Optimal low-thrust three-dimensional Earth-moon trajectories

Minimum-fuel, three-dimensional trajectories from a circular low Earth parking orbit to an inclined circular low lunar parking orbit with a fixed thrust-coast-thrust engine sequence are computed for a low-thrust spacecraft. The problem is studied in the context of the classical restricted three-body problem. The minimum-fuel transfer to a polar lunar orbit is obtained by successively solving a sequence of fixed lunar inclination problems. Minimumfuel three-dimensional transfers to a polar lunar orbit with meridian plane constraints are also computed. The minimum-fuel trajectory problems are solved using a direct/indirect method. The hybrid method utilizes the costate time histories to parameterize the three-dimensional thrust steering angle time histories. Numerical results are presented for the optimal three-dimensional Earth-moon trajectories.