A solution to two-point boundary value problem for power-limited rendezvous with constant thrust

A new solution to the two-point boundary value problem for power-limited non-coplanar elliptic orbital rendezvous with constant thrust is proposed based on the linear relative motion equations. The process of rendezvous is composed of three time intervals, i.e., the first engine maneuver, a coasting subarc, and the second engine maneuver. An analytical propagation of the relative state is obtained under a constant external acceleration. With the analytical propagation, the required relative velocity in the first maneuver is analytically solved and realized in feedback with a velocity gain guidance method. The thrust in the second engine maneuver is kept in a solved direction. Numerical simulations show that the analytical state propagation is accurate and the proposed rendezvous method is feasible.