Moon & Mars Orbiting Spinning Tether Transport - Tethers Unlimited

Rapid Interplanetary Tether Transport SystemsIAF-99-A.5.10strength of 4 GPa, and a density of 0.97 g/cc. Witha safety factor of 3, the materialÕs criticalvelocity is 1.66 km/s. Using Eqn. (1), anoptimally-tapered Spectra¨ tether capable ofsustaining a tip velocity of 3.1 km/s would requirea mass of over 100 times the payload mass.While this might be technically feasible forvery small payloads, such a large tether massprobably would not be economically competitivewith rocket technologies. In the future, veryhigh strength materials such as ÒbuckytubeÓyarns may become available with tensilestrengths that will make a 3 km/s tetherfeasible; however, we will show that a differentapproach to the system architecture can utilizecurrently available materials to perform themission with reasonable mass requirements.The tether mass is reduced to reasonablelevels if the ∆V/V c ratio can be reduced to levelsnear unity or lower. In the Cislunar system, wecan do this by placing the Earth-orbit tether intoan elliptical orbit and arranging its rotation sothat, at perigee, the tether tip can rendezvouswith and capture the payload, imparting a1.6Êkm/s ∆V to the payload. Then, when thetether returns to perigee, it can toss the payloadahead of it, giving it an additional 1.5 km/s ∆V.By breaking the 3.1 km/s ∆V up into two smallerboost operations with ∆V/V c < 1, we can reducethe required tether mass considerably. Thedrawback to this method is that it requires achallenging rendezvous between the payload andthe tether tip; nonetheless, the mass advantageswill likely outweigh that added risk.Behavior of Elliptical Earth OrbitsOne of the major challenges to designing aworkable tether transportation system usingelliptical orbits is motion of the orbit due to th eoblateness of the Earth. The EarthÕs oblatenesswill cause the plane of an orbit to regress relativeto the EarthÕs spin axis at a rate equal to: 9Ω=− ˙ 3 2J Re n cos( i)2 2 p (3)2And the line of apsides (ie. the longitude of theperigee) to precess or regress relative to theorbitÕs nodes at a rate equal to:232ω ˙ = J Re 2n ( 5cos i−1)24 p(4)In equations (3) and (4), n is the Òmean meanmotionÓ of the orbit, defined asnJ R ee= µ 2⎡2 2 ⎤− −e− ia⎢1 3 3 21 ( 1 3cos )2⎣ 4 p⎥. (5)⎦For an equatorial orbit, the nodes are undefined,but we can calculate the rate of apsidalprecession relative to inertial space as the sum˙ Ω+ω ˙ of the nodal and apsidal rates given byEqs. (3) and (4).In order to make the orbital mechanics of theCislunar Tether Transport System manageable,we place two constraints on our system design:• First, the orbits of the tether facility will beequatorial, so that i=0 and the nodalregression given by Eq. (3) will not be an issue.• Second, the tether system will throw thepayload into a lunar transfer trajectory thatis in the equatorial plane. This means that i tcan perform transfer operations when theMoon is crossing either the ascending ordescending node of its orbit.Nonetheless, we still have the problem ofprecession of the line of apsides of an orbit. If thetether orbits are circular, this is not an issue, butit is an issue for systems that use elliptical orbits.In an elliptical orbit system we wish to performall catch and throw operations at or near perigee.As illustrated in Figure 3, for the payload toreach the MoonÕs radius at the time when theMoon crosses the EarthÕs equatorial plane, thepayload must be injected into an orbit that has aline of apsides at some small angle λ from theline through the MoonÕs nodes. If the orbitLunar TransferTrajectoryTether OrbitλTether Line ofApsidesMoon'sOrbitαMoon'sNodeFigure 3. Geometry of the tether orbit and theMoonÕs orbit.4