Does Newtonian physics work on a galactic scale?

Ethan Bierlein 11/21/2015. 2 answers, 256 views
newtonian-mechanics newtonian-gravity dark-matter galaxies galaxy-rotation-curve

I'm currently working on a simulation that aims to use Newton's Law of Gravitation to simulate how a galaxy behaves gravitationally. While I haven't gotten the simulation finished yet, I have had a few people tell me that Newtonian Physics don't work on a galactic scale, and that I need a different model to accurately simulate a galaxy gravitationally.

Is this true?

2 Answers

Fabrice NEYRET 11/22/2015.

Yes, Newtonian Physics works on a galactic scale.

Still, for long distance interactions on fast objects you might want to take into account the finite speed of gravity, but I don't think it is necessary for ordinary galaxies simulations. Conversly a lot of phenomena occur that impact the galactic material: writting a decent simulation is not easy.

Mike Doonsebury 11/29/2015.

No, Newton's Second Law of motion is only an approximation and doesn't work on anything larger than a solar system. When you get into the domain where the acceleration is on the order of $10^{-14}\space km\space s^{-2}$, then you can see limits of the approximation. Stars at the edges of spiral galaxies travel much too fast to be governed by Newton's Second Law of Motion. Even backfilling a galaxy with some imaginary matter won't fix the problem. Take a look at the data for Andromeda and you'll see a rising velocity curve beyond 30 kpc that clearly conflicts with the predicted Newtonian decay.

The second law can be easily fixed, however:

$$\sum_{i} F_i = m(a_F + a_0)$$ $$a_0 = 3.74\times 10^{-14}\space km\space s^{-2}$$ Applying this to a circular orbit gives: $$v = \sqrt{\frac{M G}{r} + a_0r} $$ Where $a_F$ is the acceleration of the unbalancing force (gravity in the case of an orbiting star) and $a_0$ is the constant acceleration of the expansion of the universe. Go ahead and try it! It will fix any velocity curve problem you have without resorting to science fiction.

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