Geodesic Equation & Orbital Surface Area Around the Sun

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Discussion Overview

The discussion revolves around the interpretation of the "s" in the geodesic equation, specifically in the context of orbital surface area around the Sun or other celestial bodies. Participants explore the meaning of "s" and its relationship to spacetime intervals and affine parameters, while addressing misconceptions regarding its association with surface area.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants assert that "s" in the geodesic equation refers to surface area for portions of an orbit, particularly around stars or black holes.
  • Others argue that "s" represents the spacetime interval along the geodesic and is more generally any affine parameter.
  • A participant questions whether "s" can be understood as possible paths along a gravitationally curved area and seeks clarification on how it is measured.
  • Another participant emphasizes that "s" has no relation to area and clarifies that it is measured differently depending on the nature of the path (timelike, spacelike, or lightlike).

Areas of Agreement / Disagreement

Participants disagree on the interpretation of "s" in the geodesic equation, with competing views on whether it relates to surface area or spacetime intervals. The discussion remains unresolved regarding the correct interpretation.

Contextual Notes

There are limitations in the discussion regarding the definitions of terms like "affine parameter" and the conditions under which "s" is measured. The relationship between "s" and surface area is particularly contested.

Philosophaie
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The "s" in the geodesic equation refers to the "surface area" for that portion of the orbit around a star or black hole.

For a small enough "delta t" the surface areas are the same.

Around a small star the orbital surface area (without the other interfering gravitational sources) would look something like an sphere or an ellipsoid.

How would you describe what the surface area and the geodesic equation around the Sun?
 
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Philosophaie said:
The "s" in the geodesic equation refers to the "surface area" for that portion of the orbit around a star or black hole.
No. It is the spacetime interval along the geodesic, not a surface area. More generally, s is any affine parameter.
 
DaleSpam said:
No. It is the spacetime interval along the geodesic, not a surface area. More generally, s is any affine parameter.

The Affine parameter is along a straight or parallel path in a gravitationally curved area.

Is "s" like possible paths along that curved area? How is it measured?
 
Philosophaie said:
The Affine parameter is along a straight or parallel path in a gravitationally curved area.
The affine parameter is defined along any curve. If additionally the affine parameter satisfies the geodesic equation then the curve is a geodesic and we can reasonably call it "straight".

Philosophaie said:
Is "s" like possible paths along that curved area? How is it measured?
Again, s has nothing whatsoever to do with area. Please get that mistaken idea out of your head. It is not an area.

If the path is timelike then s is measured with a clock, if the path is spacelike s is measured with a rod (possibly a curved rod), if the path is lightlike or mixed then s is measured with both clocks and rods.
 
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