Creep tide theory. Equations for differentiated bodies with aligned layers

TL;DR

This paper develops a set of equations based on creep tide theory to model the tidal evolution of differentiated, layered celestial bodies in co-rotation, providing a more compact formalism applicable to high eccentricity systems.

Contribution

It introduces a new, compact series expansion formulation of creep tide equations for differentiated bodies with aligned layers, extending previous models to high eccentricity cases.

Findings

Equations are equivalent to Darwin's but more compact.

Application to Enceladus demonstrates model's practical use.

Formulas valid for high eccentricity systems.

Abstract

The creep tide theory is used to establish the basic equations of the tidal evolution of differentiated bodies formed by aligned homogeneous layers in co-rotation. The mass concentration of the body is given by the fluid Love number $k_f$. The formulas are given by series expansions valid for high eccentricity systems. They are equivalent to Darwin's equations, but formally more compact. An application to the case of Enceladus, with $k_f=0.942$, is discussed.