Why Schwarzschild Metric for Deflection of Light & Precession of Perihelia?

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Discussion Overview

The discussion centers on the choice of the Schwarzschild metric over the FLRW metric for deriving the deflection of light by the sun and the precession of perihelia of planets. It explores the implications of using these metrics given the non-isotropic and non-static nature of the solar system.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants question why the Schwarzschild metric is preferred over the FLRW metric for specific calculations related to light deflection and planetary motion.
  • Others argue that the FLRW metric assumes a uniformly distributed matter, which is not a good approximation for the solar system scale.
  • It is noted that while the solar system is not isotropic or static, the Schwarzschild metric still provides a good approximation due to the Sun's significant mass relative to the total mass of the solar system.
  • A participant raises a question about the terminology of "precession of perihelia," specifically why the nearest distance from the sun is used for calculations instead of the aphelion distance.
  • Another participant responds that the use of perihelion distance is simply common practice in astronomy.

Areas of Agreement / Disagreement

Participants express varying views on the appropriateness of the Schwarzschild metric versus the FLRW metric, indicating that multiple competing perspectives remain regarding the best approach for these calculations.

Contextual Notes

Participants acknowledge limitations in the applicability of the Schwarzschild metric due to the solar system's non-isotropic and non-static characteristics, but do not resolve the implications of these limitations.

davidge
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Why one uses Schwarzschild metric instead of FLRW metric when deriving things such

- deflection of light by the sun
- precession of perihelia of planets

Also, as our solar system is not isotropic nor static, it seems that by using the Schwarzschild metric we would get only an approximation on the results. So why we still get accurate result for the precession of perihelia of Mercury?
 
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davidge said:
Why one uses Schwarzschild metric instead of FLRW metric when deriving things such

- deflection of light by the sun
- precession of perihelia of planets
Because the FLRW metric assumes that spacetime is filled with uniformly distributed matter. A bad approximation on the scale of the solar system.
davidge said:
Also, as our solar system is not isotropic nor static, it seems that by using Schwarzschild metric we get only a approximation on the results. So why we still get accurate result for precession of perihelia of Mercury?
Because it's a very good approximation because the mass of the Sun is such a huge percentage of the total mass of the solar system.
 
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Ah, ok. Thanks.

A bit off topic... but, the name precession of perihelia is due to the fact the we use the nearest distance ##r## of the planet from the sun when computing the angle? Is there a special motivation for non using the aphelion distance instead?
 
No, it's just common use in astronomy.
 
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vanhees71 said:
No, it's just common use in astronomy.
Thanks.
 

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