New Families of Halo Orbits about the Photo-Gravitational Equilibrium in the Sun-Earth-Moon System’s Center of Mass Elliptic Restricted Three-Body Problem for Planetary Sunshade Missions

This paper investigates halo orbits about the photo-gravitational equilibrium point L1 between Sun and the center of mass of the Earth–Moon system. In a previous paper, the authors discussed the existence of suitable orbits for Planetary Sunshade missions in the photo-gravitational Sun - Earth–Moon system’s center of mass Circular Restricted Three Body Problem with solar radiation pressure acting on perfectly reflecting solar-sails satellites [C. L. Matonti, E. Scantamburlo, M. Romano, New Families of Halo Orbits about the Photo-Gravitational Equilibrium between Sun and the Earth–Moon System for Planetary Sunshade Missions, 74th International Astronautical Congress, Baku, 2023]. In this paper, a higher fidelity model is considered. In particular, the orbital mechanics is modeled according to the corresponding photo-gravitational Sun - Earth–Moon system’s center of mass Elliptic Restricted Three Body Problem. Furthermore, the solar pressure force is now modeled by considering the reflectance, absorption and emissivity of the surface of a non-ideal solar-sail satellite. Families of new orbits are found by using the above model. The newly introduced orbits could be utilized by a swarm of solar-sail satellites to implement a dynamic Planetary Sunshade System for Earth’s climate-change mitigation. This dynamic Planetary Sunshade System acts as a space-based geoengineering infrastructure whose aim is to reduce part of the oncoming solar radiance. In particular, for each of those families (proposed for the first time to the best knowledge of the authors), the orbits lie on different planes or cylinders, and the projection of the satellites’ sails covers a circle. That circle resides on a plane perpendicular to the line joining the Sun center and the Earth–Moon system’s center of mass. The orbit of each satellite was found by choosing the analytical expression of a periodic trajectory in that plane, and by computing the initial condition that enables a closed orbit in three dimensions. The needed continuous control force, on each solar-sail satellites, exploits the solar-radiation pressure acceleration, which is modeled with two components tangential and perpendicular to the sail. The direction of the control force is varied by controlling the satellite’s orientation about two axes. The control angles expressions were found for each satellite’s orientation history. The orbital stability of each of those families is finally discussed.