Secular Orbit Evolution in Systems with a Strong External Perturber - A Simple and Accurate Model

Eduardo Andrade-Ines, Siegfried Eggl

Research output: Contribution to journalArticlepeer-review


We present a semi-analytical correction to the seminal solution for the secular motion of a planet's orbit under gravitational influence of an external perturber derived by Heppenheimer. A comparison between analytical predictions and numerical simulations allows us to determine corrective factors for the secular frequency and forced eccentricity in the coplanar restricted three-body problem. The correction is given in the form of a polynomial function of the system's parameters that can be applied to first-order forced eccentricity and secular frequency estimates. The resulting secular equations are simple, straight forward to use, and improve the fidelity of Heppenheimers solution well beyond higher-order models. The quality and convergence of the corrected secular equations are tested for a wide range of parameters and limits of its applicability are given.

Original languageEnglish (US)
Article number148
JournalAstronomical Journal
Issue number4
StatePublished - Apr 2017
Externally publishedYes


  • binaries: general
  • celestial mechanics
  • planets and satellites: dynamical evolution and stability
  • planets and satellites: formation

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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