3-STAGE APPROACH TO OPTIMAL LOW-THRUST EARTH-MOON TRAJECTORIES

Minimum-fuel, planar trajectories from a circular low Earth parking or bit to a circular low Lunar parking orbit with a fixed thrust-coast-th rust engine sequence are computed for a low-thrust spacecraft. The pro blem is studied in the context of the classical restricted three-body problem. Since a low-thrust trajectory is a long-duration transfer wit h slowly developing spirals about Earth and the moon, the minimum-fuel Earth-moon trajectory is obtained by formulating and successively sol ving a hierarchy of three subproblems. This three-stage approach prese nts a systematic and effective method for solving the complex and nume rically sensitive minimum-fuel, low-thrust, trajectory problem. The fi rst subproblem is to obtain several optimal continuous-thrust Earth-es cape and moon-rapture trajectories. The second subproblem is to comput e a suboptimal, all-coasting, translunar trajectory between boundary c onditions provided by the first subproblem. Finally, the complete mini mum-fuel trajectory problem is solved using a ''hybrid'' direct/indire ct method. The hybrid method utilizes the costate time histories to pa rameterize the thrust steering history. Numerical results are presente d for the optimal Earth-moon trajectories.