Sun-synchronous Solar Reflector Orbits designed for Illumination from Space

The use of orbiting space mirrors to reflect sunlight onto the Earth's surface has been contemplated in a large number of applications, which include illumination from space, large terrestrial solar power farms, space-based solar power (collecting solar power directly from space), geoengineering, and Terraforming schemes. Previous studies have demonstrated the feasibility of using space-based solar reflectors to achieve such mega projects. In this work, an Earth-space mirror two-body analysis is performed, taking into account the Solar Radiation Pressure and $J_2$ Earth oblateness perturbation, such that, when the sunlight strikes the perfectly reflecting space mirror surface, the ray reflects off the mirror in the direction of Earth's center. In this study, two candidate orbits for solar reflectors were conducted: a polar orbit perpendicular to the ecliptic plane of Earth, and an in-plane orbit in the ecliptic plane of Earth. We assumed that the ecliptic and equatorial planes of Earth coincide. Using Gauss' perturbing equations, it is provided a set of orbital parameters to achieve a Sun-synchronous Solar Reflector Orbit, that distributes azimuthally the solar energy intercepted by the mirror. The characteristic acceleration of the mirror is also chosen properly from the Sun-Synchronous condition. Additionally, it is shown that, in this scenario, a Low Sun-Synchronous Earth Orbit can be accomplished only for polar orbits, but not for the in-plane motion. In this last scenario, Medium Sun-Synchronous Earth Orbits can only be achieved.