Relative Effect of Inclinations for Moonlets in the Triple Asteroidal Systems

TL;DR

This paper analyzes how various gravitational perturbations affect the inclination vectors of moonlets in triple asteroid systems, revealing periodic and elliptical motion patterns validated through numerical simulations.

Contribution

It provides a detailed analysis of inclination vector dynamics in triple asteroid systems considering multiple perturbations, with validation through numerical simulations.

Findings

Inclination vectors follow periodic elliptical motions influenced by perturbations.

The x and y components of inclination vectors exhibit elliptical and quasi-periodic behaviors.

Numerical simulations confirm the theoretical motion patterns in real asteroid systems.

Abstract

We present the analysis and computational results for the inclination relative effect of moonlets of triple asteroidal systems. Perturbations on moonlets due to the primarys non-sphericity gravity, the solar gravity, and moonlets relative gravity are discussed. The inclination vector for each moonlet follows a periodic elliptical motion; the motion period depends on the moonlets semi-major axis and the primarys J2 perturbations. Perturbation on moonlets from the Solar gravity and moonlets relative gravity makes the motion of the x component of the inclination vector of moonlet 1 and the y component of the inclination vector of moonlet 2 to be periodic.The mean motion of x component and the y component of the inclination vector of each moonlet forms an ellipse. However, the instantaneous motion of x component and the y component of the inclination vector may be an elliptical disc due to the coupling effect of perturbation forces. Furthermore, the x component of the inclination vector of moonlet 1 and the y component of the inclination vector of moonlet 2 form a quasi-periodic motion. Numerical calculation of dynamical configurations of two triple asteroidal systems (216) Kleopatra and (153591) 2001 SN263 validates the conclusion.