Results of numerical integrations of the orbits of fictive asteroids in vicinity of 2:1, 3:1 and 3:2 resonances

TL;DR

This study numerically investigates how the orbital resonance characteristics of fictive asteroids depend on planetary mass, eccentricity, and initial conditions, primarily within the planar restricted three-body problem.

Contribution

It provides detailed numerical analysis of resonance widths and frequencies near 2:1, 3:1, and 3:2 resonances, focusing on the influence of planetary parameters and initial configurations.

Findings

Resonance width varies with planetary mass and eccentricity.

Resonance frequency depends on initial orbital differences.

Results primarily applicable to planar restricted three-body problem.

Abstract

In this paper we present our results of numerical integrations of orbits of fictive massless particle in vicinity of resonance. Our goal is to study the dependences of period (frequency) of resonance perturbations and the width of the resonance on mass and orbital eccentricity of perturbing planet and on the initial difference of longitude between test particle and perturbing planet. The main attention is paid to planar restricted three body problem, but some computations are done for a spatial case.