Heliocentric Orbital Repositioning of a Sun-Facing Diffractive Sail with Controlled Binary Metamaterial Arrayed Grating

This paper investigates the performance of a spacecraft equipped with a diffractive sail in a heliocentric mission scenario that requires phasing along a prescribed elliptical orbit. The diffractive sail represents an evolution of the more traditional reflective solar sail, which converts solar radiation pressure into thrust using a large reflective surface typically coated with a thin metallic film. In contrast, the diffractive sail proposed by Swartzlander leverages the properties of an advanced metamaterial-based film to generate a net transverse thrust even when the sail is Sun-facing, i.e., in a configuration that can be passively maintained by a suitably designed spacecraft. Specifically, this study considers a sail membrane covered with a set of electro-optically controlled diffractive panels. These panels employ a (controlled) binary metamaterial arrayed grating to steer the direction of photons exiting the diffractive film. This control technique has recently been applied to achieve a circle-to-circle interplanetary transfer using a Sun-facing diffractive sail. In this work, an optimal control law is employed to execute a rapid phasing maneuver along an elliptical heliocentric orbit with specified characteristics, such as those of Earth and Mercury. The analysis also includes a limiting case involving a circular heliocentric orbit. For this latter scenario, a simplified and elegant control law is proposed based on a linearized form of the equations of motion to describe the heliocentric dynamics of the diffractive sail-based spacecraft during the phasing maneuver.