Optimal, Low-Thrust, Earth-Moon Orbit Transfer

Optimal, low-thrust, Earth ‐moon orbit transfers are found using the method of collocation with nonlinear programming. The initial spacecraft Earth orbit is arbitrary; the e nal lunar orbit is arbitrary. The moon is in its actual orbit. The vehicle dynamics include the effects of the moon’ s gravity during the Earth-departure phase and the effects of the Earth’ s gravity during the lunar-arrival phase. Total transfer time is minimized. However, because the propulsion system operates continuously, i.e., no coast arc is allowed, the trajectory is also propellant minimizing. A very low initial thrust acceleration of 10 i 4 g yields e ight times of approximately 32 days requiring many revolutions of both the Earth and the moon. Ignoring third-body gravity, i.e., solving the problem as two coupled two-body problems, changes the optimal trajectory only slightly, for example, decreasing the travel time by a few hours. The optimal trajectory is also insensitive to change in engine specie c impulse so long as the same initial thrust acceleration magnitude is used.