Moon & Mars Orbiting Spinning Tether Transport - Tethers Unlimited

Rapid Interplanetary Tether Transport SystemsIAF-99-A.5.1040000y(km)200000-20000-40000Launch from Earthz(km)400020000-2000Launch from EarthClosest Approach to Moon-60000-80000-400000Closest Approach to Moon-300000-200000x(km)-1000000100000Figure 11. Transfer of payload to lunar equatorialtrajectory, projected onto the True Earth Equator.100000Lunar Closest ApproachLaunch from Earth-4000-6000-8000-10000-100000Payload CrossesLunar Equator0100000 200000x(km)300000400000Figure 13. Projection of payload transfer onto Lunarx-z plane (Moon centered frame).y(km)0-1000002.01.5-200000-1000000100000 200000x(km)300000400000Figure 12. Projection of payload transfer onto LunarEquatorial Plane (Moon centered frame).approach to the Moon. Figure 14, which plots theMoon-relative velocity of the payload, showsthat the payloadÕs velocity at the time of lunarequatorial crossing is about 925 m/s. However, aplot of the declination of the payloadÕs velocitywith respect to the lunar equator, shown in Figure15, reveals that that the declination of theMoon-relative velocity vector is only a fewdegrees, much less than the 18¡-29¡ valuepredicted by a simple zero-patched conicanalysis; the Moon's (or Sun's) gravity has bentthe velocity vector closer to the lunar orbit plane.At the time when the payloadÕs trajectorycrosses the lunar equator, the declination of theincoming velocity vector is only 1.52¡. Thisdynamical situation permits us to bend t h eapproach trajectory into the lunar equator with avery small amount of impulse supplied by thespacecraft propulsion system. In the case shownhere, the amount of ∆V required is only 24.5 m/s,applied about 10 hours before closest approach tothe Moon, as the spacecraft crosses the lunarequator.Transfer to Polar Lunar TrajectoriesFigure 16 shows a payload transfer targetedto a polar lunar trajectory with an ascending node(with respect to the lunar prime meridian) ofÐ100.95¡. This particular trajectory is a Type I IV(km/s)1.00.50.0050Spacecraft Crosses Lunar Equator(V = 0.925 km/s)Time (hrs)100Figure 14. Moon-relative velocity of spacecraft.DecV(deg)5.04.54.03.53.02.52.01.51.00.50.0050Spacecraft Crosses Lunar Equator(Declination of Velocity = 1°.52)Time (hrs)Figure 15. Declination of Moon-relative velocityvector with respect to Lunar Equator.Earth Equatorial y (km)40000200000-20000-40000-60000-80000-100000-400000One-Hour Time TicksLunar Closest Approach-300000-200000100-100000Earth Equatorial x (km)Initial Argumentof Perigee = 11°.930y(km)150150100000Figure 16. Time history of an Earth-Moon transfertargeted to a polar lunar trajectory.14