Aucbvax.6139 fa.space utcsrgv!utzoo!decvax!ucbvax!space Wed Feb 10 04:10:18 1982 SPACE Digest V2 #103 >From OTA@S1-A Wed Feb 10 03:43:54 1982 SPACE Digest Volume 2 : Issue 103 Today's Topics: Re: half-time power from the moon possible private funding for Shuttle #5 Re: Horseshoe (and other) orbits Re: Re: sri-unix.707: Horseshoe Orbits orbital speed Orbital mechanix, please! Re: sri-unix.707: Horseshoe Orbits Re: Mooning Around Mooning Around... Mooning Around Politics of Space polar lunar solar power ---------------------------------------------------------------------- Date: Mon Feb 8 13:48:55 1982 To: Space at MIT-MC From: ucbvax!decvax!watmath!jcwinterton at Berkeley Subject: Re: half-time power from the moon Source-Info: From (or Sender) name not authenticated. I would expect that lunar power stations would go to low output every two weeks (have to use earthshine only?). ------------------------------ Date: 9 Feb 1982 0959-EST From: MPH at MIT-XX Subject: possible private funding for Shuttle #5 To: space at mc The February 12 issue of Science magazine states that the Space Transportation Company, a group of investment bankers and venture capitalists, is considering funding the fifth Shuttle. STC is considering raising one billion dollars privately, and then turning the shuttle over to NASA (or whomever is operating shuttles in 1986), in return for which STC would become the sole ticketing and marketing agent for all commercial and foreign users of the STS. ------- ------------------------------ From: MINSKY@MIT-AI Date: 02/09/82 12:20:37 MINSKY@MIT-AI 02/09/82 12:20:37 To: space at MIT-MC The lunar-polar 24 houd power station would be built on a mountain-top. It is a question of fact: is there a peak with continuous sunlight, through entire year? If not, how high a tower would it need? ------------------------------ Date: 9 Feb 1982 10:43 PST From: Ciccarelli at PARC-MAXC Subject: Re: Horseshoe (and other) orbits In-reply-to: OTA's message of 07 Feb 1982 0302-PST To: Space-Enthusiasts at MIT-MC cc: Ciccarelli @ PARC-MAXC About "horseshoe" orbits, actually about orbits in general... The higher orbit is not faster (higher *velocity*) but of higher *energy*. As the trailing moon (lower, faster, less energy) catches the leading moon (higher, slower, more energy) it takes some of the leading moon's energy, swapping orbits. It's counterintuitive -- higher energy does NOT imply higher orbital velocity. I dug up the formulas for your reference... --------------- The formula for orbital velocity (circular orbit approximation) is: V = V0 * SQRT( Earth radius / Orbit radius), where V0 = 7.86 KM/SEC ("Circular velocity at Earth's surface), Earth radius = 6400 KM (approx.), and SQRT is the Square-root operation (of course) You can check the formula for the three familiar orbit radii; calculate the velocity using the formula, then see that this velocity gives the right orbital period [distance = 2 * PI * Orbit radius; divide by velocity to get the period]. 1) near-earth: Orbit radius = Earth radius ==> V = V0 [gives 90 min. period] 2) geosynchronous: Orbit radius = 40,000 KM (approx.) [gives 24-hr period] 3) lunar: Orbit radius = 400,000 KM (approx.) [gives 28-day period] This also gives the expected result of V=0 at very great distances. --------------- The formula for orbit energy is: Total Energy = - (G * M1 * M2 / 2 * Orbit Radius), where G = Newton's gravitational constant, and M1, M2 = masses (i.e. Earth and satellite) Note that: 1) the total energy is negative (the physical interpretation is that the orbit is "bound", i.e. the satellite has less energy than that required to escape). 