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I was reading a book where Precession of Mercury's perihelion was described using general relativity. There I found the following equation:

$$ F \approx \frac{G M_m M_s}{r^2}\left(1+\frac{\alpha}{r^2}\right) $$ Where $\alpha$, he states to be expressed by speed of light, mass of sun, eccentricity of the orbit. This equation seems to be an extension of Newton's Gravitational Law but the author didn't specify how the equation came. Can anyone provide with the derivation of this equation or any reference?

Thomas Fritsch
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Afsara Tasnia Disha
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  • Also see https://en.wikipedia.org/wiki/Post-Newtonian_expansion although that article doesn't go into much detail. – PM 2Ring Dec 02 '19 at 12:11
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    Could you provide reference for the expression you cite? It is different from the usual post-Newtonian approximation provided in the Q&A indicated as duplicate by @JohnRennie and it is not explicitely contained in the wikipedia page cited by PM2Ring If it is really different it could be a case for reopening your question. – GiorgioP-DoomsdayClockIsAt-90 Dec 02 '19 at 13:27
  • The book is Computational Physics by Nicholas J. Giordano and Hisao Nakanishi 2nd Edition. It's mentioned in section 4.3, page 108 – Afsara Tasnia Disha Dec 04 '19 at 08:43
  • I do not have access to that book. However, I think the formula you cite is wrong. The first correction to Newton's formula should go like $1/r^3$ and not $1/r^4$. – GiorgioP-DoomsdayClockIsAt-90 Dec 10 '19 at 06:36

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