Relative motion of particles in coplanar elliptic orbits

A simplified solution for the relative motion of particles in coplanar elliptic orbits, applicable to the rendezvous maneuver between an unpowered ferry vehicle and an orbiting target satellite as well as to other examples of relative coplanar orbital motion, is developed. Previous solutions to the problem based on linearized differential equations of relative motion are reviewed, and the computational technique of Lancaster (1970), which uses vector subtraction of the individual orbital motions, is argued to be too complex for trajectory analysis. In the simplified approach presented here, the elliptic orbits are characterized by the orbital elements eccentricity, semilatus rectum and apsidal orientation in the plane for the two particles, and the trajectory is determined in the rotating force-centered system of coordinates. The procedure is illustrated for the cases of two particles in the same orbit, and particles in different orbits with the same eccentricity and semilatus rectum.