Orbital dynamics in the vicinity of asteroid 216 Kleopatra

This paper studies the orbital dynamics around the main-belt asteroid Kleopatra through a detailed look at the motion around the equilibria using observational data. The shapes of zero-velocity surfaces are represented at assigned values of the Jacobi integral to explore the connections between forbidden regions in three-dimensional space and the final fates of the nearby trajectories. All four equilibria are found to be nonlinearly unstable, and the degree and mode of instability are further clarified by decomposing the motion into respective local manifolds. This study suggests that there are many sensitive and uncertain trajectories near the equilibria due to the multiplicity of unstable branching trajectories around the center manifolds. Six continuous major families of periodic orbits are obtained close to the equilibria, which are proved to be unstable by Floquet theory.