An integrable model for first-order three-planet mean motion resonances

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An integrable model for first-order three-planet mean motion resonances. / Petit, Antoine C.

In: Celestial Mechanics and Dynamical Astronomy, Vol. 133, No. 8, 39, 2021.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Petit, AC 2021, 'An integrable model for first-order three-planet mean motion resonances', Celestial Mechanics and Dynamical Astronomy, vol. 133, no. 8, 39. https://doi.org/10.1007/s10569-021-10035-7

APA

Petit, A. C. (2021). An integrable model for first-order three-planet mean motion resonances. Celestial Mechanics and Dynamical Astronomy, 133(8), [39]. https://doi.org/10.1007/s10569-021-10035-7

Vancouver

Petit AC. An integrable model for first-order three-planet mean motion resonances. Celestial Mechanics and Dynamical Astronomy. 2021;133(8). 39. https://doi.org/10.1007/s10569-021-10035-7

Author

Petit, Antoine C. / An integrable model for first-order three-planet mean motion resonances. In: Celestial Mechanics and Dynamical Astronomy. 2021 ; Vol. 133, No. 8.

Bibtex

@article{48a7715698c74137944c0d8128738a84,
title = "An integrable model for first-order three-planet mean motion resonances",
abstract = "Recent works on three-planet mean motion resonances (MMRs) have highlighted their importance for understanding the details of the dynamics of planet formation and evolution. While the dynamics of two-planet MMRs are well understood and approximately described by a one-degree-of-freedom Hamiltonian, little is known of the exact dynamics of three-body resonances besides the cases of zeroth-order MMRs or when one of the bodies is a test particle. In this work, I propose the first general integrable model for first-order three-planet mean motion resonances. I show that one can generalize the strategy proposed in the two-planet case to obtain a one-degree-of-freedom Hamiltonian. The dynamics of these resonances are governed by the second fundamental model of resonance. The model is valid for any mass ratio between the planets and for every first-order resonance. I show the agreement of the analytical model with numerical simulations. As examples of application, I show how this model could improve our understanding of the capture into MMRs as well as their role in the stability of planetary systems.",
keywords = "Analytical, Exoplanets, Mean motion resonances, Planet formation, Stability",
author = "Petit, {Antoine C.}",
note = "Publisher Copyright: {\textcopyright} 2021, The Author(s).",
year = "2021",
doi = "10.1007/s10569-021-10035-7",
language = "English",
volume = "133",
journal = "Celestial Mechanics and Dynamical Astronomy",
issn = "0923-2958",
publisher = "Springer Netherlands",
number = "8",

}

RIS

TY - JOUR

T1 - An integrable model for first-order three-planet mean motion resonances

AU - Petit, Antoine C.

N1 - Publisher Copyright: © 2021, The Author(s).

PY - 2021

Y1 - 2021

N2 - Recent works on three-planet mean motion resonances (MMRs) have highlighted their importance for understanding the details of the dynamics of planet formation and evolution. While the dynamics of two-planet MMRs are well understood and approximately described by a one-degree-of-freedom Hamiltonian, little is known of the exact dynamics of three-body resonances besides the cases of zeroth-order MMRs or when one of the bodies is a test particle. In this work, I propose the first general integrable model for first-order three-planet mean motion resonances. I show that one can generalize the strategy proposed in the two-planet case to obtain a one-degree-of-freedom Hamiltonian. The dynamics of these resonances are governed by the second fundamental model of resonance. The model is valid for any mass ratio between the planets and for every first-order resonance. I show the agreement of the analytical model with numerical simulations. As examples of application, I show how this model could improve our understanding of the capture into MMRs as well as their role in the stability of planetary systems.

AB - Recent works on three-planet mean motion resonances (MMRs) have highlighted their importance for understanding the details of the dynamics of planet formation and evolution. While the dynamics of two-planet MMRs are well understood and approximately described by a one-degree-of-freedom Hamiltonian, little is known of the exact dynamics of three-body resonances besides the cases of zeroth-order MMRs or when one of the bodies is a test particle. In this work, I propose the first general integrable model for first-order three-planet mean motion resonances. I show that one can generalize the strategy proposed in the two-planet case to obtain a one-degree-of-freedom Hamiltonian. The dynamics of these resonances are governed by the second fundamental model of resonance. The model is valid for any mass ratio between the planets and for every first-order resonance. I show the agreement of the analytical model with numerical simulations. As examples of application, I show how this model could improve our understanding of the capture into MMRs as well as their role in the stability of planetary systems.

KW - Analytical

KW - Exoplanets

KW - Mean motion resonances

KW - Planet formation

KW - Stability

U2 - 10.1007/s10569-021-10035-7

DO - 10.1007/s10569-021-10035-7

M3 - Journal article

AN - SCOPUS:85112770788

VL - 133

JO - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

SN - 0923-2958

IS - 8

M1 - 39

ER -

ID: 327140069