Optimal, low-thrust, earth-moon orbit transfers

In this work optimal low-thrust Earth-moon orbit transfers are computed using the method of collocation with nonlinear programming. The initial spacecraft Earth orbit is inclined to the reference plane (which represents the Earth's equatorial plane) as is the moon's orbit. Therefore, the problem is three-dimensional requiring six independent parameters to characterize a spacecraft's motion. In addition, the vehicle dynamics also 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. Thus, this problem is a restricted three-body problem. Finally, since the propulsion system requires only a small fraction of the total spacecraft mass, and since the total transfer time is relatively long (on the order of 30 days), the total transfer time is minimized rather than minimizing the propellant usage during the transfer.