Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-10-28T04:29:34.087Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
Check for updates
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of International Astronomical Union

References

Alves-Carmo, A. J., Vaillant, T., & Correia, A. C. M. 2023, Dynamics of trans-Neptunian objects near the 3/1 mean-motion resonance with Neptune. Astronomy and Astrophysics, 677, A83.CrossRefGoogle Scholar
Couetdic, J., Laskar, J., Correia, A. C. M., Mayor, M., & Udry, S. 2010, Dynamical stability analysis of the HD 202206 system and constraints to the planetary orbits. Astronomy and Astrophysics, 519, A10.CrossRefGoogle Scholar
Dermott, S. F., Malhotra, R., & Murray, C. D. 1988, Dynamics of the Uranian and Saturnian satellite systems - A chaotic route to melting Miranda? Icarus, 76, 295–334.CrossRefGoogle Scholar
Dumas, H. S. & Laskar, J. 1993, Global dynamics and long-time stability in Hamiltonian systems via numerical frequency analysis. Physical Review Letters, 70(20), 2975–2979.CrossRefGoogle ScholarPubMed
Gastineau, M. & Laskar, J. 2011, Trip: A computer algebra system dedicated to celestial mechanics and perturbation series. ACM Commun. Comput. Algebra, 44(3/4), 194–197.CrossRefGoogle Scholar
Gomes, S. R. A. & Correia, A. C. M. 2023, Effect of the inclination in the passage through the 5/3 mean motion resonance between Ariel and Umbriel. Astronomy and Astrophysics, 674, A111.CrossRefGoogle Scholar
Ida, S., Ueta, S., Sasaki, T., & Ishizawa, Y. 2020, Uranian satellite formation by evolution of a water vapour disk generated by a giant impact. Nature Astronomy, 4, 880–885.CrossRefGoogle Scholar
Ishizawa, Y., Sasaki, T., & Hosono, N. 2019, Can the Uranian Satellites Form from a Debris Disk Generated by a Giant Impact? The Astrophysical Journal, 885(2), 132.CrossRefGoogle Scholar
Jacobson, R. A. 2014, The Orbits of the Uranian Satellites and Rings, the Gravity Field of the Uranian System, and the Orientation of the Pole of Uranus. The Astronomical Journal, 148(5), 76.CrossRefGoogle Scholar
Laskar, J. 1990, The chaotic motion of the solar system - A numerical estimate of the size of the chaotic zones. Icarus, 88, 266–291.CrossRefGoogle Scholar
Laskar, J. 1993, Frequency analysis for multi-dimensional systems. Global dynamics and diffusion. Physica D Nonlinear Phenomena, 67, 257–281.CrossRefGoogle Scholar
Peale, S. J. 1988, Speculative histories of the Uranian satellite system. Icarus, 74(2), 153–171.CrossRefGoogle Scholar
Pollack, J. B., Lunine, J. I., & Tittemore, W. C. Origin of the Uranian satellites. In Bergstralh, J. T., Miner, E. D., & Matthews, M. S., editors, Uranus 1991, pp. 469–512.CrossRefGoogle Scholar
Rufu, R. & Canup, R. M. 2022, Coaccretion + Giant-impact Origin of the Uranus System: Tilting Impact. The Astrophysical Journal, 928(2), 123.CrossRefGoogle Scholar
Smith, B. A., Soderblom, L. A., Beebe, R., Bliss, D., Boyce, J. M., Brahic, A., Briggs, G. A., Brown, R. H., Collins, S. A., Cook, A. F., Croft, S. K., Cuzzi, J. N., Danielson, G. E., Davies, M. E., Dowling, T. E., Godfrey, D., Hansen, C. J., Harris, C., Hunt, G. E., Ingersoll, A. P., Johnson, T. V., Krauss, R. J., Masursky, H., Morrison, D., Owen, T., Plescia, J. B., Pollack, J. B., Porco, C. C., Rages, K., Sagan, C., Shoemaker, E. M., Sromovsky, L. A., Stoker, C., Strom, R. G., Suomi, V. E., Synnott, S. P., Terrile, R. J., Thomas, P., Thompson, W. R., & Veverka, J. 1986, Voyager 2 in the Uranian System: Imaging Science Results. Science, 233(4759), 43–64.CrossRefGoogle ScholarPubMed
Squyres, S. W., Reynolds, R. T., & Lissauer, J. J. 1985, The enigma of the Uranian satellites’ orbital eccentricities. Icarus, 61(2), 218–223.CrossRefGoogle Scholar
Szulágyi, J., Cilibrasi, M., & Mayer, L. 2018, In Situ Formation of Icy Moons of Uranus and Neptune. The Astrophysical Journal Letters, 868(1), L13.CrossRefGoogle Scholar
Thomas, P. C. 1988, Radii, shapes, and topography of the satellites of Uranus from limb coordinates. Icarus, 73(3), 427–441.CrossRefGoogle Scholar
Tittemore, W. C. 1990, Tidal heating of Ariel. Icarus, 87(1), 110–139.CrossRefGoogle Scholar
Tittemore, W. C. & Wisdom, J. 1988, Tidal evolution of the Uranian satellites I. Passage of Ariel and Umbriel through the 5:3 mean-motion commensurability. Icarus, 74(2), 172–230.CrossRefGoogle Scholar
Tittemore, W. C. & Wisdom, J. 1989, Tidal evolution of the Uranian satellites II. An explanation of the anomalously high orbital inclination of Miranda. Icarus, 78(1), 63–89.CrossRefGoogle Scholar
Tittemore, W. C. & Wisdom, J. 1990, Tidal evolution of the Uranian satellites III. Evolution through the Miranda-Umbriel 3:1, Miranda-Ariel 5:3, and Ariel-Umbriel 2:1 mean-motion commensurabilities. Icarus, 85(2), 394–443.CrossRefGoogle Scholar
Ćuk, M., Moutamid, M. E., & Tiscareno, M. S. 2020, Dynamical history of the uranian system. The Planetary Science Journal, 1(1), 22.CrossRefGoogle Scholar