed of light are in mind) should be placed at such point near the Earth where it will be easy to reach it from our planet and where the rotating rod will not hit the Earth and will be always at the same distance from the Sun to avoid the influence of its tidal forces. The examples of such places are '''Lagrangian''' L<sub>1</sub> and/or L<sub>2</sub> points at 1.5 million km away from the Earth. If the Space Catapult is placed at one of these points then its rod can be always orthogonal to the Sun in principle, at the same time it will never collide with the Earth and also it will be quite close to the Earth since 1.5 million km distance is very negligible in space.<br />
<br />
We have got several notes regarding such approach. First, when we mentioned that the rod’s various parts can be at the same distance from the Sun this strictly speaking is not very true because the Sun can be referred as little point where its gravity “comes out” from while the rod is quite long and its initial part (placed at one of the Lagrangian points) will be attracted stronger than the utmost one (for equal attracting the rod should the arc ''with the same curviness as Sun’s surface'' and not straight line); but still this is better than to direct the rod exactly towards the Sun where the tidal forces will try to tear the rod. Second, the Space Catapult should be placed at Lagrangian L1 point which is closer to the Sun than L2 one and therefore receives by 4 % more energy per area from the Sun. Third, the rod should be in constant rotation, this requires much less energy than accelerating it from zero, then stopping it and accelerating it again. Fourth, the existence of the asteroid belt in the solar system between Mars and Jupiter will somehow restrict the actual length of the rod. Indeed, the Space Catapult should be placed at one of the Lagrangian points at 1 AU distance from the Sun while asteroid belt approximately lays at 2.7 AU, from the simple geometry it is obvious that the length of the rod ''almost reaching'' the asteroid belt can be approximately equal to 390 million km, and if the rod is longer then it may simply hit any asteroid within that belt. For 390 million km length rod and for 100 000 m/sec2 acceleration at rod’s end (where the payload will be attached) the maximal speed that the spacecraft can gain will be approximately equal to 200 000 km/sec (two thirds of the speed of light) and this can be considered as enough for practical interstellar spaceflight. Fifth, the spacecraft should be directly put on the rotating rod’s initial end (near electromotor) and then slide towards the other end with its own rocket engines. To achieve this, the spacecraft will have to cover relatively less distance on the rod and then rod’s circular motion will accelerate the spacecraft further-we have already mentioned this in this paper when speaking about deploying the Lunar Space Catapult. This action-putting the spacecraft on the rod will not be difficult since rod’s angular velocity will be quite low due to rod’s huge length, particularly for 400 million km length rod and for 200 000 km/sec linear speed the rod’s angular velocity will be 0.0000796 revolutions/sec.<br />
<br />
[[File: Lagrangian-point.jpg]] <br />
<br />
We have already mentioned that to avoid the destructive influence of the Sun’s tidal forces the rod’s plane of rotation should be orthogonal to the Earth-Sun connecting line. By the way, note that under such approach we may have to wait one year until the Lagrangian Space Catapult occupies the relevant position towards the certain point at the celestial sphere where the spacecraft should be sent to. But from the other hand it would be useful if it is feasible to rotate this whole structure around the imaginary axis directed towards the ''ecliptic poles'' (depicted as faint green dash line on the image above), the reason if this is the possible danger when the rotating rod may hit Mars or asteroids that orbit around the Sun closer than 2.7 AU distance (for example ''433 Eros'' or ''1036 Ganymed''), hence for avoiding such undesired collision the Lagrangian Space Catapult should be slightly rotated by several degrees clockwise/counterclockwise so that the rod not to collide with any celestial object. We are convinced that rotation by several degrees will be absolutely enough measurement due to rod’s gigantic length and relatively less sizes of the celestial objects in the solar system.<br />
<br />
The next issue that we should discuss refers to stability of the Lagrangian Space Catapult placed at L<sub>1</sub> point. As we see this structure will have enormously gigantic size while the Lagrangian point is relatively little mathematical one in space, so what can be done to be convinced that this structure will remain at that point and do not shift aside? The body placed at one of the Lagrangian points is affected by other celestial objects’ gravity and therefore for achieving the balance the rod needs to have the counterweight with more mass if it (counterweight) is shorter. As we clearly see the rod needs the counterweight for two reasons: not to let the Space Catapult somersault and for maintaining it at the L1 point. We think that it would be very useful if the arrays of solar panels act as counterweight since exactly they can give us energy for rotating the rod. Also, we need the second, shorter, perhaps less massive but faster-rotating rod (again-solar panel arrays) the opposite rotation of which would cancel first rod’s rotation, this issue was discussed in this paper. These arrays of solar panels are depicted on the image shown above. <br />
