Minimum-time rescue trajectories between spacecraft in circular orbits

Optimal space trajectories to be flown by a rescue vehicle so as to rendezvous with a distressed spacecraft in minimum time are investigated. Nonlinear equations describing the inverse square gravitational field are used, and large transfer angles are considered. The rocket thrust of the rescue vehicle is allowed to vary between zero and a specified upper limit. The distressed vehicle is passive. Both vehicles are initially in circular orbits, but not necessarily at the same altitude nor in the same plane. Atmospheric effects are neglected, but the minimum altitude of the rescue craft is restricted by introducing a state-variable constraint. It is found that the optimal trajectories may contain coasting arcs and that arcs lying along the state-variable constraint may be of intermediate thrust. A parametric study is made using a presently proposed space tug as the rescue vehicle. The results indicate that minimum-time trajectories could be satisfactorily flown by the tug in a low earth orbit rescue effort.