Minimum-Time Trajectories of Electric Sail with Advanced Thrust Model

The Electric Solar Wind Sail is an advanced propulsion system concept that, similar to the more conventional solar sail, is able to generate a propulsive thrust without any propellant. The main performances of such a propulsion system have been studied in different mission scenarios and are reported in the literature. However, the analyses available so far are based on a simplified thrust model that neglects the effect of the spacecraft attitude on both the thrust modulus and its direction. The recent availability of a refined thrust model requires a critical reappraisal of the simulation results and a new analysis of the optimal trajectories of a spacecraft equipped with such a propulsion system. The aim of this paper is to review the different thrust models used over the last years for mission analysis purposes, and to illustrate the optimal control law and the corresponding minimum-time trajectories that can be obtained with the new, refined, thrust model. The study highlights new analytical relations for the propulsive thrust as a function of the spacecraft attitude, whereas simple and accurate closed-form equations are also proposed for the study of a classical circle-to-circle coplanar heliocentric orbit transfer.