Algorithm for determining optimal three impulse point-to-orbit transfer with limited transfer time

A spacecraft transfers from an initial orbital point in a central Newtonian gravitational field to a final elliptical orbit. The planetocentric distance and the radial and transverse components of the spacecraft velocity are specified at the initial point in time. At the final point in time, only the pericentric and apocentric distances or a focal parameter and energy constant are specified. An algorithm is described for the determination of the space vehicle transfer which is energy optimal when the transfer flight time is constrained and the transfer is accomplished with three impulse maneuvers. The algorithm is based on an indirect optimization technique which derives the optimal trajectory from a single parameter family of trajectories which are optimal given the time constraint and obvious distance limitations. The initial approximation of the relevant boundary value problem is the well known solution of the case of a free transfer flight time. The variable parameters of the boundary value problem are analyzed in detail and the resulting algorithm with 12 main steps is discussed.