Design of impulsive Earth-Moon Halo transfers: lunar proximity and direct options

Abstract

Techniques associated with stable manifold and lunar flyby have been applied to the construction of optimal transfers to Earth-Moon $L_{1} /L_{2}$ libration point orbits. Compared with traditional design methods and to reduce maneuver cost, the design process presents a detailed analysis on the effect of lunar proximity with multiple constraints. An accurate and fast design strategy for seeking an insertion point and modifying the stable manifold to satisfy these constraints is proposed. Combined this strategy with the differential correction algorithm, the optimal transfer trajectory can be determined from a low-Earth orbit to a halo orbit around the $L_{1} /L_{2}$ libration point within a little computational time. Different amplitudes and insertion points of halo orbit in conjunction with various constraint conditions about lunar flyby are considered to deeply examine the efficiency and reliability of the design algorithm. Preliminary results indicate that the required mission cost has a significant correlation with lunar proximity constraints, and demonstrate that the method of constructing impulsive lunar halo transfer trajectories with multiple constraints is feasible.