Out-of-Plane Equilibria in the Restricted Eight-Body Problem: Dynamics and Stability

This paper investigates the out-of-plane equilibrium points in the circular restricted eight-body problem, focusing on the influence of a radiating central primary surrounded by six peripheral primaries in circular motion. Two symmetrical equilibrium points are identified along the z-axis, existing within the radiation factor range -6 < q < 0. At the critical radiation qc=-3/√2 , these points align exactly on the z-axis at a distance equal to the orbital radius of the peripheral primaries. Through linear stability analysis, it is demonstrated that these equilibrium points are inherently unstable across the entire range of radiation factors. The study also examines periodic orbits around the equilibrium points for specific values of qqq, providing valuable insights into the complex dynamical behavior of such systems. These findings enhance the understanding of celestial mechanics in multi-body systems affected by radiation and gravitational forces.