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This is a relatively quick and informal sketch of a demonstration that general relativistic corrections to the bound Kepler orbits introduce a perihelion precession. Any decent textbook on the general theory of relativity will derive this result. My analysis aligns with that found in the good old text "Introduction to General Relativity", by Adler, Bazin and Schiffer.
Torre, Charles G., "Perihelion Precession in the General Theory of Relativity" (2017). Tutorials on... in 1 hour or less. Paper 10.
Additional FilesPerihelion.pdf (551 kB)