The influence of orbital dynamics, shape and tides on the obliquity of Mercury

TL;DR

This study investigates how orbital dynamics, shape, and tidal effects influence Mercury's obliquity, providing refined initial conditions for long-term simulations and quantifying the impact of various parameters on its orientation.

Contribution

It offers a method to set initial conditions for Mercury's obliquity simulations and assesses the influence of parameters like J3, tides, and orbital variations on obliquity.

Findings

J3 affects obliquity by 250 milli-arcsec

Tides influence obliquity by 100 milli-arcsec

Secular orbital variations change obliquity by 10 milli-arcsec

Abstract

Earth-based radar observations of the rotational dynamics of Mercury (Margot et al. 2012) combined with the determination of its gravity field by MESSENGER (Smith et al. 2012) give clues on the internal structure of Mercury, in particular its polar moment of inertia C, deduced from the obliquity (2.04 +/- 0.08) arcmin. The dynamics of the obliquity of Mercury is a very-long term motion (a few hundreds of kyrs), based on the regressional motion of Mercury's orbital ascending node. This paper, following the study of Noyelles & D'Hoedt (2012), aims at first giving initial conditions at any time and for any values of the internal structure parameters for numerical simulations, and at using them to estimate the influence of usually neglected parameters on the obliquity, like J3, the Love number k2 and the secular variations of the orbital elements. We use for that averaged representations of the orbital and rotational motions of Mercury, suitable for long-term studies. We find that J3 should alter the obliquity by 250 milli-arcsec, the tides by 100 milli-arcsec, and the secular variations of the orbital elements by 10 milli-arcsec over 20 years. The resulting value of C could be at the most changed from 0.346mR^2 to 0.345mR^2.