What approximations lead to Mercury's perihelion advance formula?

[NoobixCube]

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.

 

[Mentz114]

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.

 

[HallsofIvy]

"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".

 

[NoobixCube]

Thanks for the input guys