Analysis and Design For No-SpinTethered Satellite Retrieval

Abstract

T ETHERED satellites are composed of two or more orbiting bodies connected by light, flexible members known as tethers. The study of tethered satellites began with Tsilokovsky in 1895 and was taken up by Artsutanov in the 1950s [1]. Since that time a number of researchers have studied aspects of the application of tethered satellite systems including the dynamics of tethered satellites and the architecture of tethered satellite missions [1–9]. Tethered satellites are of interest both because of the physical and mathematical problems they present and because of their many practical uses. Tethered satellite systems have been identified as candidates for novel atmospheric probes, interferometers, magnetometers, and gravity gradiometers among other devices [10–14]. Some far term applications of tethered satellites include the tethered artificial gravity (TAG) system and the momentum exchange and electrodynamic reboost (MXER) system. The TAG system is a device capable of imparting an artificial gravitational force to bodies on orbit [15], whereas the MXER system is a momentum exchange device designed to boost payloads into higher orbits without the use of chemical propellants [16]. Numerous other uses for tethered satellites in space are detailed in [17]. During the course of a tethered satellite mission, it may be necessary to shorten the overall length of the tether. The purpose of such a retrieval could be to facilitate the repair or servicing of the tethered satellite assembly, to reduce the profile of the orbital debris created by a satellite at the end of its useful life, or simply to alter the dynamical behavior of the tethered satellite system. We will show that in general, such a length contraction causes the tethered satellite system to enter a spin with respect to the orbital reference frame. In many of the instances described above, the reason for retrieving a tethered satellite system necessitates that the system not spin with respect to the orbital reference frame; such a maneuver could be achieved through the use of a sophisticated angular velocity control system. However, by exploiting the dynamics of a tethered satellite system, it is possible to reduce the length of the system without causing the system to enter a spin. Analysis of the equations of motionwill reveal that under an exponential length control law, there exist initial tethered satellite states for which the tethered satellite system can be retrieved and remain stationary with respect to the orbital reference frame during the course of the retrieval maneuver. These points, which correspond to the equilibria of the system, will be identified and classified. We will describe the motion of a simplified tethered satellite system undergoing retrieval in the neighborhood of these equilibrium points.