Geometry and control of satellite formations

Satellite formations based on the solutions to Hill's equations have amazingly simple geometric shapes. This paper shows that all such formations around a leader satellite in a circular orbit are determined by the intersection of a plane and an elliptic cylinder of eccentricity root3/2, in a moving coordinate system fixed to the leader. The parametric equations of these formations lead to a method of deploying the satellites in a formation. These equations are also essential in the design of tracking controls to herd the member satellites into a desired formation after the initial deployment, and to nudge them back into formation as soon as they start drifting due to perturbations. The adjustable parameters in these equations are key to the reconfiguration of formations from one plane to another, enabling us to aim and re-aim a satellite array which is used as sensing device.