A simple model for the location of Saturn's F ring

TL;DR

This paper presents a simplified gravitational model of Saturn's F ring, identifying stable regions where test particles form a narrow, aligned ring with sharp edges, influenced by resonances with shepherd moons Prometheus and Pandora.

Contribution

The study introduces a planar restricted five-body problem model that accurately predicts the stable location and structure of Saturn's F ring, highlighting the role of resonances and dynamical stability indicators.

Findings

Stable test particle regions form a narrow, aligned ring.

Resonances with Prometheus and Pandora influence ring edges.

Comparison shows some agreement with observed F ring data.

Abstract

In this paper, we introduce a simplified model to understand the location of Saturn's F ring. The model is a planar restricted five-body problem defined by the gravitational field of Saturn, including its second zonal harmonic $J_2$, the shepherd moons Prometheus and Pandora, and Titan. We compute accurate long-time numerical integrations of (about 2.5 million) non-interacting test-particles initially located in the region between the orbits of Prometheus and Pandora, and address whether they escape or remain trapped in this region. We obtain a wide region of initial conditions of the test particles that remain confined. We consider a dynamical stability indicator for the test particles' motion defined by computing the ratio of the standard deviation over the average value of relevant dynamical quantities, in particular, for the mean-motion and the semi-major axis. This indicator separates clearly a subset of trapped initial conditions that appear as very localized stripes in the initial semi-major axis and eccentricity space for the most stable orbits. Retaining only these test particles, we obtain a narrow eccentric ring which displays sharp edges and collective alignment. The semi-major axis of the accumulation stripes of the stable ring-particles can be associated with resonances, mostly involving Prometheus' outer Lindblad and co-rotation resonances, but not exclusively. Pandora's inner Lindblad and co-rotation resonances as well as low-order three-body resonances typically coincide with gaps, i.e., regions of instabilities. Comparison of our results with the nominal data for the F ring shows some correspondence.