Moon & Mars Orbiting Spinning Tether Transport - Tethers Unlimited

Rapid Interplanetary Tether Transport SystemsIAF-99-A.5.10tethers. 12 Using a tether reeling scheme in whichthe tether is reeled in and out once per orbit asshown in Figure 9, we find that a reeling rate of1Êm/s will reduce the eccentricity of theLunavator ª Õs orbit by 0.0011 per day, whichshould be more than enough to counteract theeffects of lunar perturbations to the tetherÕs orbit.Thus tether reeling may provide a means ofstabilizing the orbit of a polar Lunavator ªwithout requiring propellant expenditure. Thistether reeling, however, would add additionalcomplexity to the system.Cislunar System SimulationsTether System ModelingIn order to verify the design of the orbitaldynamics of the Cislunar Tether TransportSystem, we have developed a numericalsimulation called ÒTetherSimÓ that includes:• The 3D orbital mechanics of the tethers andpayloads in the Earth-Moon system, includingthe effects of Earth oblateness, using Runge-Kutta integration of CowellÕs method.• Modeling of the dynamical behavior of thetethers, using a bead-and-spring model similarto that developed by Kim and Vadali. 14• Modeling of the electrodynamic interaction ofthe Earth-orbit tether with the ionosphere.Using this simulation tool, we have developed ascenario for transferring a payload from a circularlow-LEO orbit to the surface of the Moon usingthe tether system designs outlined above. Wehave found that for an average transfer scenario,mid-course trajectory corrections of approximately25 m/s are necessary to target thepayload into the desired polar lunar trajectory toLunar Transfer OrbitC 3 = - 1.9 to -1.2 km 2 /s 2In Earth Equatorial PlaneEarthEquatorial PlaneLunar OrbitInclined 18.3° - 28.6°to Earth EquatorLunar Swingby Radius5000 to 10000 kmOne-Month Lunar Return OrbitIn Lunar EquatorNote: Apogee > Lunar OrbitPerigee < Lunar OrbitFigure 10. Schematic of one-month Òresonance-hopÓtransfer to place payload in lunar equator withoutusing propellant.enable rendezvous with the Lunavator ª . Asimulation of a transfer from LEO to the surface ofthe Moon can be viewed at www.tethers.com.Targeting the Lunar TransferIn addition to the modeling conducted withTetherSim, we have also conducted a study of theEarth-Moon transfer to verify that the payloadcan be targeted to arrive at the Moon in t h eproper plane to rendezvous with the Lunavator ª .This study was performed with the MAESTROcode, 15 which includes the effects of luni-solarperturbations as well as the oblateness of theEarth. In this work we studied targeting to bothequatorial and polar lunar trajectories.Transfer to Equatorial Lunar TrajectoriesTransfer of a payload from an equatorialEarth trajectory to an equatorial lunar trajectorycan be achieved without propellant expenditure,but this requires use of a one-month ÒresonancehopÓ transfer, as illustrated in Figure 10. In aresonance hop maneuver, the payload is sent on atrajectory that passes the Moon in such a waythat the lunar gravitational field slingshots thepayloadÕs orbit into a one-month Earth orbit thatreturns to the Moon in the lunar equatorial plane.Using MAESTRO, we have developed a lunartransfer scenario that achieves this maneuver.In order to avoid the one-month transfer time,we can instead use a small impulsive thrust asthe payload crosses the lunar equator to bend itstrajectory into the equatorial plane. A patchedconicanalysis of such a transfer predicts thatsuch a maneuver would require 98 to 135 m/s of∆V. However, our numerical simulations of thetransfer revealed that under most conditions,luni-solar perturbations of the payloadÕstrajectory will perform much of the neededbending for us, and the velocity impulse needed toplace the payload in a lunar equatorial trajectoryis only about 25 m/s. Figure 11 shows the timehistoryof a transfer of a payload from the Earthorbittether boost facility to the Moon, projectedonto the EarthÕs equatorial plane.Figure 12 shows this same transfer, projectedonto the lunar equatorial plane in a Mooncentered, rotating frame, with the x-axis pointingat the Earth. The motion of the payload relativeto the lunar equator can be observed in Figure 13,which shows the trajectory projected onto thelunar x-z plane. The payload crosses the lunarequator approximately 10 hours before its closest13