Model of J2 perturbed satellite relative motion with time-varying differential drag

Abstract

This work revisits the modeling of the relative motion between satellites flying in near-circular low-Earth-orbits. The motion is described through relative orbital elements and both Earth’s oblateness and differential drag perturbations are addressed.With respect to the former formulation, the description of the J2 effect is improved by including also the changes that this perturbation produces in both relative mean longitude and relative inclination vector during a drifting phase, when a non-vanishing relative semi-major axis is required. The second major improvement consists in a general empirical formulation to include the mean effects produced by non-conservative perturbations, such as the differential aerodynamic drag acceleration. As a result, in addition to the well-known actions on the relative semi-major axis and on the mean along-track separation, the model is able to reflect the mean variation of the relative eccentricity vector due to atmospheric density oscillations produced by day and night transitions.