Co-orbital asteroids of terrestrial planets affected by the von Zeipel–Lidov–Kozai mechanism

We investigate the dynamical behavior of co-orbital asteroids of Venus, Earth, and Mars potentially affected by the von Zeipel–Lidov–Kozai (ZLK) mechanism. Semi-analytical models of the ZLK dynamics for NEOs in the terrestrial planet regions predict that at high eccentricities and inclinations, corresponding to iₘₐₓ = [√1-e² cos (inc)] > 30∘ i max = arccos [ 1 - e 2 cos ( i n c ) ] > 30 ∘ , equilibrium points should appear at 90∘ 90 ∘ and 270∘ 270 ∘ . At low eccentricities and inclinations in the vicinity of Earth and Venus, perturbations from these two planets are dominant, with two equilibrium points occurring at 0∘ 0 ∘ and 180∘ 180 ∘ . Using numerical simulations performed with the SWIFT and REBOUND integrators, we classify the Kozai states of known co-orbitals and assess their long-term stability. Our results indicate that no current Venus co-orbital is a robust ZLK resonator, while several Earth co-orbitals and one Mars co-orbital (2017 XG62) exhibit libration around one of the four ZLK equilibrium points. Libration around the 0∘ 0 ∘ and 180∘ 180 ∘ equilibrium points protects asteroids from close encounters with their perturbing planet, Earth, enhancing long-term stability on timescales of 10⁵ ≃ 10 5 years. 2017 XG62 is the only known co-orbital asteroid of a terrestrial planet that is currently librating around the high-inclination 90∘ 90 ∘ equilibrium point. This configuration prevents this asteroid from experiencing close encounters with other terrestrial planets.