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Stability maps for the 5/3 mean motion resonance between Ariel and Umbriel with inclination

Published online by Cambridge University Press:  16 October 2024

Sérgio R. A. Gomes Open the ORCID record for Sérgio R. A. Gomes [Opens in a new window]  and
Alexandre C. M. Correia
Sérgio R. A. Gomes*
Affiliation:
CFisUC, Departamento de Física, Universidade de Coimbra, 3004-516 Coimbra, Portugal
Alexandre C. M. Correia
Affiliation:
CFisUC, Departamento de Física, Universidade de Coimbra, 3004-516 Coimbra, Portugal IMCCE, Observatoire de Paris, PSL Université, 77 Av. Denfert-Rochereau, 75014 Paris, France
*
email: sergio.ra.gomes@outlook.com
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Abstract

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The evolution of the five largest satellites of Uranus during the crossing of the 5/3 mean motion resonance between Ariel and Umbriel is strongly affected by chaotic motion. Studies with numerical integrations of the equations of motion and analysis of Poincaré surface sections provided helpful insights to the role of chaos on the system. However, they lack of a quantification of this chaos in the phase-space. Here, we construct stability maps using the frequency analysis method. We determine that for low energies (small eccentricity and/or inclinations), the phase-space is mainly stable. As the energy increases, the chaotic regions replace the stable motion, until only small, localized libration regions remain stable.

Keywords

Celestial mechanicsdynamical evolution and stabilitytides
Type
Contributed Paper
Information
Proceedings of the International Astronomical Union , Volume 18 , Symposium S382: Complex Planetary Systems II: Latest Methods for an Interdisciplinary Approach , December 2022 , pp. 103 - 109
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of International Astronomical Union

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