Orbital modifications using forced tether-length variations

Abstract

It is shown that once-per-orbit modulations of the length of an orbiting tether can be used to modify the eccentricity, energy, and line of apsides orientation of its center of mass while maintaining a constant angular momentum and orbital parameter. Appropriate length variation laws are developed and the effects are quantified and interpreted. Several applications are discussed, including modifications to the orbit of a space station, reduction by 30% of the A V to launch a satellite to 12 h orbit, and the relocation of the apogee for observation satellites. HE common observation of children pumping themselves up at a swing by rhythmically shifting their legs' weight has prompted speculation about the possibility of performing fuelless orbital changes using conformable spacecraft.1'2 Particularly intriguing are the possibilities opened by the advent of ultralong, thin tethers that can be conveniently reeled in and out from a satellite while carrying another body at its end. Obviously, any such reel-unreel operation will set up Coriolis forces that will induce in-plane libration of the tether. To conserve angular momentum, equal and opposite variations will appear in the center of mass orbital angular momentum. If these can be made to resonate with the orbital motion, it is conceivable that the system could bootstrap itself and either increase or decrease the orbital energy without setting up unbounded librations (and getting wrapped up in the process). A clear limitation of any such scheme is the need to supply mechanical power onboard. Another one is the impossibility of modifying the overall angular momentum in this manner, since operation in a central force field is assumed and no internal angular momentum is allowed to accumulate. The question of whether the center of mass motion can be affected by means of forces internal to the mass-tether system is more subtle; although it is true that the acceleration of the center of mass is due to only the net external force, nonrigid changes to the configuration of the system can affect the net external force for a given center of mass location and hence can affect the center of mass motion. In this paper we show how this can be accomplished using a rewindable tether. The practical application of the concept to several space transportation missions is also discussed. The analysis presented here is restricted to the small oscillation of a dumbbell satellite whose cable length is assumed fully controllable by means of powered winches on board one or both of the connected masses.