Precise modelling of relative trajectory for formation flying spacecraft

Balaji, S.K. and Tatnall, A.R.L. (2003) Precise modelling of relative trajectory for formation flying spacecraft. In Proceedings of the 54th International Astronautical Federation (IAF) Congress. American Institute of Aeronautics and Astronautics..

Abstract

Relative spacecraft motion has long been a problem for mission analysts who plan rendezvous maneuvers. These planners look to the solution devised by Clohessy and Wiltshire as their primary analysis tool. The Clohessy-Wiltshire (CW) equations are usually sufficient for the rendezvous problem that is of short duration and has frequent thruster firings. Consequently, the long-term accuracy of the equations of motion is not as important in the rendezvous problem as in the formation-flying problem. The errors resulting from the assumptions made in the CW equations such as circular reference orbit, very close target orbit are unacceptable for the long-term prediction of relative motion needed for formation flying satellites. A precise analytic solution for the relative motion of and formation flying satellites is needed to minimize fuel consumption and maximize lifetime. In this paper, we derive the relative coordinates of a deputy satellite with respect to a master satellite by a series of transformations and translations from the Earth-centered inertial frame to the spacecraft centered rotating frame. The equations of relative coordinates derived in this paper are very precise and can be used to analyze orbits of any eccentricity and of any initial separation with or without the inclusion of orbit perturbations.

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