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

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Cited by in corpus (11)

• Orbital Stability of Circumstellar Planets in Binary Systems
• Long-Term Stability of Tightly Packed Multi-Planet Systems in Prograde, Coplanar, Circumstellar Orbits within the $\alpha$ Centauri AB System
• Long-Term Stability of Planets in the $\alpha$ Centauri System, II: Forced Eccentricities
• Exomoons in Systems with a Strong Perturber: Applications to $\alpha$ Cen AB
• Obliquity Evolution of Circumstellar Planets in Sun-like Stellar Binaries
• Evolution of $\alpha$ Centauri B's protoplanetary disc
• Updated Studies on Exomoons in the HD 23079 System
• Fear the Shadows of the Giants: On Secular Perturbations in Circumstellar Habitable Zones of Double Stars
• On the stability of planetary orbits in binary star systems I. The S-type orbits
• Moon-packing around an Earth-mass Planet
• Secular Dynamics of Multiplanetary Circumbinary Systems