Solar Sail Trajectory Analysis with Asymptotic Expansion Method

An analytical expression for the trajectory equation of a solar sail-based spacecraft is available in special cases only, such as the well known logarithmic spiral, which 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 this context, the spacecraft dynamics are approximated using an asymptotic series expansion in terms of non-singular (dimensionless) generalized orbital elements. 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, provided the sail lightness number is sufficiently small. The analytical approximation is validated by simulation.