Exact Solution to the Relative Orbital Motion in a Central Force Field

The paper presents the exact solution to the relative orbital motion that takes place in a central force field. This problem is a generalization of the problem of the Keplerian relative motion in a central force field. The solution is presented in a coordinate free vectorial form, offering closed form expressions for the law of motion and the velocity. The solution is offered to the non-linear model of the relative motion problem, and it generalizes the solutions found by Clohessy-Wiltshire, Lawden and Tschauner-Hempel for the case of the Keplerian relative motion. The applications of this problem are in satellite formation flying, satellite constellations and orbital rendezvous.