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This paper analyzes relative orbit design for multi-satellite radar missions aimed at multistatic SAR tomography. To this end, formation requirements and performance parameters are derived by adapting existing models for SAR tomography to single pass techniques. Then, relative trajectory design is carried out on the basis of an analytical relative motion model including secular J 2 effects. By properly scaling the differences in orbital parameters, different formation geometries enable uniform sampling of the effective baseline along the whole orbit. The difference among the possible choices lies in latitude coverage, formation stability, and collision avoidance aspects. A numerical example of relative trajectory design is discussed considering L-band as operating frequency. In particular, achievable height resolution and unambiguous height along the orbit are pointed out for a multi-cartwheel, a multi-pendulum, and a multi-helix formation. In view of future implementation of a multi-satellite SAR tomography mission, new concepts aimed at the reduction of required satellites, and long term evolution of designed formations, are also discussed.

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.

In the latest years there has been a growing interest in satellite formation flight and distributed satellite systems, in the context of such missions as space-based radar or interferometry. For example, different strategies and configurations have been proposed to complement SAR constellations with along-track and cross-track interferometry, and mission analyses have been carried out in the framework of several on-going projects. This recent flurry of research lead to the development of several sets of equations to predict and understand relative motion between satellites in a cluster, trying to improve Hill’s equations by inclusion of Earth oblateness effects. Actually, most of these studies were devoted to formation control, rather than orbital configuration design. In this paper, the authors present an analytical model which allows a time-explicit representation of relative motion on the basis of orbital parameters’ differences between satellites. In this way, it is possible to easily understand relations between orbital parameters and relative kinematics. In particular, first a new set of equations is developed, which generalizes, in the context of unperturbed dynamics, previous results. Two different sets of equations are derived, referring to the case of one of the satellites on a circular orbit, or both satellites on low eccentricity orbits, respectively. Then, these equations are improved by incorporating J2 secular effects, without changing the line of reasoning followed in their derivation. Numerical simulations have been performed in order to show how accurately can the new equations predict the relative motion. In particular, modeling errors are evaluated by calculating approximate and exact (non linear) solution, and achievable accuracy performance is compared with that of other linear models. Achieved results show that the new equations are able to capture J2 secular effects with a good approximation on an acceptable timescale, with respect to design requirements.