A systematic study about orbit flips of test particles caused by eccentric von Zeipel-Lidov-Kozai effects

Abstract

The problem of orbit flips caused by eccentric von Zeipel-Lidov-Kozai effects is systematically investigated by means of three approaches, including Poincaré sections, dynamical system theory (periodic orbits and invariant manifolds) and perturbation treatments. Poincaré sections show that orbit flips are due to the existence of islands of libration centered at inclination of $90^{\circ }$, dynamical system theory shows that orbit flips are due to the existence of polar periodic orbits and invariant manifolds, and perturbative treatments indicate that orbit flips are due to the libration of a certain critical argument. Using these approaches, the boundaries of flipping regions in the entire parameter space are produced and they are in excellent agreement with each other. Through analysis, the essence of flipping orbits is reached: (a) flipping orbits are a kind of quasi-periodic trajectories around polar periodic orbits and invariant manifolds at the same level of Hamiltonian provide boundaries of flipping regions, and (b) flipping orbits are a kind of resonant trajectories and resonant width measures the size of flipping regions.

20 pages, accepted for publication in AJ

References in corpus (10)

• Hot Jupiters from Coplanar High-eccentricity Migration
• Chaos in the Test Particle Eccentric Kozai-Lidov Mechanism
• Quasi-satellite orbits in the general context of dynamics in the 1:1 mean motion resonance. Perturbative treatment
• Long term dynamics beyond Neptune: secular models to study the regular motions
• Long-term orbital dynamics of trans-Neptunian objects
• The eccentric Kozai-Lidov effect as a resonance phenomenon
• Study and application of the resonant secular dynamics beyond Neptune
• On the Divergence of First Order Resonance Widths at Low Eccentricities
• Secular resonance of inner test particles in hierarchical planetary systems
• Dynamical structures of retrograde resonances: analytical and numerical studies

Cited by in corpus (2)

• Extremely Inclined Orbit of S-type Planet $\gamma$ Cep Ab Induced by Eccentric Kozai-Lidov Mechanism
• Quadrupole and octupole order resonances in non-restricted hierarchical planetary systems