Optimal solar system escape trajectories for gradient-index solar sails via saturation functions

Solar System escape is a necessary step for interstellar missions and requires long-term, advanced spacecraft propulsion capabilities when the heliocentric trajectory does not include gravity assist maneuvers. In this context, solar sails are becoming an attractive option due to their increasing technological maturity, which enables their effective use in interplanetary missions. Among these propellantless propulsion systems, the gradient-index solar sail is a promising concept capable of providing a transverse component of the thrust vector even when the sail is in a (passively stable) Sun-facing attitude. The presence of this transverse thrust component enhances escape performance compared to a classical reflective solar sail with a fixed Sun-facing orientation or a piecewise-constant attitude profile. This paper investigates the capabilities of a Sun-facing gradient-index solar sail for escaping the Solar System. The problem is formulated within the framework of indirect optimal control to determine the time-optimal escape trajectory. Additionally, a path inequality constraint limiting the minimum solar distance is handled using a saturation function and incorporated into the mathematical model.