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

Abstract

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 (1978). A comparison between analytical predictions and numerical simulations allows us to determine corrective factors for the secular frequency and forced eccentricity in the co-planar 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 Heppenheimer's 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.

13 pages, 6 figures, accepted for publication in The Astronomical Journal

References in corpus (4)

• Direct detection of exoplanet host star companion gamma Cep B and revised masses for both stars and the sub-stellar object
• Eccentricity evolution in hierarchical triple systems with eccentric outer binaries
• Secular dynamics of planetesimals in tight binary systems: Application to Gamma-Cephei
• Titan's rotation: A 3-dimensional theory

Cited by in corpus (2)

• Long-Term Stability of Planets in the $\alpha$ Centauri System, II: Forced Eccentricities
• Secular Dynamics of Multiplanetary Circumbinary Systems