Relative motion of satellites in elliptical orbits

The classic treatment of rendezvous mechanics, or other problems involving the relative motion of two spacecraft, assumes a circular reference orbit, allowing a relatively simple closed-form description of the motion. This paper develops a solution for an elliptical reference orbit, expanding the state transition matrix in powers of eccentricity, and gives matrix elements up to second order in eccentricity for both Cartesian and cylindrical coordinates. An example application is given for the proposed LISA (Laser Interferometer Space Antenna) gravity wave experiment.