A perturbative treatment of the Yarkovsky-driven drifts in the 2:1 mean motion resonance

¹ School of Astronomy and Space Science, Nanjing University Nanjing 210023, PR China
e-mail: houxiyun@nju.edu.cn
² Institute of Space Environment and Astrodynamics, Nanjing University, Nanjing 210023, PR China
³ Key Laboratory of Modern Astronomy and Astrophysics, Ministry of Education, Nanjing 210023, PR China

Received: 28 February 2024
Accepted: 5 July 2024

Abstract

Aims. Our aim is to gain a qualitative understanding as well as to perform a quantitative analysis of the interplay between the Yarkovsky effect and the Jovian 2:1 mean motion resonance under the planar elliptic restricted three-body problem.

Methods. We adopted the semi-analytical perturbation method valid for arbitrary eccentricity to obtain the resonance structures inside the Jovian 2:1 resonance. We averaged the Yarkovsky force so it could be applied to the integrable approximations for the 2:1 resonance and the ν₅ secular resonance. The rates of Yarkovsky-driven drifts in the action space were derived from the quasi-integrable approximations perturbed by the averaged Yarkovsky force. Pseudo-proper elements of test particles inside the 2:1 resonance were computed using N-body simulations incorporated with the Yarkovsky effect to verify the semi-analytical results.

Results. In the planar elliptic restricted model, we identified two main types of systematic drifts in the action space: (Type I) for orbits not trapped in the ν₅ resonance, the footprints are parallel to the resonance curve of the stable center of the 2:1 resonance; (Type II) for orbits trapped in the ν₅ resonance, the footprints are parallel to the resonance curve of the stable center of the ν₅ resonance. Using the semi-analytical perturbation method, a vector field in the action space corresponding to the two types of systematic drifts was derived. The Type I drift with small eccentricities and small libration amplitudes of 2:1 resonance can be modeled by a harmonic oscillator with a slowly varying parameter, for which an analytical treatment using the adiabatic invariant theory was carried out.