Optimal Low-Thrust Trajectories to the Interior Earth-Moon Lagrange Point

Minimum-time and hence minimum-fuel trajectories are found for a spacecraft using continuous low-thrust propulsion to leave low-Earth orbit and enter a specified periodic orbit about the interior Earth-Moon Lagrange point. The periodic orbit is generated with a new method that finds a periodic orbit as a solution to a numerical optimization problem, using an analytic approximation for the orbit as an initial guess. The numerical optimization method is then employed again to determine the low-thrust trajectory from low-Earth orbit to the specified periodic orbit. The optimizer chooses the thrust pointing angle time history and the point of arrival into the periodic orbit, in order to minimize the total flight time. The arrival position and velocity matching conditions are obtained from a parameterization of the orbit using cubic splines since no analytic description of the orbit exists.