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Resonant Laplace-Lagrange theory for extrasolar systems in mean-motion resonance

  • M. SansotteraEmail author
  • A.-S. Libert
Original Article
  • 29 Downloads
Part of the following topical collections:
  1. 50 years of Celestial Mechanics and Dynamical Astronomy

Abstract

Extrasolar systems with planets on eccentric orbits close to or in mean-motion resonances are common. The classical low-order resonant Hamiltonian expansion is unfit to describe the long-term evolution of these systems. We extend the Lagrange-Laplace secular approximation for coplanar systems with two planets by including (near-)resonant harmonics and realize an expansion at high order in the eccentricities of the resonant Hamiltonian both at orders one and two in the masses. We show that the expansion at first order in the masses gives a qualitative good approximation of the dynamics of resonant extrasolar systems with moderate eccentricities, while the second order is needed to reproduce more accurately their orbital evolutions. The resonant approach is also required to correct the secular frequencies of the motion given by the Laplace-Lagrange secular theory in the vicinity of a mean-motion resonance. The dynamical evolutions of four (near-)resonant extrasolar systems are discussed, namely GJ 876 (2:1 resonance), HD 60532 (3:1), HD 108874 and GJ 3293 (close to 4:1).

Keywords

Extrasolar systems n-Body problem Mean-motion resonances Perturbation theory 

Notes

Acknowledgements

The authors seize the opportunity of the Topical Collection for the 50th birthday of CM&DA to dedicate this paper to the memory of Jacques Henrard. This work follows the path traced in his two contributions published in the first volume of Celestial Mechanics. The work of M. S. has been partially supported by the National Group of Mathematical Physics (GNFM-INdAM). Computational resources have been provided by the PTCI (Consortium des Équipements de Calcul Intensif CECI), funded by the FNRS-FRFC, the Walloon Region, and the University of Namur (Conventions No. 2.5020.11, GEQ U.G006.15, 1610468 et RW/GEQ2016).

Compliance with ethical standards

Conflicts of interest

The authors have no conflict of interest to declare.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MilanMilanItaly
  2. 2.naXys, Department of MathematicsUniversity of NamurNamurBelgium

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