Approximate Solutions to Circle-to-Circle Solar Sail Orbit Transfer

Abstract

S OLAR sailing is known to be a feasible solution for deep space missions requiring extremely high values of Δv. As such, it represents a valid option for heliocentric trajectories involving significant variations of orbital inclination, in particular for missions toward the inner region of the solar system [1,2]. Among the scenarios envisaging a substantial plane change, those involving a heliocentric transfer between circular orbits of different radii have stimulated different research studies [3,4]. In principle, themission analysis does not constitute a challenge in this case, as it may be reduced to a classical trajectory optimization problem [5,6]. However, especially for solar sails of current or next generation with low–medium performance [7–9], the optimal trajectory design often requires a significant amount of simulation time. This is mainly due to the long transfer times, on the order of some years, and to the trajectory complexity, which is characterized by a number of revolutions around the sun and by a continuous variation of the sail control parameters [10]. For these reasons, different mathematical models [4,11,12] have been developed to give, with a reduced amount of simulation time, not only an estimate of the main mission performances, but also accurate information about the structure of the optimal trajectory in a three-dimensional circle-to-circle (direct) orbit transfer. This is exactly the context within which the contribution of this Note is inserted. More precisely, the aim of this work is to reappraise the analytical model originally proposed byWiesel and Alfano [13] for a spacecraft equippedwith a low-performance solar electric propulsion system, and to apply it, in a similar mission scenario, to a heliocentric transfer trajectory tracked by a low-performance, ideal, flat solar sail. In this sense, the obtained results extend to a three-dimensional case the semi-analytical model recently discussed in [14].