Geometric optimal control and transfer between elliptic Keplerian orbits

This paper concerns the time minimum transfer of a satellite between Keplerian elliptic orbits. We study the controllability properties of the system and we make a preliminary analysis of the local time optimal control constructing a nilpotent model. Second order conditions for optimally are given using the concept of conjugate time and the time optimal trajectory to transfer the system from an initial low orbit with large excentricity to a geostationary orbit is obtained numerically.