Computational and Applied Mathematics

, Volume 37, Supplement 1, pp 122–132 | Cite as

Comparison between Laplace-Lagrange secular theory and numerical simulation: the case of \(\upsilon \) Andromedae planetary system

  • Barbara C. B. CamargoEmail author
  • Othon C. Winter
  • Dietmar W. Foryta


The large increase in exoplanet discoveries in the last two decades showed a variety of systems whose stability is not clear. In this work, we chose the \(\upsilon \) Andromedae system as the basis of our studies in dynamical stability. This system has a range of possible masses, as a result of detection by radial velocity method, so we adopted a range of masses for the planets c and d and applied the secular theory. We also performed a numerical integration of the 3-body problem for the system over a time span of 30,000 years. The results exposed similarities between the secular perturbation theory and the numerical integration, as well as the limits where the secular theory did not present good results. The analysis of the results provided hints for the maximum values of masses and eccentricities for stable planetary systems similar to \(\upsilon \) Andromedae.


Secular theory Numerical simulation Exoplanets \(\upsilon \) Andromedae system Orbital stability 

Mathematics Subject Classification




The authors are grateful for the support from CAPES, Fapesp—proc 2016/24561-0 and CNPq—proc 312813/2013-9. We thank Gabriel Borderes Motta and Alexandros Ziampras for the suggestions. We also would like to acknowledge the hard work made by the referees.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018

Authors and Affiliations

  1. 1.Grupo de Dinâmica Orbital e PlanetologiaSao Paulo State University (UNESP)GuaratinguetaBrazil
  2. 2.Physics DepartmentFederal University of Parana (UFPR)CuritibaBrazil

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