Advance of Perihelion: Mercury's Formula & Approximations

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The formula for the advance of the perihelion of Mercury is given as :
\Delta T = \frac{c^{2}a(1-\epsilon^{2})P}{3GM_{sun}}
for the time taken to advance through 2\pi. I was wondering what approximations were made from the Schwarzschild solution to get to this result.
 
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The full derivation takes a couple of pages and the only approximation is near the end, when a Newtonian value is substituted into the full EOM with the assumption that

\frac{M}{r} << 1

An oscillating term is dropped from the result of this substitution. Please see any standard textbook of GR.
 
"The Mathematical Theory of Relativity" written by Sir Arthur Eddington, in the 1920's and still available through Dover Books, devotes a chapter to the derivation of the "advance of periheliion".
 
Thanks for the input guys
 

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