New Families of Halo Orbits about the Photo-Gravitational Equilibrium between Sun and the Earth-Moon System for Planetary Sunshade Missions

This paper introduces new families of halo orbits about the photo-gravitational equilibrium point L1 between Sun and the center of mass of the Earth-Moon system. The orbital mechanics is modeled according to the circular restricted three body problem with solar radiation pressure. The newly introduced orbits could be utilized by a swarm of solar-sail satellites to implement a planetary sunshade for Earth's climate-change mitigation. In particular, five halo-orbit families are here proposed. For each of those families, the orbits do not intersect each other, 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 can be modeled as being perpendicular to the sail. The direction of the control force is varied by controlling the satellite's orientation about two axes. The analytical expression was found for each satellite's orientation history.