Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T20:51:05.315Z Has data issue: false hasContentIssue false
  • English
  • Français

Evolution and stability of Laplace-like resonances under tidal dissipation

Published online by Cambridge University Press:  30 May 2022

A. Celletti ,
E. Karampotsiou Open the ORCID record for E. Karampotsiou [Opens in a new window] ,
C. Lhotka ,
G. Pucacco  and
M. Volpi
A. Celletti
Affiliation:
Department of Mathematics, University of Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma (Italy) email: [email protected]
E. Karampotsiou
Affiliation:
Department of Mathematics, University of Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma (Italy) email: [email protected] Department of Physics, Aristotle University of Thessaloniki, 54124, Thessaloniki (Greece)
C. Lhotka
Affiliation:
Department of Physics, Aristotle University of Thessaloniki, 54124, Thessaloniki (Greece)
G. Pucacco
Affiliation:
Department of Physics, University of Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma (Italy)
M. Volpi
Affiliation:
Department of Mathematics, University of Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma (Italy) 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 Laplace resonance is a configuration that involves the commensurability between the mean motions of three small bodies revolving around a massive central one. This resonance was first observed in the case of the three inner Galilean satellites, Io, Europa, and Ganymede. In this work the Laplace resonance is generalised by considering a system of three satellites orbiting a planet that are involved in mean motion resonances. These Laplace-like resonances are classified in three categories: first-order (2:1&2:1, 3:2&3:2, 2:1&3:2), second-order (3:1&3:1) and mixed-order resonances (2:1&3:1). In order to study the dynamics of the system we implement a model that includes the gravitational interaction with the central body, the mutual gravitational interactions of the satellites, the effects due to the oblateness of the central body and the secular interaction of a fourth satellite and a distant star. Along with these contributions we include the tidal interaction between the central body and the innermost satellite. We study the survival of the Laplace-like resonances and the evolution of the orbital elements of the satellites under the tidal effects. Moreover, we study the possibility of capture into resonance of the fourth satellite.

Keywords

Celestial mechanicsPlanets and satellitesGeneral methodsNumerical
Type
Research Article
Information
Proceedings of the International Astronomical Union , Volume 15 , Symposium S364: Multi-scale (Time and Mass) Dynamics of Space Objects (Oct 2021) , October 2019 , pp. 128 - 133
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of International Astronomical Union

References

Celletti, A., Karampotsiou, E., Lhotka, C., Pucacco, G. & Volpi, M. 2021, arXiv e-prints, arXiv:2109.02694Google Scholar
David, T.J., Petigura, E.A., Luger, R. 2019, ApJ, 885, L12 CrossRefGoogle Scholar
Ellis, K.M. & Murray, C.D. 2000, Icarus, 147 129 CrossRefGoogle Scholar
Ferraz-Mello, S., Rodrguez, A. & Hussmann, H. 2008, Celestial Mechanics and Dynamical Astronomy, 101, 171 CrossRefGoogle Scholar
Lari, G., Saillenfest, M. & Fenucci, M. 2020 A&A, 639, A40 Google Scholar
Murray, C.D. & Dermott, S.F. 1999 Cambridge university press Google Scholar
Pichierri, G., Batygin, K., & Morbidelli, A., A&A, 625, A7 Google Scholar
Showman, A.P., & Malhotra, R. 1997, Icarus, 127, 93 CrossRefGoogle Scholar
Amari, S., Hoppe, P., Zinner, E., & Lewis, R.S. 1995, Meteoritics, 30, 490 CrossRefGoogle Scholar
Anders, E., & Zinner, E. 1993, Meteoritics, 28, 490 CrossRefGoogle Scholar
Bernatowicz, T.J., Messenger, S., Pravdivtseva, O., Swan, P., & Walker, R.M. 2003, Geochim. Cosmochim. Acta, 67, 4679 CrossRefGoogle Scholar
Busso, M., Gallino, R., & Wasserburg, G.J. 1999, ARAA, 37, 239 CrossRefGoogle Scholar
Croat, T.K., Stadermann, F.J., & Bernatowicz, T.J. 2005, ApJ, 631, 976 CrossRefGoogle Scholar
Draine, B.T. 2003, ARAA, 41, 241 CrossRefGoogle Scholar
Hoppe, P., & Zinner, E. 2000, J. Geophys. Res., A105, 10371 CrossRefGoogle Scholar
Hoppe, P., Ott, U., & Lugmair, G.W. 2004, New Astron. Revs, 48, 171 CrossRefGoogle Scholar
Lodders, K., & Fegley, B. 1998, Meteorit. Planet. Sci., 33, 871 CrossRefGoogle Scholar
Meyer, B.S., Clayton, D.D., & The, L.-S. 2000, ApJ (Letters), 540, L49 CrossRefGoogle Scholar
Nittler, L.R. 2003, Earth Planet. Sci. Lett., 209, 259 CrossRefGoogle Scholar
Nittler, L.R., Alexander, C.M.O’D., Gao, X., Walker, R.M., & Zinner, E. 1997, ApJ, 483, 475 CrossRefGoogle Scholar
Ott, U. 1993, Nature, 364, 25 CrossRefGoogle Scholar
Ott, U. 2002, New Astron. Revs 46, 513 CrossRefGoogle Scholar
Ott, U., Altmaier, M., Herpers, U., Kuhnhenn, J., Merchel, S., Michel, R., & Mohapatra, R.K. 2005, Meteorit. Planet. Sci., 40, 1635 CrossRefGoogle Scholar
Yin, Q.-Z., Lee, C.-T. A., & Ott, U. 2006, ApJ, 647, 676 CrossRefGoogle Scholar
Zinner, E. 1998, Ann. Rev. Earth Planet. Sci., 26, 147 CrossRefGoogle Scholar
Zinner, E. 2004, in: Turekian, K.K., Holland, H.D. & Davis, A.M. (eds.), Treatise in Geochemistry 1 (Oxford and San Diego: Elsevier), p. 17Google Scholar