Spacecraft trajectory targeting by boundary-condition orbit fitting

A technique is developed for extending the orbital boundary value problem to permit multiple choices of position, velocity, flight path angle and transfer angle in a guidance algorithm. The method involves the initial (IP) and target (TP) positions and the velocity vectors at the IP which follow the feasible transfer orbit for reaching the TP. A chord is drawn between the points and is shown that there are an infinite number of velocity vectors at the IP which would yield the chord as an asymptote of the hyperbola whose locus is the IP. If either the target velocity or target flight path angle are not specified, then the other three values can be selected as desired to achieve the TP. Techniques for applying the principle are defined and the results of trajectory simulations using a fourth-order Runge-Kutta integration for a single-stage-to-orbit 100,000 kg vehicle to LEO and an orbit transfer vehicle from LEO to GEO are provided. The method is recommended for early design work when optimal trajectories are not needed.