Einstein's perihelion advance formula can be given a geometric interpretation in terms of the curvature of the ellipse. The formula can be obtained by splitting the constant term of an auxiliary polar equation for an elliptical orbit into two parts that, when combined, lead to the expression of this relativistic effect. Using this idea, we develop a general method for dealing with orbital precession in the presence of central perturbing forces, and apply the method to the determination of the total (relativistic plus Newtonian) secular perihelion advance of the planet Mercury.
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We shall consider cases in which the independent variable is u, v, and κ. Sometimes a primed expression can also mean a derivative evaluated at some point. This practice, here introduced for a graphical cleanliness of the formulas, while potentially confusing, actually causes no problems because the context always makes clear what is intended.
The residue secular effect would be of order . Therefore it can be neglected.
In Ref. 31, p. 294, ω depends on time, and so the angular mean motion n multiplies the constants A and B. Since the relation between θ and t is (Ref. 30, p. 41), it is evident that changing, in the equation of the secular motion, the variable from t to θ leaves the two constants A and B unchanged except that the factor n disappears.
