An alternative representation of the relative motion: The local orbital elements

The study of the relative motion between two very-close non-massive objects has been usually done through Hill equations. More recent approaches use the differences of orbital elements to extrapolate relative motion. In this paper, we present another possible representation of the relative motion. This representation takes advantage of the very particular most common relative trajectory: the ellipse. Our representation induces a better temporal comprehension of the motion but it also provides the topology of the natural relative motions. Our approach is useful for circular and slightly eccentric reference orbits.