Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T09:45:40.108Z Has data issue: false hasContentIssue false
  • English
  • Français

Secular dynamics in extrasolar systems with two planets in mutually inclined orbits

Published online by Cambridge University Press:  30 May 2022

Rita Mastroianni Open the ORCID record for Rita Mastroianni [Opens in a new window]  and
Christos Efthymiopoulos
Rita Mastroianni
Affiliation:
Dep. of Mathematics Tullio Levi-Civita, University of Padua via Trieste 63, 35121 Padova, Italy email: [email protected]
Christos Efthymiopoulos
Affiliation:
Dep. of Mathematics Tullio Levi-Civita, University of Padua via Trieste 63, 35121 Padova, 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.

We revisit the problem of the secular dynamics in two-planet systems in which the planetary orbits exhibit a high value of the mutual inclination. We propose a ‘basic hamiltonian model’ for secular dynamics, parameterized in terms of the system’s Angular Momentum Deficit (AMD). The secular Hamiltonian can be obtained in closed form, using multipole expansions in powers of the distance ratio between the planets, or in the usual Laplace-Lagrange form. The main features of the phase space (number and stability of periodic orbits, bifurcations from the main apsidal corotation resonances, Kozai resonance etc.) can all be recovered by choosing the corresponding terms in the ‘basic Hamiltonian’. Applications include the semi-analytical determination of the actual orbital state of the system using Hamiltonian normalization techniques. An example is discussed referring to the system of two outermost planets of the ν-Andromedae system.

Keywords

Celestial mechanicsPlanetary systems
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. 191 - 196
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

Beaugé, C., Ferraz-Mello, S., Michtchenko, T.A. 2003, ApJ, 593, 1124 CrossRefGoogle Scholar
Deitrick, R., Barnes, R., McArthur, B., Quinn, T. R. Luger, R., Antonsen, A., Benedict, G. F. 2015, ApJ, 798, 46 CrossRefGoogle Scholar
Henrard, J., Libert, A.S. 2005, Dynamics of Populations of Planetary Systems IAU Colloq. 197, 49–54 CrossRefGoogle Scholar
Jacobi, M. 1842, Astr. Nachrichten, 20, 81 CrossRefGoogle Scholar
Kozai, Y. 1962, AJ, 67, 591–598 CrossRefGoogle Scholar
Laskar, J., Robutel, P. 1995, Cel. Mec. and Dyn. Astr., 62, 193–217 CrossRefGoogle Scholar
Laughlin, G., Chambers, J., Fischer, D. 2002, ApJ, 579, 455–467 CrossRefGoogle Scholar
Lee, M.H., Peale, S.J. 2003, ApJ, 592, 1201–1216 CrossRefGoogle Scholar
Libert, A.S., Henrard, J. 2007, Icarus, 191, 469–485 CrossRefGoogle Scholar
Libert, A.S., Tsiganis, K. 2009, A&A, 493, 677–686 Google Scholar
Marchesiello, A., Pucacco, G. 2016, Inter. Jour. of Bif. and Chaos, 26, 1630011 CrossRefGoogle Scholar
McArthur, B.E., Benedict, G.F., Barnes, R., Martioli, E., Korzennik, S., Nelan, Ed., Butler, R.P. 2010, ApJ, 715, 1203 CrossRefGoogle Scholar
Murray, C.D. and Dermott, S.F. 1999, Solar syst. dyn. Google Scholar
Naoz, S. 2016, ARAA, 54, 441–489 CrossRefGoogle Scholar
Robutel, P. 1995, Cel. Mec. and Dyn. Astr., 62, 219–261 CrossRefGoogle Scholar