Obliquity of Mercury with a fluid core and a deformable mantle

¹ LTE, Observatoire de Paris, Université PSL, Sorbonne Université, Université de Lille, LNE, CNRS, 61 Avenue de l’Observatoire, 75014 Paris, France
² Instituto de Matemática e Estatística, Universidade de São Paulo, R. do Matão, 1010, São Paulo, SP 05508-090, Brazil

^★ Corresponding authors: valentin.etienne@obspm.fr; gwenael.boue@obspm.fr; ragazzo@usp.br

Received: 9 May 2025
Accepted: 8 June 2025

Abstract

In anticipation of BepiColombo’s orbital insertion in 2026, this study revisits the rotation of Mercury, modelling it with a fluid core and a deformable mantle. For this well-established physical model, we provide an analytical solution based on a novel Lagrangian formalism. Our approach enables a comprehensive 3D solution for the mantle’s orientation, including the phase in longitude at the perihelion. The model incorporates dissipative torques from core-mantle boundary friction and tidal deformations, conservative pressure torques, and the effect of the planet’s apsidal precession. We validate the equilibrium positions obtained numerically in previous studies, but identify discrepancies in earlier analytical works. These inconsistencies overestimated the out-of-Cassini-plane offset induced by tidal deformation by a factor of 100. Additionally, we explore the parameter space to determine where the spin axis deviates most from the Cassini plane and identify a region exhibiting bifurcation in the spin axis equilibrium position. This region cannot be adequately analysed using a model linearised with respect to the obliquity angle.