Modeling orbital relative motion to enable formation design from application requirements

While trajectory design for single satellite Earth observation missions is usually performed by means of analytical and relatively simple models of orbital dynamics including the main perturbations for the considered cases, most literature on formation flying dynamics is devoted to control issues rather than mission design. This work aims at bridging the gap between mission requirements and relative dynamics in multi-platform missions by means of an analytical model that describes relative motion for satellites moving on near circular low Earth orbits. The development is based on the orbital parameters approach and both the cases of close and large formations are taken into account. Secular Earth oblateness effects are included in the derivation. Modeling accuracy, when compared to a nonlinear model with two body and J₂ forces, is shown to be of the order of 0.1% of relative coordinates for timescales of hundreds of orbits. An example of formation design is briefly described shaping a two-satellite formation on the basis of geometric requirements for synthetic aperture radar interferometry.