Rotation of a synchronous viscoelastic shell

TL;DR

This paper models the rotational response of a viscoelastic icy crust on natural satellites, accounting for elastic and dissipative effects, to better understand their librations and obliquity variations.

Contribution

It introduces a novel iterative algorithm combining numerical rotation simulations with tensor of inertia filtering to model viscoelastic crustal responses.

Findings

Algorithm works well in elastic case without resonance

Tidal dissipation introduces phase lags affecting convergence

Provides a framework for studying rotational dynamics of icy shells

Abstract

Several natural satellites of the giant planets have shown evidence of a global internal ocean, coated by a thin, icy crust. This crust is probably viscoelastic, which would alter its rotational response. This response would translate into several rotational quantities, i.e. the obliquity, and the librations at different frequencies, for which the crustal elasticity reacts differently. This study aims at modelling the global response of the viscoelastic crust. For that, I derive the time-dependency of the tensor of inertia, which I combine with the time evolution of the rotational quantities, thanks to an iterative algorithm. This algorithm combines numerical simulations of the rotation with a digital filtering of the resulting tensor of inertia. The algorithm works very well in the elastic case, provided the problem is not resonant. However, considering tidal dissipation adds different phase lags to the oscillating contributions, which challenge the convergence of the algorithm.