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. It is based on preliminary results of Geffroy [Généralisation des techniques de moyennation en contrôle optimal, application aux problèmes de rendez-vous orbitaux à poussée faible, Ph.D. Thesis, Institut National Polytechnique de Toulouse, France, Octobre 1997] where the optimal trajectories are approximated using averaging techniques. The objective is to introduce the appropriate geometric framework and to complete the analysis of the averaged optimal trajectories for energy minimization, showing in particular the connection with Riemannian problems having integrable geodesics.