The advance of perihelion, in particular for Mercury, is regarded as a classical test of general relativity, but a number of other (in some cases much larger) contributions to this phenomenon are seldom discussed in detail in textbooks. This paper presents a unified framework for evaluating the advance of perihelion due to (a) general relativity, (b) the solar quadrupole moment, and (c) planetary perturbations, the last in a ring model where the mass of each perturbing planet is “smeared out” into a coplanar circular orbit. The exact solution of the ring model agrees to within 4% with the usually quoted figure. Time-dependent contributions beyond the ring model contain some surprising features: they are not small, and some with long periods could mimic a secular advance.

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This is analogous to a simple harmonic oscillator with natural frequency 1 and responding at the driving frequency m.

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This is analogous to a simple harmonic oscillator driven at resonance, and responding with secular terms.

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Whether Pluto is regarded as a planet is irrelevant.

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This is evidenced by the first-order expansion in X=ra in arriving at their Eq. (10).

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In our formalism and in that of Stewart,22 it does not matter whether the expansion is carried out around u1=a1 or u2=σ1, since all terms are kept.

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