This paper presents the solution for minimum-fuel, free-time transfer between coplanar elliptical orbits with the possible use of a planetary atmosphere to generate a decelerative braking force. The optimal pure propulsive two-impulse transfer is first considered. It is shown that the solution is obtained by solving a set of three equations for three unknowns. Reduction of the general equations is made for the case of symmetrical transfer and a complete first-order solution is provided for the case of transfer from nearly circular orbit.
In aeroassisted transfer atmospheric braking at the perigee can be used to circularize the orbit, and in the circular configuration the orbit can be arbitrarily rotated without fuel consumption. It is shown that complete circularization of this intermediary orbit is optimal only when the rotation angle is large, and an explicit formula for evaluating this critical angle is provided. A complete solution is presented for the case of optimal rotation of an orbit. An example of optimal aeroassisted transfer is provided for the case of a transfer from a low-energy orbit to a high-energy orbit.