Long-term orbital and rotational motions of Ceres and Vesta

TL;DR

This study analyzes the long-term orbital and rotational stability of Ceres and Vesta, revealing their obliquity variations and the influence of giant impacts and planetary perturbations on their rotational dynamics.

Contribution

The paper provides the first detailed long-term analysis of Ceres and Vesta's obliquity variations and rotational stability using symplectic integration and secular equations.

Findings

Ceres' obliquity varies between 2° and 20° over 20 million years.

Vesta's obliquity varies between 21° and 45°, potentially reaching 48° near resonance.

Perturbations from Jupiter and Saturn dominate the orbital dynamics of Ceres and Vesta.

Abstract

Context. The dwarf planet Ceres and the asteroid Vesta have been studied by the Dawn space mission. They are the two heaviest bodies of the main asteroid belt and have different characteristics. Notably, Vesta appears to be dry and inactive with two large basins at its south pole. Ceres is an ice-rich body with signs of cryovolcanic activity. Aims. The aim of this paper is to determine the obliquity variations of Ceres and Vesta and to study their rotational stability. Methods. The orbital and rotational motions have been integrated by symplectic integration. The rotational stability has been studied by integrating secular equations and by computing the diffusion of the precession frequency. Results. The obliquity variations of Ceres over $[-20:0]\,\mathrm{Myr}$ are between $2$ and $20{\deg}$ and the obliquity variations of Vesta are between $21$ and $45{\deg}$. The two giant impacts suffered by Vesta modified the precession constant and could have put Vesta closer to the resonance with the orbital frequency $2s_6-s_V$. Given the uncertainty on the polar moment of inertia, the present Vesta could be in this resonance where the obliquity variations can vary between $17$ and $48{\deg}$. Conclusions. Although Ceres and Vesta have precession frequencies close to the secular orbital frequencies of the inner planets, their long-term rotations are relatively stable. The perturbations of Jupiter and Saturn dominate the secular orbital dynamics of Ceres and Vesta and the perturbations of the inner planets are much weaker. The secular resonances with the inner planets also have smaller widths and do not overlap, contrary to the case of the inner planets.