2) Orbit radius appears in the denominator again, thus the total energy will become greater (still negative, but closer to zero) as orbit radius increases. At very great distance, the energy goes to zero (as expected). [ Source: "Introductory Astronomy and Astrophysics", by Smith and Jacobs ] /John ------------------------------ Date: 9 Feb 1982 11:17 PST From: Lynn.ES at PARC-MAXC Subject: Re: Re: sri-unix.707: Horseshoe Orbits In-reply-to: ETC!dennis's message of Sun Feb 7 10:51:10 1982 To: Space-Enthusiasts at MIT-MC cc: Lynn.es Nice try on the orbital explanation, but it's unfortunately not right (even ignoring the ground speed business). Both linear velocity and angular velocity increase for satellites closer to the body they are orbiting. Take the moon (radius 238,000 miles, period 27+ days => 2200 mph, 0.04 rev/day) versus a low earth orbit satellite (radius 4000 miles, period 1.5 hrs => 17,000 mph, 16 rev/day). The angular velocity decreases with the 1.5 power of distance, the linear velocity decreases with the 0.5 power (square root) of distance. The actual explanation of why adding speed moves a satellite away from the body is this: With additional speed, the satellite tends to go in more of a straight line (has less time to fall toward the parent body), and increases its orbital distance. While increasing its distance, it is slowed by gravitation. It reaches equilibrium at a greater distance and a slower orbital speed than it originally had. This can be viewed another (equivalent) way: an orbiting body, given extra speed, has too much kinetic energy for that orbit, so it exchanges some of its kinetic energy for potential energy. The equilibrium is reached when the extra speed we gave it and some of its original speed are exchanged, ending up quite a bit higher and moving a little slower than originally. Point of view is important in understanding the name "horseshoe". Imagine two horseshoes, of slightly different size, mouth to mouth, on a plate. The plate spins quickly. As seen by a viewer on the plate, the satellite on the inner orbit is moving slowly counterclockwise along the smaller horseshoe, while the outer one is moving slowly clockwise on the larger horseshoe. The spinning of the plate represents the average rate of revolution of the two satellites, and so the viewer on the plate sees only the DIFFERENCE between a satellite's orbital speed and the average (plate's) speed. At encounter, we switch the sizes of the horseshoes, and the satellites (still seen from our spinning point of reference) seem to each reverse direction and traverse their (now slightly larger or smaller) respective horseshoes in the opposite directions. /Don Lynn ------------------------------ Date: 9 Feb 1982 21:51:13-EST From: csin!cjh at CCA-UNIX To: space at mit-mc Subject: orbital speed I suppose a lot of people will wake up on this one, but I might as well put in my nickel's worth. High orbits \are/ slower in linear velocity than low orbits. Local example (remember, earth orbits are measured from the surface, so add ca. 3900 miles to these figures): A satellite at LEO is ca. 150 miles up and has ca. 90-minute orbit; orbital velocity ca. 140 miles per minute. A satellite at GEO is ca. 22,300 miles up and has (by definition) a 24-hour orbit; orbital velocity ca. 57 miles per minute. The moon is around .25e6 miles up, orbits in 28+ days; orbital velocity ca. 19 miles per minute. Need more data? Start with Pluto being at 39 AU (earth-orbit radii) with a period of 200+ years. All of these figures are out of my head, but date from a grade-school infatuation with space and so are tolerably accurate. More precise figures are welcome. What happens when you add energy to an orbiting body is not that simple; the only way the body can maintain a stable orbit is by turning all that energy (and some of its own kinetic) into potential energy, i.e. take a higher orbit. What the shuttle is doing when it turns around and blasts in the direction it was going is throwing away enough KE that it can't keep a stable orbit above the Earth's surface; if you got rid of the atmosphere and dug a trench it could drop into a stable orbit below the net surface. C'mon, guys, even Brunner got this right (and used it to make an effective point in THE SHOCKWAVE RIDER). ------------------------------ Date: 9 February 1982 2232-EST (Tuesday) From: David.Smith at CMU-10A (C410DS30) To: space at mit-mc Subject: Orbital mechanix, please! Message-Id: <09FEB82 223233 DS30@CMU-10A> In fact, higher orbits are slower any way you want to measure. But due to the gravity well, they are still at a higher energy level. Consider: f = GMm/r^2 where f is the force