Planar Optimal Two-Impulse Transfers with Closed-Form Solutions of the Transverse Transfers

The problem of finding a planar two-impulse transfer orbit between two known elliptical orbits that minimizes the total characteristic velocity of the transfer arc is examined. Using a transformation of variables presented in previous work, necessary conditions for an optimal transfer are determined, followed by a proof that an optimal transfer exists. We then consider the problem of finding a minimizing planar two-impulse transfer over the set of two-impulse transverse transfers. A minimizing solution for this problem requires that either each of the boundary orbits has an apse that is the same distance from the center of attraction as the other, or else the boundary orbits are coaxial. The transfer orbits are tangent to the boundary orbits at apses. Minimizing solutions of the transverse transfer problem are found in closed form.