Modeling and Control of Satellite Formations in High Eccentricity Orbits

Abstract

An analytical method has been developed to propagate the relative motion between two satellites in highly elliptic orbits. The method is kinematically exact. It maintains a high degree of accuracy even in the presence of J2 perturbations arising from the nonspherical nature of the Earth. The true anomaly of the reference satellite is treated as the independent variable, instead of time. The relative orbit kinematics is studied by using a projection onto a unit sphere. This procedure allows the relative position variables to be treated as angles that depend on the orbital element differences. Mean orbital elements are used for orbit propagation and expansions involving the powers of eccentricity are not utilized. The final results are obtained by converting the mean elements into osculating elements using Brouwer’s theory. The effect of adding short-period corrections to the mean elements is also studied. The developed analytical model and numerical optimization are employed to perform reconfiguration maneuvers by application of impulsive thrust.