A simple method is presented for calculating the effect of a perturbing central force on an elliptic Keplerian orbit. It has the advantage of being direct, and along the lines of the conventional canonical perturbation theory of celestial mechanics. It is applied to the problem of Mercury’s perihelion precession using for the averaged radial force an expression derived by Price and Rush [Am. J. Phys. 47, 531 (1979)].

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