Galaxies as systems extended from the solar system

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    Galaxy Kepler Rotation
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Discussion Overview

The discussion revolves around the applicability of Kepler's third law to galaxies and whether galactic behavior can be modeled similarly to the Solar System. Participants explore the implications of using Newtonian mechanics and general relativity in understanding galaxy dynamics, as well as the role of dark matter and alternative theories like Modified Newtonian Dynamics (MOND).

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants question whether it is a valid assumption that galaxies should follow Kepler's third law, suggesting that the Solar System may not be a sufficient example for such a broad assumption.
  • Others assert that galaxies do not follow Kepler's laws, which are applicable only to two masses, and instead are modeled using Newton's laws, with some suggesting that general relativistic corrections are negligible.
  • One participant proposes that galactic behavior is purely Newtonian, emphasizing the need to understand dark matter.
  • Another viewpoint suggests that while Newton's laws are applicable, there may be a need to consider general relativistic corrections in a Newtonian framework.
  • Some participants mention Modified Newtonian Dynamics (MOND) as a potential modified theory to explore, but note that it is not the only model available and may be considered a "toy-model."

Areas of Agreement / Disagreement

Participants do not reach a consensus on the applicability of Kepler's laws to galaxies, with multiple competing views on the correct modeling approach for galactic dynamics remaining unresolved.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the applicability of Kepler's laws and the definitions of the models being discussed, as well as the unresolved status of various mathematical steps in the proposed theories.

Martyn Arthur
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TL;DR
The application of Kepler's third law to galaxies
Is it a big assumption that Galaxies should follow Kepler's third law with rotation speeds decreasing with distance from the centre. Is the small tet of the behaviour of the Solar System not too small an example to make such a substantial assumption?
Thanks
Martyn
 
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Martyn Arthur said:
Is it a big assumption that Galaxies should follow Kepler's third law
They don't follow Kepler's laws. Those only apply to two masses.

They are modelled as following Newton's laws (GR corrections are too small to worry about).
Martyn Arthur said:
Is the small tet of the behaviour of the Solar System not too small an example to make such a substantial assumption?
With the caveat that you mean Newton's laws not Kepler's the answer is:

1 - no, galactic behaviour is purely Newtonian, we just need to work out what dark matter is.

2 - sort of, we need to include general relativistic corrections to a Newtonian model.

3 - yes, all we need to do is work out how the modified theory, Modified Newtonian Dynamics (MOND), works.

Take your pick which is the correct one...
 
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Thank you!
Martyn
 
Ibix said:
They don't follow Kepler's laws. Those only apply to two masses.
Technically they apply to problems of central motion in a Kepler potential (proportional to 1/r). The second law applies more generally to any central potential as it is related to conservation of angular momentum. However, the first and third laws are contingent on the problem actually being a Kepler central potential.

The gravitational two-body problem of course reduces to a Kepler central potential problem once the center of mass motion is factored out.
 
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Ibix said:
They don't follow Kepler's laws. Those only apply to two masses.

They are modelled as following Newton's laws (GR corrections are too small to worry about).

With the caveat that you mean Newton's laws not Kepler's the answer is:

1 - no, galactic behaviour is purely Newtonian, we just need to work out what dark matter is.

2 - sort of, we need to include general relativistic corrections to a Newtonian model.

3 - yes, all we need to do is work out how the modified theory, Modified Newtonian Dynamics (MOND), works.

Take your pick which is the correct one...
There is more than one modified theory. MOND is not the only game in town and is at best a "toy-model".
 

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