Time-Explicit Representation of Relative Motion Between Elliptical Orbits

Abstract

Theclassictreatmentofrendezvousmechanicsandotherproblemsinvolvingtherelativemotionoftwospacecraft assumesa circularreferenceorbit, allowing a simpleclosed-form description ofthemotion. Asolution isdeveloped using an elliptical reference orbit, expanding the state transition matrix in powers of eccentricity, while retaining the explicit time dependence of the three-dimensional motion. The solution includes separate matrix elements for e rst-and second-order terms in eccentricity and for both Cartesian and cylindrical coordinates. Assessment of the maximum errors in position and velocity components over one complete revolution of the reference satellite shows that the solution is accurate for practical purposes with eccentricities in the range 0 ‐0.3. An example application is given for the proposed laser interferometer space antenna gravity wave experiment.