Advance of Perihelion: Mercury's Formula & Approximations

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Discussion Overview

The discussion centers on the formula for the advance of the perihelion of Mercury, specifically the derivation and approximations made from the Schwarzschild solution in General Relativity. The scope includes theoretical considerations and references to standard texts in the field.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents the formula for the advance of the perihelion and inquires about the approximations made from the Schwarzschild solution.
  • Another participant notes that the derivation involves a significant approximation at the end, where a Newtonian value is substituted under the assumption that M/r << 1, and mentions that an oscillating term is dropped as a result.
  • A third participant references a specific textbook, "The Mathematical Theory of Relativity" by Sir Arthur Eddington, which discusses the derivation of the advance of perihelion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the details of the approximations or the derivation process, indicating that multiple perspectives on the topic exist.

Contextual Notes

There are limitations regarding the assumptions made in the derivation, particularly the condition M/r << 1, and the implications of dropping the oscillating term are not fully explored.

NoobixCube
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The formula for the advance of the perihelion of Mercury is given as :
[tex]\Delta T = \frac{c^{2}a(1-\epsilon^{2})P}{3GM_{sun}}[/tex]
for the time taken to advance through [tex]2\pi[/tex]. 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

[tex]\frac{M}{r} << 1[/tex]

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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