<br />
How such a gigantic structure as Lagrangian Space Catapult can be assembled in space? In our paper we discussed the possible ways for delivering the rod from the Earth to the Space Elevator’s counterweight, now we will try to show that it is possible ''in principle'' to assemble the extra-long rod in space. <br />
<br />
If it is possible from the technical point of view to manufacture extra-long rod then we can use this approach and make 1.5 million km length rod (this is the distance between the Earth and Lagrangian L<sub>1</sub>/L<sub>2</sub> point) that will be mechanically directed to the base station at L<sub>1</sub> point. The capturing devices there will catch the rod and attach it to the electro motor’s shaft after which the rod should be spun by 90º so that it to be orthogonal to Earth-Sun connecting line (for this purpose the additional mechanisms will be needed), this spin is necessary because L<sub>1</sub> point is located on the Earth-Sun connecting line (that is towards the Sun if we look from the Earth) and when directing the rod from the Moon it will lay ''along'' this line while we need across. After this the rod should be slid to another side and then the next rod should be directed to the Lagrangian Space Catapult where it will be attached to the previous rod and etc. In other words, the extra-long rod will be assembled from one side and its length will “grow” from this side to other one, this is necessary because the distance between Moon (the rod should be manufactured exactly there and not on the Earth due to our planet’s relatively more gravity, atmosphere and problematic space debris belt around it) and L<sub>1</sub> point is constant and rod’s parts cannot be more. Due to whole rod’s and its parts’ lengths (400 million and 1.5 million km correspondingly) we think that about 260-270 such operations will be needed to finish assembling the rod (400/1.5). The process of assembling the Lagrangian Space Catapult is shown on the image below:<br />
<br />
[[File: Lagrangian-point-assemble.jpg]]<br />
<br />
=Conclusion=<br />
<br />
As we have seen, for leaving the Solar system and reaching the remote celestial bodies (stars, nebulas) there is no need to develop advanced and complicated technologies that mostly are not capable for gaining extra high velocities nevertheless. In any case, until the Space Elevator is really built (scheduled for construction by 2031) we have got much time for developing the idea of Space Catapult in technical aspect, like finding appropriate materials for the rod, perfect the ways how the Space Catapult can be assembled in space and etc. The concept of Space Catapult itself is the easiest one, does not need developing neither complex and sophisticated technologies, nor some exotic methods (such as ''Gravitoelectromagnetic toroidal launchers'', ''Antimatter rocket'' and etc.) and can be easily implemented in near future; in other words the Space Catapult is not some sophisticated structure that would need profound science research and the fact that it will enable us to gain whatever high speed will justify its developing and building by the humankind. As for other technologies like Ion Drive, they could be used by the spacecraft during flight for other purposes, for example for correcting/changing the flight direction.<br />
<br />
<br />
'''References:'''<br />
<br />
1. http://en.wikipedia.org/wiki/Space_Elevator<br />
<br />
2. http://www.isec.info/index.php?option=com_content&view=article&id=14&Itemid=9<br />
<br />
3. http://www.space-track.org/perl/geo_report.pl (provided data updates regularly, registering is needed) <br />
<br />
4. http://www.oosa.unvienna.org/pdf/reports/ac105/AC105_720E.pdf page 24 (data as at 21 August, 1997) <br />
<br />
5. http://www.amostech.com/ssw/presentations/Session7/S7-1Molotov.pdf page 16<br />
<br />
6. http://www.esa.int/SPECIALS/ESOC/SEMN2VM5NDF_mg_1_s_b.html <br />
<br />
7. http://eetd.lbl.gov/ecs/aerogels/sa-physical.html<br />
<br />
8. http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant<br />
<br />
9. http://www.you.com.au/news/2005.htm, http://www.spacedaily.com/news/ssp-03b.html<br />
<br />
10. http://www.efunda.com/formulae/solid_mechanics/beams/casestudy_display.cfm?case=simple_uniformload<br />
<br />
11. http://en.wikipedia.org/wiki/Young%27s_modulus<br />
<br />
<br />
'''Appendix''': <br />
<br />
Animation illustrating the payload’s departure from the Lagrangian Space Catapult:<br />
[[File: Lagrangian-point-animation.gif]]</div>Eagle9http://keithcu.com/wiki/index.php?title=OpenSpace_5&diff=3663OpenSpace 52013-09-21T12:49:05Z<p>Eagle9: </p>
<hr />
<div><div style="float:right; border:#CCCCCC solid 1px; background-color: #F7F7F7"><br />
<table cellspacing=0 cellpadding=0 width=550><br />
<br />
<tr><td colspan="3" align="center" style="background-color:#CCCCCC"><b>Title:</b> Place Title Here</td></tr><br />
<br />
<tr><br />
<td align="center" valign="middle" height=125 width=100 style='padding:10px'><br />
<div style="background-color:#CCCCFF; height:110px; width:90px"><br />
[Cover Img]<br />
</div><br />
</td><br />
<br />
<td align="left" valign="top"><br />
