Control Laws for Minimum Orbital Change-The Satellite Retrieval Problem

Abstract

Introduction I N a typical trajectory optimization problem the time of  ight or propellant consumed is minimized, resulting in signiŽ cant changes in one or more orbital elements. In situations where an upper-stage engine has failed to burn completely or a solid motor remains unŽ red, the optimization task is reversed; the goal is to expend as much propellant as possible, sometimes with little or no change in the orbital elements. In such cases the payload is often not in the desiredorbit, and mission plannersmight want to retrieve the payloadusing the space shuttle and subsequentlyrelaunch it. Safety concernsmight prohibit returningthe payloadand upper stage in the shuttle cargo bay with propellants still onboard. This problem was Ž rst encountered in 1984 with the Westar and Palapa B spacecraft, which failed to achieve their intended orbits. The solid-propellant apogee kick motors were Ž red to deplete the propellants, and the spacecraft were safely retrieved. Generally, there are no means to vent liquid propellants,and they must be consumed by reigniting the engine. The space shuttle itself must use this method in the event that one of the orbital maneuvering system pods is leaking propellant; standard procedure calls for consumingthis leakingpropellantby Ž ring the thrusterout of plane, thus minimizing the changes in semimajor axis and eccentricity. In this Note it is assumed that the vehicle is presently in an orbit compatible with shuttle operations for satellite retrieval. Using only a single sustained burn, the thrust generated needs to be directed so as to minimize the changes in semimajor axis a, eccentricitye, and inclination i , ensuring that the new orbit would be accessible by a later shuttle mission.