Moon & Mars Orbiting Spinning Tether Transport - Tethers Unlimited

(5) vinf = sqrt(vp^2 - 2*mu/rp)(6) vp^2 = vinf^2 + 2*mu/rpwhere mu is the gravitational parameter of the planet. If the period of rotation of the tether isarranged so that it is posigrade and vertical at periapsis when the tether separates, the tip velocity ofthe tether will be subtracted from the lower payload and added to the upper one. As can be seen byinspection of equation (1), addition of a small number to a number that is squared has adisproportionate effect. In this case, the outgoing payload acquires a vinf of(7) vinf^2 = (vp+vtip)^2 - 2*mu/rpThe velocity of the lower payload is reduced. If vp^2 is close to -2*mu/rp, then vinf becomesimaginary, which is to say that the energy of the orbit has become negative with respect to infinity.The lower payload is thus captured. Again, by inspection, one sees that one can produce this stateof affairs by making rp small enough. One should note that the payloads are not released preciselyat rp, but are lower or higher due to the length of the tether. Unless the tether length is a significantfraction of the Jovian radius, this can be ignored for first order work. In keeping with the 2001theme of this conference, Gerald Nordley studied a combined Jupiter/Pluto mission with a personalcomputer model based on the above and got the following results.Table 1: Dual Payload Tether Jupiter/Pluto Performancetip Jupiter P/L Pluto transfervel. orbit per. injection vel coast timem/s days km/s years400. 1473.82 21.22 10.24500. 227.23 21.73 9.72600. 101.55 22.21 9.28700. 60.36 22.67 8.90800. 41.09 23.11 8.58900. 30.28 23.53 8.301000. 23.51 23.94 8.04*Based on near-minimum encounter velocity of 5.63 km/s, a perijove of 2 RJ, Pluto at 31 AU attime of encounter, a zero flight path angle leaving Jupiter, and no encounters with monolithsAt 2 RJ, the velocity of the incoming tethered system reaches about 42.5 km/s. With a 1 km/sincrease in this velocity for the upper "Pluto" payload, the payload reaches a hyperbolic excessvelocity with respect to Jupiter of 10.9 km/s, almost double what it had as it entered Jupiter'sgravity field. If, for simplicity, this velocity is added in parallel to Jupiter's orbital velocity, onegets a periapsis velocity for the Pluto transfer orbit of 23.94 km/s. Using the time of flightequations in Bate for periapsis to a given radius, one gets the coast times in the final column.Strictly speaking, this transfer time is for the approximate distance from the sun of Pluto in some14 years; no effort was made to work out the phasing or calculate an actual launch windows.Initial comparisons with a rough model of an equivalent rocket mission yielded roughlycomparable masses, however improvements in tether material strength and synergistic use of thetether in an electromagnetic mode for Jupiter orbit propulsion may make this an attractive option.13