Dynamics of Drag Free Formations in Earth Orbit
In this paper the translational equations of motion of a formation of n spacecraft in Earth orbit, n(sub f) of which are drag-free spacecraft, are derived in a coordinate-free manner using the balance of linear momentum and direct tensor notation. A drag-free spacecraft consists of a spacecraft bus and a proof mass shielded from external disturbances in an internal cavity. By controlling the spacecraft so that the proof mass remains centered in the cavity, the spacecraft follows a purely gravitational orbit. The results described in this paper provide a first step toward coupling drag-free control technology with formation flying in order to mitigate the effect of differential aerodynamic drag on formation flying missions (e.g., Earth imaging applications) in low Earth orbit.