3. Relative Trajectory Design

An analysis of orbital relative motion models is presented with emphasis on their application to formation design. Relative motion model evolution from the first Hill’s schematization (circular orbit, close satellites) is described, considering the inclusion of chief’s orbit eccentricity and orbital perturbations. In particular, the inclusion of J₂-secular effects is treated in depth considering various approaches in literature. Literature is also reviewed for both small and large eccentricities. Further details are presented to model formations with small chief’s eccentricity (order of 10⁻³), which are typical of Earth observation missions, for both the case of close formations, i.e. with satellite distance of the order of tens of kilometers, and large formations, i.e. satellite distance up to hundreds of kilometers. Finally, design applications are presented, with derivation of relative trajectories from application requirements. As an example, relative orbits for SAR interferometry are derived from the requested altitude measurement uncertainty and considering different candidate geometries (pendulum, cartwheel, etc.). Relative orbits for SAR tomography and large baseline bistatic SAR applications are also analyzed.