Some additional results of the Hilda group orbital elements approximations

TL;DR

This paper introduces a new numerical method for approximating the orbital elements of Hilda group asteroids near the 3:2 resonance with Jupiter, enhancing understanding of their dynamical behavior.

Contribution

It presents a novel approximation technique for orbital elements using perturbations with combinational frequencies based on numerical integration results.

Findings

Provided orbital element approximations for Hilda group members

Demonstrated the effectiveness of the approximation method

Improved understanding of minor bodies near resonances

Abstract

The quantitative characterization of amplitudes and periods of perturbations in orbital elements can help to our understanding the minor bodies dynamics, especially in case motion in vicinity of resonances. The main goal of this study is to present the new way of the orbital elements approximation by the results of numerical integration. We develop the approximation of orbital elements of the small body by the perturbations with combinational frequencies. We use a criterion of minimum of the standard error in our approximation. In result we give the approximation of orbital elements for the selected members of the Hilda group in the 3:2 mean motion resonance with Jupiter.