Fast design method of moon-to-earth transfer trajectory

Design of moon-to-earth transfer trajectory is generally divided into two phases, preliminary orbit design and precise orbit design. Among them, the accuracy of preliminary design is the key to the convergence of precise design. A fast design method of moon-to-earth transfer trajectory based on Lambert algorithm was proposed. The time when the probe piercing the lunar sphere of influence, the position and the velocity at that moment were used as intermediate variables. The moon-to-earth transfer trajectory was divided into two segments to calculate separately, geocentric segment and lunar segment. In the rapid calculation of geocentric segment, the geocentric flight from the point where the probe piercing the lunar sphere of influence to the specified reentry point was simplified as a Lambert problem, which was solved by Newton iterative method. It greatly improved the computational efficiency by avoiding a large number of hypergeometric functions or series calculations. In the rapid calculation of lunar segment, a new method was presented to obtain the moon centered hyperbolic orbit elements according to the velocity vector at the sphere of influence, the inclination and perilune altitude of the lunar parking orbit. Making the position and velocity vectors of the two segments continuous at the lunar sphere of influence, a complete moon-to-earth transfer trajectory meeting the constraints at both ends was obtained by iterative calculation. The accuracy of the fast design method is relatively high besides the fast calculation. The results were also used as inputs of the precise orbit design.