Integrated Design of Moon-to-Earth Transfer Trajectory Considering Re-Entry Constraints

The exploration of the Moon has always been a hot topic. The determination of the Moon-to-Earth transfer opportunity and the design of the precise transfer trajectory play important roles in manned Moon exploration missions. It is still a difficult problem to determine the Moon-to-Earth return opportunity for accurate atmospheric re-entry and landing, through which the actual return trajectory can be easily obtained later. This paper proposes an efficient integrated design method for Moon-to-Earth window searching and precise trajectory optimization considering the constraints of Earth re-entry and landing. First, an analytical geometry-based method is proposed to determine the state of the re-entry point according to the landing field and re-entry constraints to ensure accurate landing. Next, the transfer window is determined with the perilune heights, which are acquired by inversely integrating the re-entry state under the simplified dynamics as criterion. Then, the precise Moon-to-Earth trajectory is quickly obtained by a three-impulse correction. Simulations show the accuracy and efficiency of the proposed method compared with methods such as the patched-conic method and provide an explicit reference for future Moon exploration missions.