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 final 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^-4 g yields flight 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 specific impulse so long as the same initial thrust acceleration magnitude is used.