Optimal law for inclination change in an atmosphere through solar sailing

The aim of this paper is to devise a local optimal strategy for orbital inclination change of solar sail spacecraft in low Earth orbit, combining the effects of the solar radiation pressure and atmospheric forces. The spacecraft is modeled as a reflective flat plate. The acceleration due to the effects of atmospheric forces and solar radiation pressure is computed, depending on the orbital parameters and attitude of the sail. Then, the attitude that maximizes the instantaneous orbital inclination change is found through Gauss' equations. When either one of these effects dominates over the other (and so one can be neglected), analytic expressions are found. When both effects are considered, a numerical optimization is used. An additional constraint is introduced to avoid a decrease in orbital semi-major axis, and, therefore, prevent losses of orbital energy, while increasing the inclination. Different regions are identified, depending on whether the atmospheric effects dominate, the solar radiation pressure dominates, or the two are comparable. Arcs along the orbit are determined in which the optimal attitude can be found analytically, and the expression is derived. Numerical results show that a consistent increase of inclination can be achieved in a one year mission, starting from different circular orbits, by applying the proposed control laws.