Exact analytical formulation of planar relative motion

Exact analytical representations for the instantaneous changes in the orbital elements of both station and probe (with arbitrary mass ratio) resulting from an impulsive separation are derived. These results serve as parameters in an exact solution to the unperturbed relative motion problem which is determined by means of a few simple transformations from the two Keplerian ellipses and retains full accuracy for small separation distances. Furthermore, a formulation in terms of slowly varying relative elements allowing for arbitrary perturbing forces upon both bodies is presented. The relevance of the present formulation to a long-term valid description of subsatellite motion is apparent.