<div><br />
<b>About:</b><br /><br />
* Moderator: [[OpenSpace#Place lead user name here|Mr. Giorgi Lobzhanidze]]<br /><br />
* Contact e-mail: giorgi9@gmail.com<br />
* Created: July 26, 2008<br /><br />
* Modified: July 26, 2008<br /><br />
</div><br />
</td><br />
<br />
<td align="left" valign="top"><br />
<div><br />
'''[[Article Tags|Tags]]''':<br /><br />
* This is open space for development<br />
</div><br />
</td><br />
</tr><br />
<br />
</table></div><br />
<br />
<br />
== '''Space Catapult''' ==<br />
<br />
'''Author: Mr. Giorgi Lobzhanidze''' <br />
<br />
'''Address: Tbilisi, Republic of Georgia, Europe''' <br />
<br />
'''Email: mailto:giorgi9@gmail.com'''<br />
<br />
=INTRODUCTION=<br />
<br />
<br />
The new method for sending the spacecrafts in deep space is presented here. The paper describes the long rod rotated by electro motor placed at the Space Elevator’s counterweight and at Lagrangian points. This simple structure will enable the rod to gain high velocity and carry the payload with it. After reaching the desired speed the rod will release the payload that will fly in space along the imaginary circle’s tangent. This structure we called Space Catapult and it should work with the assist of Space Elevator. This latter should be used for carrying the payload from the Earth to Space Catapult’s rod.<br />
<br />
For exploring the outer space the humankind generally uses the rocket engines, mostly chemical-propelled ones. They enable us the explore near-Earth celestial bodies and other planets in the solar system. They even enabled us to send several deep space missions beyond the solar system such as '''Pioneer-10''', '''Pioneer-11''', '''Voyager-1''', '''Voyager-2''', however by means of this technology the flight lasts undesirably long and it seems to be impossible to reach remote celestial bodies in space such as stars, so new technologies are necessary for this purpose. However new technologies do not necessary imply new kind of rocket engines, such as ''Ion Drives'' because they are capable for gaining several ten times higher speeds only, but for remote celestial bodies even they are not suitable. Besides, they need a huge amount of energy to be stored onboard the spacecraft and this will make additional problems. So, high speed should be achieved with absolutely different approach. How this can be done?<br />
<br />
High speed can be easily achieved by means of fast-rotating rod around the electric motor. The motor’s rotational speed can be very high; the rod also can be quite long, hence the rod’s end’s linear speed can be extremely high, absolutely unachievable for any other technologies nowadays. The payload should be fastened at the rod’s end where the linear speed generally reaches maximal value. After reaching the necessary speed the rod will release the payload that will fly along the tangent from the current position. Thus the electric energy can be turned into payload’s speed and its velocity could be as high as we wish (except the ''speed of light'' of course). In principle the '''Space Catapult''' (thus we call this structure) would be the simplest, the most convenient and direct way for converting the energy/electricity into speed and conveying it to payload. <br />
<br />
As we see the Space Catapult is quite uncomplicated structure, however if we wish to gain high speeds we should deploy it in space, not on the Earth. Indeed, our planet is surrounded with dense atmosphere that impedes any quick motion, so if we rotate the rod quickly the atmospheric drag and generated heat would burn it very soon, therefore the Space Catapult should be built and deployed in space only, and as we suppose-at the Space Elevator’s counterweight. In other words, the Space Elevator’s counterweight will operate as Space Catapult. See image below:<br />
[[File:Space-catapult.jpg]]<br />
Generally, what is the Space Elevator <sup>1</sup> <sup>2</sup>? According to modern concepts it will be the tall vertical structure built on equator and will have height of several ten thousand kilometers with its thin cable fastened to the base station on the Earth and with counterweight placed higher geostationary orbit. Because of balance between centrifugal force and gravity this structure will be stretched and the cabin will move along its cable carrying the goods into high orbit. After delivering the payload, the cabin will descend and carry the next one.<br />
In Space Elevator’s concepts several solutions have been proposed to act as a counterweight: <br />
<br />
1. Heavy, captured asteroid <br />
<br />
2. Space dock, space station or spaceport positioned past geostationary orbit <br />
<br />
3. Extension of the cable itself far beyond geostationary orbit. <br />
<br />
The third idea has gained more support in recent years due to the relative simplicity of the task and the fact that a payload that went to the end of the counterweight-cable would acquire considerable velocity relative to the Earth, allowing it to be launched into interplanetary space. However this idea cannot be completely shared by us due to following reason: <br />
<br />
It is well-known that the values of both '''Orbital''' and '''Escape Velocities''' decreases with increasing the altitude while the '''tangential velocity''' of Space Elevator’s cable increases. We can see the differences between them from the chart presented below:<br />
