Moon & Mars Orbiting Spinning Tether Transport - Tethers Unlimited

Tethers Unlimited, Inc.Cislunar Tether Transportapogee altitude h a,0 = 411.8 kmeccentricity e 0 = 0.0575After catching the payload, the central facilityclimbs up the tether to the counterbalance mass,changing the rotation rate to:• adjusted rotation rate ω 0 = 0.00929rad/s• adjusted tip velocity V t,2 = 1.645 km/sPayload Delivery:• drop-off altitude h = 1 km(top of a lunar mountain)• velocity w.r.t. surface v = 0 m/sPayloadfromEarthOrbit priorto catchOrbit aftercatchLunavator ª Orbit: Polar vs. EquatorialFigure 9. Lunavatorª orbits before and afterIn order to provide the most consistent transfer payload capture.scenarios, it is desirable to place the Lunavator ªmay provide a means of stabilizing the orbit ofinto either a polar or equatorial lunar orbit. Each the Lunavator ª without requiring expenditure ofchoice has relative advantages and drawbacks, propellant. Tether reeling can add or removebut both are viable options.energy from a tetherÕs orbit by working against1Êm/s will reduce the eccentricity of theFortunately, the techniques of orbital Lunavator ª Õs orbit by 0.0011 per day, whichmodification using tether reeling, proposed by should be more than enough to counteract theMart’nez-S‡nchez and Gavit 7 and by Landis 10Equatorial Lunar OrbitThe primary advantage of an equatorial orbitfor the Lunavator ª is that equatorial lunar orbitsare relatively stable. An equatorial Lunavator ª ,however, would only be able to service traffic tobases on the lunar equator. Because the lunarequatorial plane is tilted with respect to theEarthÕs equatorial plane, a payload boosted bythe Earth-orbit tether facility will require a ∆ Vmaneuver to bend its trajectory into the lunarequatorial plane. For most transfer opportunities,this correction can be accomplished by a smallrocket thrust on the order of 25 m/s.the non-linearity of a gravitational field. Thebasic concept of orbital modification using tetherreeling is illustrated in Figure 10. When a tetheris near the apoapsis of its orbit, the tidal forceson the tether are low. When it is near periapsis,the tidal forces on the tether are high. If it isdesired to reduce the eccentricity of the tetherÕsorbit, then the tether can be reeled in when it isnear apoapsis, under low tension, and thenallowed to unreel under higher tension when it isat periapsis. Since the tidal forces that cause thetether tension are, to first order, proportional tothe inverse radial distance cubed, more energy isdissipated as the tether is unreeled at periapsisPolar Lunar Orbitthan is restored to the tetherÕs orbit when it isA polar orbit would be preferable for the reeled back in at apoapsis. Thus, energy isLunavator ª for several reasons. First, direct removed from the orbit. Conversely, energy cantransfers to polar lunar trajectories are possible be added to the orbit by reeling in at periapsiswith little or no propellant expenditure required. and reeling out at apoapsis. Although energy isSecond, because a polar lunar orbit will remain removed (or added) to the orbit by the reelingoriented in the same direction while the Moon maneuvers, the orbital angular momentum of th erotates inside of it, a polar Lunavator ª could orbit does not change. Thus the eccentricity of theservice traffic to any point on the surface of the orbit can be changed.Moon, including the potentially ice-rich lunarpoles. Low polar lunar orbits, however, are The theories developed in references 7 and 10unstable. The odd-harmonics of the MoonÕs assumed that the tether is hanging (rotating oncepotential cause a circular, low polar orbit to per orbit). Because the Lunavator ª will bebecome eccentric. Eventually, the eccentricity rotating several times per orbit, we havebecomes large enough that the perilune is at orbelow the lunar surface. For the 178 km circularextended the theory to apply to rapidly rotatingtethers. 8 Using a tether reeling scheme in whichorbit, the rate of eccentricity growth is the tether is reeled in and out once per orbit asapproximately 0.00088 per day.shown in Figure 10, we find that a reeling rate of9