Nutation-orbit resonances: The origin of the chaotic rotation of Hyperion and the barrel instability

TL;DR

This paper develops an analytical model of Hyperion's 3D spin-orbit dynamics, revealing that its chaotic rotation is due to nutation-orbit resonances, challenging previous beliefs of tumbling chaos and explaining long-term spin variations.

Contribution

The authors derive a Hamiltonian model for a 3D spinning satellite without simplifying assumptions, identifying nutation-orbit resonances as key to Hyperion's rotation behavior.

Findings

Hyperion's rotation is near or in a nutation-orbit resonance.

Hyperion's motion is less chaotic than previously thought.

Barrel instability relates to nutation-orbit resonances.

Abstract

While numerous planetary and asteroid satellites show evidence for non-trivial rotation states, none are as emblematic as Hyperion, which has long been held as the most striking example of chaotic spin-orbit evolution in the Solar System. Nevertheless, an analytically tractable theory of the full 3D spin-orbit dynamics of Hyperion has not been developed. We derive the Hamiltonian for a spinning axisymmetric satellite in the gravitational potential of a planet without assuming planar or principal axis rotation and without averaging over the spin period. Using this model, we demonstrate the emergence of resonances between the nutation and orbital frequencies that act as the primary drivers of the spin dynamics. This analysis reveals that, contrary to long-held belief, Hyperion is not tumbling chaotically. Instead, it lies near or in a nutation-orbit resonance that is first-order in eccentricity, allowing it to rotate quasi-regularly. The most reliable observations are consistent with either nonchaotic motion or chaos that is orders of magnitude smaller than originally claimed. A separate phenomenon, the so-called barrel instability, is shown to be related to a different set of nutation-orbit resonances that generalize the planar spin-orbit resonances. Finally, we show that changes in spin states over long timescales are best understood by considering chaotic diffusion of quasi-conserved quantities.