Energy minimization of single input orbit transfer by averaging and continuation

This article deals with the transfer between Keplerian coplanar orbits using low propulsion. We focus on the energy minimization problem and compute the averaged system, proving integrability and relating the corresponding trajectories to a three-dimensional Riemannian problem that is analyzed in details. The geodesics provide approximations of the extremals of the energy minimization problem and can be used in order to evaluate the optimal trajectories of the time optimal and the minimization of the consumption problems with continuation methods. In particular, minimizing trajectories for transfer towards the geostationary orbit can be approximated in suitable coordinates by straight lines.