MOTIONS AROUND THE OUT-OF-PLANE EQUILIBRIUM POINTS FOR BINARY LALANDE 21258, BD+195116, ROSS 614, 70 OPHIUCHI AND 61 CYGNI SYSTEMS

This study explores the orbital behaviour surrounding out-of-plane equilibrium points (OEPs) within the circular restricted three-body problem (CR3BP) framework, with a particular emphasis on binary star systems where the primary stars are represented as oblate and radiating entities. The research centres on the stability (Lyapunov-wise) of two pairs of OEPs, and, respectively, which are influenced by the oblateness and radiation pressure coefficients of the primary stars. By applying the theoretical framework to five specific binary systems—Lalande 21258, BD+195116, Ross 614, 70 Ophiuchi, and 61 Cygni—we assess the stability properties of these equilibrium points. Our findings indicate that the OEPs exhibit instability across all five systems, as evidenced by the positive real parts of the complex roots linked to their perturbations. This instability implies that any perturbations will amplify over time, resulting in significant deviations from the equilibrium states. The implications of this research are significant for the design of satellite constellations and the planning of space missions, as a thorough understanding of the stability of these equilibrium points is essential for successful mission execution and orbital insertion strategies. This work contributes to the wider domain of celestial mechanics by deepening our comprehension of dynamical behaviours in intricate binary systems.