Optimal orbit design of returning from the moon

Considering influence factor of rotation of moon and geostrophic force, a precise three-dimensional dynamics model for lunar probe returning from the moon was presented. To realize the minimal fuel consumption, an optimal open-loop control law in the propulsion direction of the engine was proposed based on the Pontryagin's maximum principle. The optimal orbit of returning from the moon was obtained when the velocity and position restrictions were considered. The design in this paper is favorable for engineering application.