Behavior of nearby synchronous rotation of a Poincar\'e-Hough satellite at low eccentricity

TL;DR

This study investigates the rotational behavior of a Poincaré-Hough satellite model with a fluid core, revealing complex dynamics such as polar motion and librations even at low orbital eccentricity.

Contribution

It provides a numerical analysis of the Poincaré-Hough model for satellites with fluid cores, highlighting the effects of core shape and flattening on rotational equilibria and dynamics.

Findings

Complex behaviors occur without orbital eccentricity.

Highly flattened cores induce polar motion and librations.

Core shape influences obliquity and equilibrium positions.

Abstract

This paper presents a study of the Poincar\'e-Hough model of rotation of the synchronous natural satellites, in which these bodies are assumed to be composed of a rigid mantle and a triaxial cavity filled with inviscid fluid of constant uniform density and vorticity. In considering an Io-like body on a low eccentricity orbit, we describe the different possible behaviors of the system, depending on the size, polar flattening and shape of the core. We use for that the numerical tool. We propagate numerically the Hamilton equations of the systems, before expressing the resulting variables under a quasi-periodic representation. This expression is obtained numerically by frequency analysis. This allows us to characterize the equilibria of the system, and to distinguish the causes of their time variations. We show that, even without orbital eccentricity, the system can have complex behaviors, in particular when the core is highly flattened. In such a case, the polar motion is forced by several degrees and longitudinal librations appear. This is due to splitting of the equilibrium position of the polar motion. We also get a shift of the obliquity when the polar flattening of the core is small.