Optimal low-thrust/invariant manifold Earth Moon transfer trajectories

Minimum-time and hence minimum-fuel trajectories are found for a spacecraft using continuous low-thrust propulsion to leave geosynchronous transfer orbit and enter a low-lunar orbit, transiting via the stable and unstable manifolds of a periodic orbit about the interior Earth-Moon Lagrange point. The optimizer chooses the thrust pointing angle time history, the points of arrival/departure from the stable and unstable manifold respectively and the size of the halo orbits, in order to minimize the powered 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 manifolds exist.