Geometric interpretation of the Tschauner–Hempel solutions for satellite relative motion

The fundamental solutions of the Tschauner–Hempel equations, which describe the motion of a deputy satellite relative to a chief satellite with arbitrary eccentricity, are interpreted geometrically as generalizations of the drifting two-by-one ellipse that describes relative motion in circular orbits. General solutions are formed by taking linear combinations of these fundamental solutions. The amplitudes of these fundamental solutions are proposed as a parameterization of relative motion in elliptic orbits. A simple maneuver scheme is also developed to achieve arbitrary desired changes in the fundamental-solution amplitudes.