A dynamical study of Hilda asteroids in the Circular and Elliptic RTBP

TL;DR

This study investigates the stability and dynamics of Hilda asteroids using the Circular Restricted Three-Body Problem, revealing stable periodic orbits and emphasizing the importance of frequency analysis over traditional orbital elements.

Contribution

The paper demonstrates the existence of stable periodic orbits in the CRTBP for Hilda asteroids and highlights the effectiveness of frequency analysis for classification.

Findings

Stable periodic orbits exist around Hilda asteroids in the CRTBP.

Frequencies of quasi-periodic motions match well between CRTBP and ERTBP models.

Frequency analysis outperforms orbital elements in classifying Hilda asteroids.

Abstract

The Hilda group is a set of asteroids whose mean motion is in a 3:2 orbital resonance with Jupiter. In this paper we use the planar Circular Restricted Three-Body Problem (CRTBP) as a dynamical model and we show that there exists a family of stable periodic orbits that are surrounded by islands of quasi-periodic motions. We have computed the frequencies of these quasi-periodic motions and we have shown how the Hilda family fits inside these islands. We have compared these results with the ones obtained using the Elliptic Restricted Three-Body Problem and they are similar, showing the suitability of the CRTBP model. It turns out that, to decide if a given asteroid belongs to the Hilda class, it is much better to look at its frequencies in the planar CRTBP rather than to use two-body orbital elements as it is commonly done today.