Optimal bi-impulse transfer between coplanar, equal energy, orbits

Energy, eccentricity, and argument of periapsis are three parameters that affect the velocity change required for the optimal transfer between coplanar orbits. In this paper, optimal bi-impulse transfer between two coplanar orbits of same specific energy is considered. The assumption of transfer between orbits of the same orbital energy has been done to disentangle, in the evaluation of the optimal for the transfer, the roles of the shape change from that of the apoapsis extension. We study the bi-impulse minimization problem for a set of orbital energies at varying eccentricity and argument of periapsis. From our numerical results, the optimal required is increased by increasing the argument of periapsis of final orbit. Its maximum refers to the case that the apoapsis of the initial and final orbits are in the opposite direction. Furthermore, the optimal required is increased by increasing the eccentricity of the orbits. Finally, an accurate fitting function is found.