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

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 Planétaire 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.

92 pages, 15 figures

References in corpus (10)

• Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology
• Observational constraint on the radius and oblateness of the lunar core-mantle boundary
• Spin-orbit coupling for close-in planets
• The coupling between inertial and rotational eigenmodes in planets with liquid cores
• Rotation of a rigid satellite with a fluid component. A new light onto Titan's obliquity
• Cassini states of a rigid body with a liquid core
• Tidal synchronization of an anelastic multi-layered body: Titan's synchronous rotation
• Tidal friction in satellites and planets. The new version of the creep tide theory
• Homogeneous model for the TRAPPIST-1e planet with an icy layer
• Rotation of a synchronous viscoelastic shell

Cited by in corpus (2)

• Equivalence between simple multilayered and homogeneous laboratory-based rheological models in planetary science
• A Simplified Model for the Forced Libration of Icy Moons with Subsurface Oceans: Application to Enceladus and Mimas