karn@allegra.UUCP (Phil Karn) (12/22/83)
Someone mentioned the relative delta-vee requirements needed to get to geostationary orbit as compared to to the moon. I did some research and calculations to get some real numbers. Apollo 11 (a representative moon trip) started with a 192 x 190.6 km parking orbit. Trans-lunar injection required 3182 m/sec from the S-IVB, while lunar orbit insertion required only 889.2 m/sec. However, landing required 2,065 m/sec and liftoff 1,850; you can see the advantage of the separate LM approach. The return to earth required 999.4 m/sec. Here's the numbers for a typical geostationary satellite launch from the shuttle. Assume a 28.5 deg inclination 300 x 300 km parking orbit. The PAM (payload assist module) perigee kick motor produces about 2579.7 m/sec to put the spacecraft into a 23.5 deg elliptical transfer orbit. About 170 m/sec of this burn is used to reduce the inclination by about 5 degrees. (I don't know why they do this, it should be more efficient to change the plane out at apogee.) At one of the following apogees, the kick motor on the satellite itself produces 1879 m/sec. Most of this circularizes the orbit at geostationary altitude, while 231.6 m/sec goes toward making the inclination zero. Now when comparing these figures you have to take into account the different initial parking orbits, but this is enough to give the general idea. Note the big difference, though, between getting to lunar orbit and getting to the lunar surface. 192 km LEO to lunar orbit: 4071.2 m/sec 192 km LEO to lunar surface: 6136.2 m/sec 300 km LEO to GEO: 4458.7 m/sec Phil
dietz%usc-cse%USC-ECL%SRI-NIC@sri-unix.UUCP (12/26/83)
Of course I meant going to lunar orbit, not to the lunar surface. One figure you didn't mention is the delta-vee for returning from GEO. Retrofire to put you into an atmosphere skimming orbit for aerobraking will take about as much delta-vee as the orbit circularization burn (maybe a little more). Perhaps a better (albeit more time consuming) maneuver would be to boost into an elongated orbit that passed near the moon, which would then put the vehicle onto an earth-intersecting orbit. I read somewhere that someone (Krafft Ehricke?) has proposed landing payloads on the moon by sliding them on a flat strip of lunar soil (sifted to remove rocks). Energy would be dissipated by heating and accelerating the loose sand-like material, which would be smoothed over before the next landing. Orbital velocity at the lunar surface is around 1650 m/sec, so this sounds semi-plausible. Deceleration at 10 gee's would mean a strip 14 km long. A more refined scheme could use a solid aluminum strip for magnetic flight. The incoming vehicle would have magnets for repulsive magnetic levitation. The vehicle could be decelerated by eddy currents in the strip, by coils in the strip (which could deliver usable power to a launch system) or by shooting gas derived from lunar soil (oxygen or argon) at the front of the vehicle. After being decelerated to less than 100 m/sec the vehicle would use wheels. Such a scheme could also make rocket lift-off from the lunar surface more efficient by eliminating the need for the rocket to support the mass of the vehicle against lunar gravity -- all thrust would go into increasing the orbital velocity of the vehicle. Of course, the mass of the magnets would probably negate any advantage gained.