Locally optimal control laws for Earth-bound solar sailing with atmospheric drag

Solar sailing is a spacecraft propulsion method relying solely on solar radiation pressure to provide thrust and is therefore propellantless by nature. Although it represents a practical and promising propulsion system particularly suited for heliocentric flight regimes, the majority of sailcraft missions flown to date have remained Earth-bound and more Earth-bound missions are scheduled for the near future. However, the fundamental dynamics and trajectory optimization of a solar sail around the Earth have only been investigated to a limited extent, often neglecting the effect of non-negligible perturbations in the dynamics and the optimal control problem. Among these perturbations are the effect of eclipses, non-spherical gravity, and aerodynamic drag. Their magnitude can be comparable to, or even exceed that of solar radiation pressure and their effect on the solar-sail dynamics should be investigated to ensure the sailcraft's transfer capabilities and controllability. This article does so by including these perturbations in the dynamics and by considering aerodynamic drag in the optimal control problem. Using this formulation, it is shown that the optimal control problem is independent of the solar-sail loading parameter and that, by solving it, locally optimal steering laws can be derived to effectively change individual orbital elements. These newly derived steering laws form an extension to the laws found by McInnes for unperturbed solar-sail Earth-bound motion. By accounting for the perturbations in the derivation of the steering laws, it is possible to characterize how the perturbations affect the solar-sail maneuvering capabilities. This is quantified based on the established increase of the targeted orbital element. Furthermore, a range of different starting orbits will be considered to analyze the effects of perturbations in different orbital regimes. As demonstration of the real need for this investigation, NASA's Advanced Composite Solar Sail System (ACS3) mission will be considered as real-case scenario. This mission is scheduled for launch in mid-2022 and may benefit from the steering laws derived in this article to prove the maneuverability of solar sails in Earth orbit.