Librations of a body composed of a deformable mantle and a fluid core

TL;DR

This paper develops a comprehensive 3D model for the rotational dynamics of celestial bodies with deformable mantles and fluid cores, enabling better understanding of librations and their physical interpretations.

Contribution

It introduces a new, physically interpretable, and easily implementable 3D model for body librations considering linear viscoelastic mantle rheology.

Findings

Validated model with Moon, Earth, and Mercury data

Formulas for free librations in various spin-orbit states

Insights into mantle hydrostaticity and deformation effects

Abstract

We present fully three-dimensional equations to describe the rotations of a body made of a deformable mantle and a fluid core. The model in its essence is similar to that used by INPOP (Integration Plan\'{e}taire de l'Observatoire de Paris), e.g. Viswanathan et al. (2019), and by JPL (Jet Propulsion Laboratory), e.g. Folkner et al. (2014), to represent the Moon. The intended advantages of our model are: straightforward use of any linear-viscoelastic model for the rheology of the mantle; easy numerical implementation in time-domain (no time lags are necessary); all parameters, including those related to the "permanent deformation", have a physical interpretation. The paper also contains: 1) A physical model to explain the usual lack of hydrostaticity of the mantle (permanent deformation). 2) Formulas for free librations of bodies in and out-of spin-orbit resonance that are valid for any linear viscoelastic rheology of the mantle. 3) Formulas for the offset between the mantle and the idealized rigid-body motion (Peale's Cassini states). 4) Applications to the librations of Moon, Earth, and Mercury that are used for model validation.