Kozai-Lidov Mechanism inside Retrograde Mean Motion Resonances

TL;DR

This paper investigates the Kozai-Lidov mechanism within retrograde mean motion resonances, combining analytical and numerical methods to understand the dynamics of minor bodies in these resonances, with applications to real celestial objects.

Contribution

It develops a semi-analytical framework for studying Kozai-Lidov cycles in retrograde resonances, including phase-space portraits and analysis of real minor bodies.

Findings

Retrograde 1:1 resonance shows distinct Kozai-Lidov states.

Numerical results agree with semi-analytical phase-space portraits.

Different bifurcations observed in 2:1 and 2:5 retrograde resonances.

Abstract

As the discoveries of more minor bodies in retrograde resonances with giant planets, such as 2015 BZ509 and 2006 RJ2, our curiosity about the Kozai-Lidov dynamics inside the retrograde resonance has been sparked. In this study, we focus on the 3D retrograde resonance problem and investigate how the resonant dynamics of a minor body impacts on its own Kozai-Lidov cycle. Firstly we deduce the action-angle variables and canonical transformations that deal with the retrograde orbit specifically. After obtaining the dominant Hamiltonian of this problem, we then carry out the numerical averaging process in closed form to generate phase-space portraits on a $e-\omega$ space. The retrograde 1:1 resonance is particularly scrutinized in detail, and numerical results from a CRTBP model shows a great agreement with the our semi-analytical portraits. On this basis, we inspect two real minor bodies currently trapped in retrograde 1:1 mean motion resonance. It is shown that they have different Kozai-Lidov states, which can be used to analyze the stability of their unique resonances. In the end, we further inspect the Kozai-Lidov dynamics inside the 2:1 and 2:5 retrograde resonance, and find distinct dynamical bifurcations of equilibrium points on phase-space portraits.