OPTIMAL, LOW-THRUST, EARTH-MOON ORBIT TRANSFER

Optimal, low-thrust, Earth-moon orbit transfers are found using the me thod of collocation with nonlinear programming, The initial spacecraft Earth orbit is arbitrary; the final lunar orbit is arbitrary, The moo n 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 ti me is minimized, However, because the propulsion system operates conti nuously, i.e., no coast are is allowed, the trajectory is also propell ant minimizing. A very low initial thrust acceleration of 10(-4) g yie lds flight times of approximately 32 days requiring many revolutions o f both the Earth and the moon. Ignoring third-body gravity, i.e., solv ing 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 en gine specific impulse so long as the same initial thrust acceleration magnitude is used.