Out-of-plane equilibrium points in CR3BP under radiation and albedo effects: theory, trajectories, and stability

This research explores the impact of reflected radiation on the formation and stability of out-of-plane equilibrium points within the circular restricted three-body problem (CR3BP). The study focuses on scenarios where the larger primary body emits radiation and the smaller primary reflects this radiation. Three distinct cases are analyzed based on the parameter λ, representing the ratio of radial distances from the infinitesimal mass to the primary bodies. The research identifies the conditions under which symmetric out-of-plane equilibrium points can form and evaluates their stability, concluding that these points are linearly unstable in all examined cases. The study also delves into the nature of orbits surrounding these equilibrium points, offering important insights into the complex dynamics influenced by albedo effects. Finally, the findings of this study are applied to a realistic model, specifically the Sun-Earth-Satellite system, to validate the theoretical analysis. Upon applying the theoretical framework to the Sun–Earth–Satellite system, we confirm that out-of-plane equilibrium points do not exist in this real planetary setup. This result is consistent with the derived mathematical conditions, showing that the gravitational and dynamical constraints of the system inhibit the formation of such equilibria. Here, the parameter λ plays a key role in classifying the possible configurations. These insights contribute to a more comprehensive understanding of equilibrium structures in celestial mechanics and their implications for planetary motion and space dynamics.