Optimal low-thrust, limited power transfers between arbitrary elliptical orbits☆

Abstract This study is a generalization of Edelbaum's work on coplanar and on coaxial transfers. As before, the solution is valid only if the fixed transfer duration is sufficiently long to allow a large number of revolutions around the planet. The determination of the optimal trajectories in the orbital elements space is facilitated by the use of the notion of “mean Hamiltonian” and can be reduced to the solution of a differential system of order two, followed by two quadratures. This integration, as well as the determination of the conjugate point, generally necessitates a numerical treatment. The global optimum can be determined for the transfers starting from a circle and possibly for the transfers between symmetrical orbits.