Optimal multiple-impulse nonlinear orbital rendezvous

A method for determining optimal impulsive trajectories is applied to minimum fuel, multiimpulse, circle to circle rendezvous for the fixed transfer time case. The optimal trajectory is assured by satisfying the Lawden's necessity conditions expressed in terms of the primer vector. Results are presented and compared to previously obtained linearized solutions to assess the accuracy of the linearized solutions. The optimal nonlinear multiimpulse fixed time cost is always equal to or lower than the optimal linearized cost. The effects of inclination of the target orbit and initial position of the target for different final orbit radii are also considered. Two, three and four impulse optimal solutions are obtained for the nonlinear case. Results are compared with known time open optimal solutions.