Optimization design and analysis of spacecraft formations on elliptic orbits

The differential J₂ influence is a big challenge to design periodic relative motion between two spacecrafts on neighboring eccentric orbits. A linearized time-variant equation is presented to describe the formation dynamics in the presence of J₂ disturbances. For five kinds of basic formation configurations, numerical simulations show that the spacecrafts will not separate over time, when the initial inclination, initial argument of perigee and initial mean anomaly of the reference orbit are set to be special values. Some simple results can be demonstrated with the theory of mean orbit elements, but iteration need to be used for the others. Therefore, an optimization design involving the above osculating orbital elements is proposed to reduce relative orbit drifts due to J₂ effects. The results indicate that, the optimal formation can avoid considerable in-plane relative motion drifts and provide substantial fuel savings for formation maintenance.