Optimal Earth-Moon Trajectories Using Nuclear Electric Propulsion

Abstract

Minimum-fuel, two-dimensional and three-dimensional, Earth ‐moon trajectories are obtained for a nuclear electric propulsion spacecraft. The initial state is a circular low Earth parking orbit and the terminal state is a circular low lunar parking orbit. For the three-dimensional problem, the lunar orbit is inclined 90 deg to the Earth‐moon plane. The trajectory has a e xed thrust-coast-thrust engine sequence and is governed by the classical restricted three-body problem dynamic model. An analytical expression for quasicircular low-thrust transfers is usedtoapproximateandreplacethehundredsofinitialande nalorbitsabouttheEarthandmoon.Acostate-control transformation is also utilized to enhance convergence to the optimal solution. Numerical results are presented for the optimal Earth ‐moon trajectories.