Optimal multiple-impulse time-fixed rendezvous between circular orbits

Abstract

Minimum-fuel, multiple-impulse, time-fixed solutions are obtained for circle-to-circle rendezvous. The coplanar case and a restricted class of noncoplanar cases are analyzed. For several initial phase angles of the target relative to the vehicle, optimal solutions are obtained for a range of fixed transfer times and terminal radii. Primer vector theory is used to obtain the optimal number of impulses, their times and positions, and the presence of initial or final coasting arcs. For sufficiently large transfer times, the optimal solutions become the well-known time-open solutions, such as the Hohmann transfer for the coplanar case. The results obtained can be used to perform a time vs fuel trade-off for missions which have operational time constraints, such as space rescue operations and avoidance maneuvers.