Optimal three impulse orbital transfer: Between coplanar non co-axial orbits

The goal of this paper is to find the global minimum for three impulses orbital transfer between coplanar non co-axial orbits. Since there is no analytical solution for the problem, it is necessary to resort to a numerical approach. As first step, we extensively cover the space of possible solutions with the aim to get approximations for independent parameters to use as initial values for a gradient-based optimization method to seek for exact values. A comparison between the optimal solutions in the two impulse and three impulse cases shows that optimality depends on the ratio of semi-latus recti, argument of periapsis and on the eccentricity of initial and final orbits. We see also that the three impulses transfer case leads to different local minima, which could be useful when there are imposed contsraints on the problem.