Optimal Solar Sail Phasing Trajectories for Circular Orbit

The concept of using a solar sail for the repositioning maneuver of a spacecraft on a heliocentric orbit was first proposed by McInnes [1]. In particular, assuming a circular orbit and a linearized dynamics model, Ref. [1] discusses the performance of a small (ideal) solar sail, subjected to a piecewise constant steering law, and compares its effectiveness with a situation in which a chemical (high-thrust) propulsion system is employed to perform the same maneuver. Subsequently, the study was extended by Mengali and Quarta [2], who solved the problem within an optimal framework, generalizing it to an elliptic orbit, a solar sail with an optical force model, and a scenario in which two spacecraft are simultaneously repositioned along the same starting orbit. The analysis of Ref. [2] was conducted using a nonlinear dynamics model for the solar sail’s heliocentric motion, which is, of course, fully general, but whose results can only be managed through numerical simulations. The aim of this Note is to show that, under the assumption of a linearized mathematical model [1], the optimal repositioning problem of an ideal, low-performance, solar sail can be solved within a semi-analytical framework. In particular, starting from a circular parking orbit, it is shown that the truly optimal steering law may be recovered in closed form.