Analysis of relative motion in non-Keplerian orbits via modified equinoctial elements

This paper discusses a mathematical model to determine an analytical form of the equations describing the relative motion of two spacecraft that, using a suitable continuous-thrust propulsion system, track highly non-Keplerian orbits, whose orbital plane does not contain the primary's center-of-mass. The relative motion is described within a rotating reference frame via modified equinoctial elements, thus eliminating the singularities that arise when a set of classical orbital elements is used. In this sense, the paper completes and extends the recent analysis of the relative motion of two spacecraft in closed (either circular or elliptic) displaced orbits. When the eccentricity of the displaced orbits is sufficiently small, the method is able to calculate the approximate bounds of the two spacecraft relative distances using a semi-analytical approach and with a reduced computational effort. Some numerical simulation results provide an evidence of the effectiveness of the proposed method.