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Well, I'm searching for a rigorous derivation of the famous "perihelium precession problem in General Relativity".
Did anyone do it...?
Daniel.
Did anyone do it...?
Daniel.
dextercioby asked for a rigorous approach, pervect I think you'll find that to justify the procedure you outlined rigorously you do need elliptic functions.pervect said:It's fairly easy and straightforwards to work out that the full relativistic treatment of the Schwarzschild orbit involves only replacing coordinate time with proper time, the r coordinate with the Schwarzschild coordinate by the same name (r), and adding an extra term to the Hamiltonian, proportional to 1/r^3
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There's no real need for elliptic functions with this approach.
The Perihelium Precession Problem is a phenomenon observed in the orbit of Mercury around the Sun. It refers to the slight shift in the point at which Mercury is closest to the Sun (perihelion) every time it completes an orbit. This shift cannot be fully explained by classical mechanics and was one of the first pieces of evidence that led to the development of the theory of General Relativity.
General Relativity is a theory of gravity that was developed by Albert Einstein in the early 20th century. It is used to explain the behavior of objects in the presence of strong gravitational fields, such as the Sun. General Relativity predicts that the curvature of space-time around massive objects, like the Sun, can cause the orbit of a smaller object, like Mercury, to deviate from what is expected in classical mechanics. This deviation is what causes the Perihelium Precession Problem.
The derivation of the Perihelium Precession Problem in General Relativity is a complex mathematical process that involves the use of Einstein's field equations and the Schwarzschild metric. The equations are used to calculate the curvature of space-time around the Sun, and the resulting effects on the orbit of Mercury are then calculated. The final result is an equation that predicts the amount of precession that should occur in Mercury's orbit due to the curvature of space-time.
Yes, the Perihelium Precession Problem has been observed in the orbit of other planets, such as Venus and Earth. However, the magnitude of the precession is much smaller for these planets compared to Mercury, making it more difficult to detect. This further supports the validity of General Relativity as a theory of gravity.
No, the Perihelium Precession Problem is no longer considered a mystery. The predictions made by General Relativity have been confirmed by numerous experiments and observations, including the Perihelium Precession Problem. This problem was one of the first pieces of evidence that led to the acceptance of General Relativity as the most accurate theory of gravity we have today.