An analytical solution for relative motion with an elliptic reference orbit

A method for the determination of accurate analytical expressions for the time dependence of the relative motion of two noninteracting masses under the gravitational influence of a spherical primary mass is presented and discussed. The case of the elliptic reference orbit is considered and the case of a circular reference orbit is analyzed as a special case. The approach also leads to accurate initial conditions for the elimination of drift away from periodic relative motion. The solution for the relative motion is in closed-form in terms of the eccentric anomalies of the target and chaser orbits, while the eccentric anomalies themselves are expressed in terms of the orbits' respective eccentricities, using an iterative method.