Optimal time-free nodal transfers between elliptical orbits

Abstract

This paper presents the necessary conditions for the minimum fuel, time-free transfer between two non-coplanar elliptical orbits. It is shown that the solution is obtained by solving a system of three non-linear equations for three unknowns. In the second part, we discuss the case where the impulses are applied along the line of nodes. In general, this nodal transfer is non optimal, but the characteristic velocity for the best nodal transfer, called the minimizing nodal transfer, is reasonably close to the one for the optimal transfer for it to be useful as a substitute for a practical transfer. Furthermore, when we continuously vary the relative position of the two terminal orbits, the two characteristic velocities, for the minimizing nodal transfer and the optimal transfer, exhibit the same trend in the sense that they pass through their maxima and minima at nearly the same relative position. This makes the set of explicit formulas for computing the minimizing nodal transfer, as presented in this paper, a useful tool for designing a minimum fuel transfer between several orbits.