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We present a semi-analytical correction to the seminal solution for thesecular motion of a planet's orbit under gravitational influence of an externalperturber derived by Heppenheimer (1978). A comparison between analyticalpredictions and numerical simulations allows us to determine corrective factorsfor the secular frequency and forced eccentricity in the co-planar restrictedthree-body problem. The correction is given in the form of a polynomialfunction of the system's parameters that can be applied to first-order forcedeccentricity and secular frequency estimates. The resulting secular equationsare simple, straight forward to use and improve the fidelity of Heppenheimer'ssolution well beyond higher-order models. The quality and convergence of thecorrected secular equations are tested for a wide range of parameters andlimits of its applicability are given.

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