A Hamiltonian for 1/1 Rotational Secondary Resonances, and Application to Small Satellites of Saturn and Jupiter

TL;DR

This paper analyzes the rotational dynamics of small Saturn and Jupiter satellites, revealing secondary resonances that influence their libration amplitudes and providing an analytical Hamiltonian framework for understanding these phenomena.

Contribution

The study applies and extends Hamiltonian theory to characterize secondary resonances in satellite rotation, offering new insights into their libration behavior.

Findings

Secondary resonances exist in satellite rotation phase space.

Libration amplitudes are larger near secondary resonances.

Current satellite rotations are likely influenced by these resonances.

Abstract

In this work, we study the dynamics of rotation of the small satellites Methone and Aegaeon and revisit previous works on the rotation of Prometheus, Metis, and Amalthea. In all cases, the surfaces of section computed with the standard spin-orbit model reveal that the synchronous regime with small amplitude of libration shares another large domain in the phase space. We reproduce and apply the hamiltonian theory given in Wisdom (2004) to analytically characterize the detected structure as being a secondary resonance where the period of oscillation of the physical libration is similar to the orbital period of the satellite. We also show that the amplitude of libration around the secondary resonance is always larger than in the case of the other mode. Since the current rotational states of these sorts of satellites should be synchronous, our results can be considered in evolutionary studies of their rotation.