[[Image: Cxrili.gif]]<br />
<br />
As we see from this chart the ''tangential velocity'' of the Space Elevator even at its end (144 000 or 200 000 km altitude) is not very high to decrease the necessary time for covering the distance from the Earth to remote celestial bodies significantly. To achieve this, even the longer Space Elevator would be needed (its ''tangential velocity'' is directly proportional to its length) and this circumstance would complicate the technical task for building such Space Elevator. Because of this, there is no necessity to extend the cable itself far beyond geostationary orbit as proposed in the third variant. In any case, we have already seen that by means of Space Catapult it is possible to gain such huge velocities that are absolutely unachievable with other technologies, for example with Space Elevator. Therefore, using the counterweight and placing the Space Catapult there definitely has got some technical sense. <br />
<br />
However, we think that the question where the Space Catapult should be placed needs further discussion. Theoretically, the Space Catapult with its payload and nuclear reactor/solar panel needed for rotating the rod may be mounted not only at the counterweight, but on the Space Elevator’s cabin also that can carry all these goods to space in a usual way, as it should do it according to Space Elevator’s modern concepts. This option is quite possible, however for realizing this we need to know the mass of the payload, nuclear reactor/solar panels’ mass plus Space Catapult’s mass from one hand and Space Elevator’s lifting capacity (this ''must'' be more) from other hand, but these data are not available nowadays, therefore we think that the Space Catapult should be still mounted at the Space Elevator’s counterweight where it will be possible to send the payloads into deep space in ''continuous mode'' at high velocities.<br />
<br />
As we saw the Space Catapult is capable to gain very high velocities; however there is being developed other technologies and they in future will enable the spacecraft to fly at high speeds in space. These are Ion Drive systems, more precisely the most perspective one-''Variable Specific Impulse Magnetoplasma Rocket'' (VASIMR) which still under development can be used in future for deep space missions. Can these engines and Space Catapult be the rivals in space? Since none of them have been built and used in space yet we cannot give a persuasive answer to this question; however still it is possible to underline Space Catapult’s one significant advantage: if the future spacecraft uses the VASIMR (or any other kind of Ion Drive) engine it will definitely need to be equipped with nuclear reactor, otherwise the spacecraft will not be able to gain high speeds, also it will need to carry fuel tanks for this purpose. As for the Space Catapult, it can give much higher speed to spacecraft, besides it will have ''stationery'' power plant (see ''Energy source placed on the Space Elevator’s counterweight'') at the Space Elevator’s counterweight, so the payload will ''not'' have to carry the nuclear reactor onboard and this circumstance will lighten the work for deep space spacecraft. Besides, we should not forget that unlike the spacecrafts equipped with ion drive engines the Space Catapult will need no fuel for gaining high velocities. <br />
<br />
Briefly, Space Catapult’s advantages over any kind of propulsion systems are: <br />
<br />
1. Ability to gain any speed that is absolutely unachievable by means of other kinds of engines. <br />
<br />
2. No need by spacecraft to carry energy source that would make it too heavy and impracticable.<br />
<br />
=The Space Catapult needs long rod=<br />
<br />
When building the Space Catapult at Space Elevator’s counterweight we should install quite long rod there, the shorter the rod is, the easier would be installing it, however we should note that rod cannot be extremely short, let’s say 1 km length or so due to following reason:<br />
<br />
When we are going to send some payload into space, we need not only high velocity, but one certain direction also. The little inaccuracy in direction, inclination in several arcminutes is actually acceptable since the spacecraft would easily balance it with its engines; however great inclination from the initial direction would send the spacecraft into the completely different direction and in such case the whole mission will fail.<br />
<br />
If two Space Catapult’s rods have the length of let’s say 1 kilometer and 10 kilometers, then for giving to payload some certain linear speed (for instance 100 km/sec) these rods should rotate at different angular velocity. It is easy to ascertain that the shorter rod should rotate 10 times faster to gain the same linear speed than the rod with more length. But the faster the rod rotates, the more difficult will be to “catch” the needed moment for releasing the payload from the rod for sending it towards some certain direction. If the rod is too short, then it has to rotate very quickly for gaining some certain linear speed and therefore it will be extremely difficult catching the needed moment for releasing the payload. Hence, too short rod can make problem for sending the payload to some certain direction in space especially at high velocities. So, based on payload’s needed velocity we should find rod’s desired, mi