An optimized analytical solution for geostationary debris removal using solar sails

Abstract

Debris in geostationary Earth orbits is often uncontrollable, consisting of launch-vehicle upper stages and non-operational payloads. To help mitigate orbital debris congestion, a solar-sailing satellite concept is proposed which retrieves and relocates large debris for placement into the “graveyard” orbit above the geostationary regime. This work derives an analytical deorbit solution based on Lyapunov control theory combined with the calculus of variations. A dynamic constraint vector is introduced as a result, which dictates the orbital response of a spacecraft to some controlled perturbation. The resulting controller is simulated for various solar sailing platforms to characterize deorbit capability based on a system's area to mass ratio. User design parameters in these solutions are then optimized using a Particle Swarm Optimizer (PSO) to produce robust, locally time optimal solutions for orbital debris removal using solar sails. Solar sail deorbit times are shown to decrease as the reflective area increases, with additional performance dependencies based on the Earth's relative position from the sun.