The current orbit of Atlas (SXV)

TL;DR

This study investigates the chaotic nature of Atlas's current orbit, revealing it is in a chaotic boundary region near the 54:53 mean-motion resonance with Prometheus, with detailed analysis of resonance dynamics and stability challenges.

Contribution

The paper provides a detailed mapping of the Atlas-Prometheus 54:53 resonance, highlighting the chaotic regions and the difficulty of identifying long-term periodic motions.

Findings

Atlas's orbit is in a chaotic boundary region near the 54:53 resonance.

Resonance domains include chaotic layers and a narrow center.

Long-term periodic motion within the resonance is difficult to identify.

Abstract

With the success of the Cassini-Huygens mission, the dynamic complexity surrounding natural satellites of Saturn began to be elucidated. New ephemeris could be calculated with a higher level of precision, which made it possible to study in detail the resonant phenomena and, in particular, the 54:53 near mean-motion resonance between Prometheus and Atlas. For this task, we have mapped in details the domains of the resonance with dense sets of initial conditions and distinct ranges of parameters. Our initial goal was to identify possible regions in the phase space of Atlas for which some critical angles, associated with the 54:53 mean motion have a stable libration. Our investigations revealed that there is no possibility for the current Atlas orbital configuration to have any regular behavior since it is in a chaotic region located at the boundary of the 54:53 mean-motion resonance phase space. This result is in accordance with previous works (Cooper et al. 2015, Renner et al. 2016). In this work, we generalize such investigations by showing detailed aspects of the Atlas-Prometheus 54:53 mean-motion resonance, like the extension of the chaotic layers, the thin domain of the center of the 54:53 resonance, the proximity of other neighborhood resonances, among other secondary conclusions. In particular, we have also shown that even in the deep interior of the resonance, it is difficult to map periodic motion of the resonant pair for very long time spans.