Moon & Mars Orbiting Spinning Tether Transport - Tethers Unlimited

Tethers Unlimited, Inc.Appendix K: Facility Reboost StudyAppendix KTETHER FACILITY REBOOSTRob HoytTethers Unlimited, Inc.IntroductionA key factor in the economic viability of a Tether Boost Facility will be the frequency with which thefacility can boost payloads. The throughput capacity of a tether facility will be determined largely by thetime required to restore the facility’s orbit after each payload boost operation. In this document wepresent analytical methods for calculating the changes in a tether facility’s orbit due to a boost operation,and use numerical simulation to estimate the time required to reboost the facility orbit using electrodynamictether propulsion.Changes In Momentum-Exchange Tether Facility Orbit:When the facility catches and tosses a payload, it imparts a fraction of its orbital energy andmomentum to the payload, and thus its orbit is lowered. In this section we present a brief summary of ananalytical method for calculating the facility orbit changes. This method assumes that the orbits areKeplerian.Useful equations for calculating the semimajor axis and eccentricity of an orbit from the velocity andradius at perigee or apogee are:Semimajor Axis:Eccentricity:2⎡2V ⎤a = ⎢ −⎣ r µe⎥⎦re =± ( − )a−11 , where sign is (+) for values calculated at perigee, (2)and (–) for apogeeWhen the tether boost facility and payload rendezvous, the tether facility has a center of mass radiusr facility,0 and velocity V facility,0 , and the payload has radius and velocity r payload,0 & V payload,0 .. In calculatingthe facility position and velocity, one must account for the tether. The Tether Boost Facility will use atapered tether to minimize the tether’s mass; the location of the tether’s center-of-mass (COM) relative tothe facility is computed numerically.Facility+Payload Orbit After Payload Acquisition:After catching the payload, the new system COM radius and velocity are:(1)rCOM,1=r, 0( M + M )+ r, 0MM + M + Mfacility facility tether payload payloadfacility tether payload(3)VCOM,1V, 0( M + M )+ V, 0M=M + M + Mfacility facility tether payload payloadfacility tether payloadand we use Eqns. (1) & (2) to calculate the new semimajor axis a 1 and eccentricity e 1 ., (4)Tether System Tip VelocityWhen the facility catches the payload, the rotational inertia of the system is conserved, and thus theangular velocity ω remains constant. However, the COM of the system shifts closer to the payload end ofthe tether when the mass of the payload is added to the system. Thus the tip velocity of the systemdecreases. The new velocity of the tether tip relative to the system’s COM can be estimated as:V= ω L , (5)tip,1 1K-1