Two-segment lunar free-return trajectories design using the pseudostate theory

Accurate initial solutions for two-segment Earth-Moon free-return trajectories, with midcourse transfer opportunities for favorable lunar targeting, are developed analytically by using the pseudostate theory. A constrained flight-path angle quasi-Lambert problem is formulated to determine the lunar-orbiting phase of the free-return trajectory. Gradient and direct-shooting algorithms are used to correct the initial estimates of certain two-body parameters. Numerical simulations with a high-fidelity model are undertaken to verify the accuracy of the pseudostate solutions and to illustrate the efficiency of the proposed algorithm. Perilune altitude errors for the pseudostate method are less than 10% of their corresponding values for the patched conic technique. The differences between the pseudostate and the high-fidelity solutions can be eliminated rapidly.