Differential Orbit Element Constraints for Coulomb Satellite Formations

Recently the concept of controlling the relative motion of spacecraft using electrostatic charging has been proposed. For tight spacecraft formations with separation distances ranging from 10‐100 meters, the Coulomb forces between the spacecraft can be exploited to provide a very fuel and power efficient means of propulsion. As the charge of a single craft is varied, the relative motion of the entire formation is affected. The Coulomb force vector a craft experiences is restricted to be directed along the relative position vector, which results in constraints being imposed on how the Coulomb force can be used to control a formation. This paper investigates how the conservation of angular momentum and the formation center of mass limits the types of relative orbits that can be controlled. Considering the spacecraft formation to be a system of N particles, this internal force can not change the inertial system angular momentum vector. The center of mass definition and angular momentum constraint are expressed using differential orbit elements to describe the relative motion. First order transformations to the nonlinear solutions are presented. Their accuracy is evaluated both analytically and using numerical simulations.