Moon & Mars Orbiting Spinning Tether Transport - Tethers Unlimited

Rapid Interplanetary Tether Transport SystemsIAF-99-A.5.10injected into an elliptical, equatorial Earth-orbitwith an apogee that just reaches the MoonÕsorbital radius will have a C 3 relative to theMoon of approximately 0.72 km 2 /s 2 . For a lunartransfer trajectory with a closest-approachaltitude of several hundred kilometers, thepayload will have a velocity of approximately2.3 km/s at perilune. As a result, it would bemoving too slowly to rendezvous with the uppertip of Moravec lunar Skyhook, which will havea tip velocity of 2.9 km/s at the top of itsrotation. Consequently, the design of the lunartether system must be modified to permit a tetherorbiting the Moon at approximately 1.5 km/s tocatch a payload to at perilune when thepayloadÕs velocity is approximately 2.3 km/s,then increase both the tether length and theangular velocity so that the payload can be setdown on the surface of the Moon with zerovelocity relative to the surface. Simply reelingthe tether in or out from a central facility willnot suffice, because reeling out the tether willcause the rotation rate to decrease due toconservation of angular momentum.A method that can enable the tether to catcha payload and then increase the tether rotationrate while lowering the payload is illustrated inFigure 6. The ÒLunavator ª Ó tether system iscomposed of a long tether, a counterbalance massat one end, and a central facility that has thecapability to climb up or down the tether.Initially, the facility would locate itself nearthe center of the tether, and the system wouldrotate slowly around the center-of-mass of thesystem, which would be located roughly halfwaybetween the facility and the counterbalancemass. The facility could then capture an inboundpayload at its perilune. The facility would thenuse energy from solar cells or other power supplyto climb up the tether towards the counterbalancemass. The center-of-mass of the system willremain at the same altitude, but the distancefrom the tether tip to the center-of-mass willincrease, and conservation of angular momentumwill cause the angular velocity of the system toincrease as the facility mass moves closer to thecenter-of-mass.AnalysisA first-order design for the Lunavator ª can beobtained by calculating the shift in the systemÕscenter-of-mass as the central facility changes itsposition along the tether. We begin by specifyingthe payload mass, the counterbalance mass, thefacility mass, and the tether length. Therequired tether mass cannot be calculated simplyby using MoravecÕs tapered tether mass equation,because that equation was derived for a freespacetether. The Lunavator ª must support notonly the forces due to centripetal acceleration ofthe payload and tether masses, but also the tidalforces due to the MoonÕs gravity. The equationsfor the tether mass with gravity-gradient forcesincluded are not analytically integrable, so thetether mass must be calculated numerically.Prior to capture of the payload, the distancefrom the counterbalance mass to the center-ofmassof the tether system isMLf f+ MLt cm,tLcm,0=, (15)Mc + Mf + Mtwhere L f is the distance from the counterbalanceto the facility and L cm,t is the distance from thecounterbalance to the center-of-mass of thetether. L cm,t must be calculated numerically for atapered tether.If the Lunavator ª is initially in a circularorbit with radius a 0 , it will have a center-ofmassvelocity ofmvcm,0= µ . (16)a0At the top of the tether swing, it can capturea payload from a perilune radius ofrp = a0 + ( Lt − Lcm, 0). (17)A payload sent from Earth on a near-minimumenergy transfer will have a C 3,m of approximately0.72 km 2 /s 2 . Its perilune velocity will thus bevp=2µm+ C3, m. (18)a + ( L − L )0 t cm,0In order for the tether tipÕs total velocity tomatch the payload velocity at rendezvous, thevelocity of the tether tip relative to the center ofmass must bev = v − v , (19)t, 0 p cm,0and the angular velocity of the tether systemwill bevt,0ω t , 0= . (20)L − Ltcm,010