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I am researching Mercury's orbital precession. I have considered most perturbations and general relativity. I am still not satisfied. I need your help.

I need a solution to Exercise 13, Chapter 6, in Ref. 1 (which is Exercise 26, Chapter 7, in both Ref. 2 and Ref. 3).

The exercise is copied below:

Show that the relativistic motion of a particle in an attractive inverse square law of force is a precessing motion. Compute the precession of the perihelion of Mercury resulting from this effect. (The answer, about 7" per century, is much smaller than the actual precession of 43" per century which can be accounted for correctly only by general relativity.)

I have the solution to Exercise 7, Chapter 3.

References:

  1. H. Goldstein, Classical Mechanics, 1st edition, 1959.

  2. H. Goldstein, Classical Mechanics, 2nd edition, 1980.

  3. H. Goldstein, Classical Mechanics, 3rd edition, 2000.

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This paper might help you: arxiv.org/pdf/1012.5438v1 –  Pulsar May 24 '13 at 8:46
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