Coplanar Two-Impulse Rendezvous in General Elliptic Orbit with Drag

Abstract

The numerical solution of the two-impulse terminal rendezvous for the formation flying of two spacecraft with different ballistic coefficients in general elliptic orbit is presented. The motion of the passive vehicle is described by the inverse-square gravitational field of the primary body and by atmospheric drag. The center of a rotating reference frame is attached to this vehicle, and the motion of the active maneuvering vehicle is described relative to this accelerating frame. This allows for the solution of the exact, arbitrary duration two-impulse rendezvous problem, with both vehicles continuously subject to drag in their respective orbits during the maneuvering period, meaning between the application of the first or initiating impulse, and the final or terminating impulse which achieves the desired rendezvous. Examples of rendezvous which bring the vehicles to close proximity for various transfer durations are presented to support this analysis.