On the rotational dynamics of Prometheus and Pandora

TL;DR

This study investigates the rotational states of Saturn's moons Prometheus and Pandora, revealing potential chaotic rotation and proposing that certain phase space structures may prevent capture into regular synchronous rotation.

Contribution

It provides a detailed numerical analysis of the stability and chaos in the rotation of Prometheus and Pandora, introducing the idea of phase space belts as barriers to synchronous capture.

Findings

Rotation may be chaotic for both satellites.

Attitude instability zones form concentric belts around the synchronous resonance.

Chaotic rotation can mimic regular synchronous behavior for extended periods.

Abstract

Possible rotation states of two satellites of Saturn, Prometheus (S16) and Pandora (S17), are studied by means of numerical experiments. The attitude stability of all possible modes of synchronous rotation and the motion close to these modes is analyzed by means of computation of the Lyapunov spectra of the motion. The stability analysis confirms that the rotation of Prometheus and Pandora might be chaotic, though the possibility of regular behaviour is not excluded. For the both satellites, the attitude instability zones form series of concentric belts enclosing the main synchronous resonance center in the phase space sections. A hypothesis is put forward that these belts might form "barriers" for capturing the satellites in synchronous rotation. The satellites in chaotic rotation can mimic ordinary regular synchronous behaviour: they preserve preferred orientation for long periods of time, the largest axis of satellite's figure being directed approximately towards Saturn.