Dynamics of Tethered-Coulomb Formation for Debris Deorbiting in Geosynchronous Orbit

In order to reduce the population of space debris in geosynchronous orbit, a tethered-Coulomb formation (TCF) is proposed that consists of a space tug and a cluster of charged debris connected by elastic massless tethers. The charged debris introduces repulsive coulomb forces to avoid collisions among the pieces of debris. In this way, the system is able to maintain a stable configuration when proper system parameters are given. To determine this relationship, a dynamics model of the formation was derived by using Lagrange's equation. Then, precise and approximate equilibrium solutions of the debris item charges and tether lengths were derived analytically according to the different number of debris items in pyramid configurations of the TCF. Based on the analytical results, pyramid and double-pyramid TCF configurations were studied via numerical simulations. The results showed that oscillations of the debris had little impact on the motion of the tug. When designing a double-pyramid TCF system, two clusters of debris with large relative positions in different phases would show good performance in a deorbit mission.