Averaging and optimal control of elliptic Keplerian orbits with low propulsion

This article deals with the optimal transfer of a satellite between Keplerian orbits using low propulsion and is based on preliminary results of S. Geffroy where the optimal trajectories are approximated using averaging techniques. The objective is to introduce the geometric framework and to make an analysis of the averaged optimal trajectories in the energy minimization problem, showing in particular the connection with Riemannian problems, with integrable geodesics.