Solar Sail Trajectory Analysis with Asymptotic Expansion Method

An analytical expression for the trajectory equation of a solar sail spacecraft is available in special cases only, including the well known logarithmic spiral. The latter, however, cannot be used when the parking orbit is circular. This paper presents an approximate solution to this problem, obtained by considering the propulsive acceleration as a perturbation effect acting on a Keplerian trajectory in a heliocentric (two-dimensional) mission scenario. In this context, the spacecraft dynamics are approximated by an asymptotic series expansion in terms of non-singular generalized orbital elements. Under the assumption that the propulsive acceleration is small compared to the local Sun's gravitational attraction, a first order approximation is shown to be very accurate in predicting the trajectory of the spacecraft and the evolution of the non-singular orbital parameters of the osculating orbit. A periodic rectification procedure improves the method accuracy without significantly affecting the computational time, as is confirmed by numerical simulations.