exerted between two bodies, G is the gravitational constant, M is the mass of the primary, m the mass of the satellite, and r the radius between centers. Assume M >> m. For a circular orbit, we use f = ma (force, mass, acceleration) a = rw^2 (acceleration, radius, angular velocity) w = v/r (angular velocity, tangential velocity, radius) Equating gravitational force on the satellite with the force required to keep it in circular orbit, GMm/r^2 = mrw^2 = mv^2/r which produces w = sqrt( GM/r^3 ) v = sqrt( GM/r ) which clearly shows angular and tangential velocity dropping as radius rises. Low earth satellites travel at nearly 18,000 mph; geosynchronous satellites travel at around 6,000 mph; the moon travels at around 2,000 mph with respect to earth's center. Consider the task of moving a satellite from LEO to GEO. (I'll pull a few numbers out of my hat because I'm lazy, but the exact numbers aren't the point.) Starting at 18,000 mph at 150 miles up, you burn the rockets to accelerate it to 22000 mph. With more than circular velocity, the satellite climbs, trading speed for altitude, until it reaches apogee at geosynchronous height (around 23,000 miles) with 2000 mph. Since circular velocity there is 6000 mph, the satellite will drop back. It falls until it reaches 22000 mph at its next perigee, 150 miles up. At next apogee (23,000 miles, 2,000 mph), you burn the engines again to raise the speed to 6,000 mph. This raises the perigee to put the satellite into synchronous orbit. The satellite has gone from a 18,000 mph circular orbit to a 6,000 mph one purely by firing its rockets to increase speed. - David Smith ------------------------------ Date: 10 February 1982 01:27-EST From: Robert Elton Maas Subject: Re: sri-unix.707: Horseshoe Orbits To: HPLABS!MENLO70!UCBVAX!IHNSS!CBOSG!HARPO!CHICO!DUKE!PHS!DENNIS at MIT-MC cc: SPACE at MIT-MC You're mistaken (wrong). Under inverse-square law, such as gravity, higher orbits actually travel slower, not faster! If energy is added to a satellite, it rises into a higher orbit, but more knetic energy is converted into potential energy than was applied to make it rise to the new orbit and it has less knetic energy (but much more potential energy) than when it was lower. Earth-based common sense, if add energy an object travels faster, doesn't apply in orbital mechanics; add energy and the object ends up in a new slower orbit. Here's an example if you don't believe me. The moon is about 225,000 miles from Earth, while geosynchronous satellites are about 25,000 miles from Earth. Thus the moon has to travel about 10 times as far to get around, but takes about 29 times as long to do it because it is traveling only about a third as fast in linear velocity. ------------------------------ Date: Tue Feb 9 23:02:53 1982 To: Space at MIT-MC From: ucbvax!decvax!watmath!bstempleton at Berkeley Subject: Re: Mooning Around Source-Info: From (or Sender) name not authenticated. Rick suggests that a geosynch sps would be in shadow half the time. where do you get this from? If in shadow at all, it would only be for a limited time due to bad design. also, projecting to a station in lunar 'geo'synch orbit is a little silly, if you think about what the distance of this orbit is. (Hint: name an object that stays fixed in the lunar sky) ------------------------------ Date: Wed Feb 10 00:26:45 1982 To: Space at MIT-MC From: ucbvax!decvax!watmath!pcmcgeer at Berkeley Subject: Mooning Around... Source-Info: From (or Sender) name not authenticated. Oops, Brad's right. I goofed. The moon does rotate with respect to the sun, but unfortunately the postion of a satellite that could take advantage of that would be in the L5 position - rather further away than practicable. However, I'm not so sanguine about solving the problem of half time shadow by better design. The angular diameter of the Earth as seen by an 35,000 KM above the equator position is quite enough - comfortably enough - to blot out the Sun. Remember, the Moon is large enough to cover the Sun, and it's 400,000 KM away. Admittedly, the Earth wouldn't block the sun for 12 hours out of every day - six is actually more near correct. A