I Galaxies as systems extended from the solar system

[Martyn Arthur]

TL;DR Summary

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

 

[Ibix]

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).

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...

 

[Martyn Arthur]

Thank you!
Martyn

 

[Orodruin]

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.

 

[ohwilleke]

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".