Title: 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.