Relative motion model including J2: derivation and application to INSAR

In the growing field of formation flying, most models in literature are devoted to control problems rather than to the issue of designing the orbits on the basis of mission requirements. 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 the case of a reference satellite moving on a circular or slightly eccentric orbit. Both derivations take into account secular Earth oblateness effects. Numerical analyses show that, in typical cases of interest, equations’ errors are of the order of 0.1% of relative motion coordinates, and grow very slowly with time. Application of the derived model to interferometric and bistatic missions proposed in literature allows to rediscover and better interpret results of numerical optimization of given formations, and to point out possibilities deriving from the evolution of relative trajectory.