solution would be to put two SPS in high earth orbit, but this involves taking up not one but two geostationary slots, which are pretty valuable. There are only 90 all told, since there has to be a 4 degree separation between any two satellites due to possible interference. Further, a quick glance at a globe will convince the military that one of the SPSs will be over hostile territory permanently. Rick. ------------------------------ Date: Tue Feb 9 20:35:00 1982 To: Space at MIT-MC From: ucbvax!decvax!watmath!pcmcgeer at Berkeley Subject: Mooning Around Source-Info: From (or Sender) name not authenticated. The Lunar SPS would, of course, deliver power only for half the time. Of course, this could be said about a geostationary SPS, since it would be in the shadow of the earth for 12 hours out of 24. The Lunar SPS proposal has some merits, though : 1) We could keep it stable. Precisely how would we keep a free-floating SPS, several square kilometers, from tumbling about a planar axis? And if we could, precisely how do we stress something like that? These really are mundane questions, but do we know how to do these things? A lunar SPS, on the other hand, has no such problems. It's merely a large, flat plain of collectors. We transmit from the surface (probably Mare Crisium) to a sattelite in Geosynch orbit above the moon, which transmits to a buddy in High Earth Orbit. The principal advantage is no large, freestanding structure; 2) The materials are there, or at least we hope they are. Siliates are, for sure. 3) (A cheap advantage, certainly) There would probably be much more public support for a Lunar base than for one in High Earth Orbit. The Moon has always had an emotional appeal that HEO doesn't share. The space program, like all government programs, depend in the long run on their public support; therefore, the chances are better that we will be able to build the Lunar SPS, if it's technically feasible; Which it might not be. The power-half-the-time problem can be solved by putting another SPS over on Farside. Another, better question, which I haven't got the foggiest idea about, is how we transmit the power - even a laser spreads somewhat over 400,000 KM, and the satellites orbiting moon and the earth, the ends of this game of celestial pitch - and - catch, will have a velocity difference between them. This is further complicated by the 3-sec feedback loop. To another question - yes, the Moon does orbit in the plane of the ecliptic, or near enough as to make no difference. This fact, plus the low tug-of-war ratio for the moon (about .46, as against an empirical minimum of 30.00 for a true satellite, led Asimov to speculate that the Earth-Moon system is in fact a binary planet system.. Cheers, Rick. ------------------------------ Date: 10 February 1982 04:39-EST From: Jerry E. Pournelle Subject: Politics of Space To: Ward at USC-ISIF cc: SPACE at MIT-MC What's really needed is a skilled politician who'll undertake to become the champion for space; someone to lead what is, after all, the most fundamental revolution since the evoluton of lungs. At the L-5 Convention (Los Angeles Airport Hyatt, April 2-4 1982) we're going to try to generate some strategy; and we might even have the politicians to help out. ------------------------------ Date: 10 February 1982 04:41-EST From: Jerry E. Pournelle Subject: polar lunar solar power To: ucbvax!decvax!duke!cjp at UCB-C70 cc: SPACE at MIT-MC Those really interested in direct power from the moon ought to come to the L-5 Convention and hear Criswell on the subject. Dave Criswell used to have the lunar rocks, and he is a lunar fanatic. ------------------------------ End of SPACE Digest ******************* ----------------------------------------------------------------- gopher://quux.org/ conversion by John Goerzen of http://communication.ucsd.edu/A-News/ This Usenet Oldnews Archive article may be copied and distributed freely, provided: 1. There is no money collected for the text(s) of the articles. 2. The following notice remains appended to each copy: The Usenet Oldnews Archive: Compilation Copyright (C) 1981, 1996 Bruce Jones, Henry Spencer, David Wiseman.