Analytical solution of the optimal steering law for non-ideal solar sail

This paper analyzes the problem of finding the optimal steering law for a flat solar sail whose propulsive acceleration is described by an optical force model. In particular, the problem amounts to looking for the optimal direction of the unit vector normal to the sail plane that maximizes the projection of the propulsive acceleration along a given direction. Starting from the known results from the literature, according to which a close form solution for the general case of not (fully) specularly reflecting sail cannot be retrieved, the propulsive acceleration is approximated by a mathematical model that closely resembles the classical optical force model. Using this new approach, the solution of the optimal steering law is shown to be written in an analytical form that is fully general and extremely accurate. In this sense, the proposed mathematical model may effectively be used to analyze the impact of the thermo-optical characteristics of the sail film on the optimal steering law within a wide range of different mission scenarios.