Moon & Mars Orbiting Spinning Tether Transport - Tethers Unlimited

Tethers Unlimited, Inc.Appendix K: Facility Reboost Studythese methods in more detail.Variation of Thrust Power:This method is relatively obvious, and easiest to perform in theory. Thrusting while the tether is nearperigee boosts the apogee but not the perigee. However, this method would require the system tooperate at higher thrust levels at perigee, which is undesirable considering the already high-power levelof 1 MW that has been baselined.Tether Reeling:A second method of adjusting the orbit shape would be to perform tether reeling maneuvers to addenergy to the orbit without adding orbital momentum, thus increasing the orbit eccentricity. 1 To boost theorbit eccentricity, the tether system would reel in the tether while it is near perigee and the gravitygradient forces are high, and allow it to deploy when it is at apogee and the gravity gradient forces arelow.In order to achieve the desired final eccentricity of 0.387, the tether reeling must add eccentricity tothe orbit at a rate of approximately 2.2e-4 per day. If the distance from the tether facility’s control stationto the center of mass of the tether is L, and the control station reels the tether in and out according to aprogram ∆L(t), the rate of eccentricity change is approximated by:ddt e3 µ m=⎡a ⎣⎢ m⎤⎧orbt Tt Tt − t⎛orb−Tt ⎞ ⎫⎨2cos( ω )sin( ω )cos( ω ) sin( ω ) 1 3 sin ( ω ) L L t⎦⎥ ⎩ ⎝⎠ ⎬⎭ [ +∆ ( )]. (1)27 212 2 2where µ = GM e , a is the orbit semimajor axis, ω t is the tether rotation rate, ω orb is the orbital rate, m is thetotal mass of the tether system, and m 12 is the reduced mass of the system. Integrating this equation overan orbit, we find that if the tether control station reels the tether in and out sinusoidally once per orbit,with an amplitude of 1 km, the rate of eccentricity change is approximately 2.2e-4. The peak reeling ratewould be approximately 0.7 m/s. The tether tension at the control station end of the tether isapproximately 157,000 N. The power required to reel the tether in during perigee thus would be 110 kW.Although this power could be recovered when the tether is unreeled at apogee, this scheme would stillrequire the tether facility to process a higher level of power during the perigee passage.Thrust Vector VariationThe third method takes advantage of the fact that the tether is rotating, and thus the direction of theelectrodynamic thrust varies relative to the direction of motion. Rather than always thrusting when thetether is near a local vertical orientation, the tether boost facility can instead vary its current to applythrust along the –r direction on its inbound trajectory, along the velocity vector when the system is nearperigee, and along the +r direction on its outbound trajectory, as illustrated in Figure 8. This adds energyto the orbit without adding as much orbital momentum. The green plot in Figure 7 shows the increase ofeccentricity with the semimajor axis using this thrusting program. The variation of eccentricity with thesemimajor axis is increased to e ∝ 6.7e-8 a, which is more than enough to achieve the desired final orbiteccentricity. Because this method does not require additional power capability nor tether reelingcapability, it is the preferred method for tuning the rates of eccentricity and semimajor axis boosting toachieve the desired final orbit.1. Hoyt, R. P., “Maintenance Of Rotating Tether Orbits Using Tether Reeling”, Appendix F in Cislunar TetherTransport System, Tethers Unlimited, Inc. Final Report on NASA Institute for Advanced Concepts Contract NIAC-07600-011.K-8