Fuel- or Time-Optimal Transfers Between Coplanar, Coaxial Ellipses Using Lambert's Theorem

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Undoubtedly, minimum-fuel and minimum-time orbit transfer are the two major goals of the optimal orbit maneuver. This paper considers two coplanar elliptic orbits when the apsidal lines coincide. We analytically e nd the conditions for the two-impulse minimum-time transfer orbit using Lambert’ s theorem. In the minimum-time transfer the transfer time is a decreasing function of a variable related to the transfer orbit’ s semimajor axis. Consequently there exists no unique minimum-time solution. Thus for the minimum-time case, there is a limiting solution only; however, there exists a unique solution in the case of minimum-fuel transfer, for which we e nd the necessary and sufe cient conditions. Furthermore, as a special case, we consider when the transfer angle is 180 deg. In thiscaseweshowthat weobtainthefuel-optimal Hohmann transfer orbit.Wealso derivetheHohmann transfer time and delta-velocity equations from more general equations, which are also obtained using Lambert’ s theorem. There is a tradeoff between minimum-time and minimum-fuel transfer. Finally, we propose an optimal coplanar orbit maneuver algorithm for trading off the minimum-time goal against the minimum-fuel goal.