# Does Newtonian physics work on a galactic scale?

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?

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.

• Thanks for the answer! What kind of phenomenon would I have to take into account when writing the simulation? – Ethan Bierlein Nov 22 '15 at 2:57
• One might add that newtonian physics emerges from underlying General Relativity laws, but GR effects are too 'weak' to be necessary to explore the mathematics for gallactic computations ( in contrast for the GPS system where great accuracy is necessary, the corrections are important) – anna v Nov 22 '15 at 8:52
• Ethan: first, which kind of solver do you plan to use ? SPH ? second: you will need to use a coarse resolution compare to objects. gaz condense or advect, stars migrates, so your particles have to exchange material. this is fluidish but not totally. there are also birth and depth of stars that modify the content (amount, nature and velocity of gaz). BTW stars and gaz don't travel at the same speed. Black matter is required, some people wonder whether magnetic fields could count. – Fabrice NEYRET Nov 22 '15 at 9:24
• Whilst I am no fan of MOND, I do think it unwise to be quite so dogmatic. Newtonian gravity may work on very large scales, if we also accept dark matter. Or it may have a problem when at the very large scales, as the MOND proponents claim. – Rob Jeffries Nov 22 '15 at 9:54
• well, physics is about models, and many galactic simulations do work with pure newtonian physics acting on a mix of star particles, gaz particles and black matter particles, which was quite the question. – Fabrice NEYRET Nov 23 '15 at 11:00

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.

• This is non mainstream physics and as such it does not belong on this site. The velocity curves have a well established explanation in the form of dark matter. – Javier Nov 29 '15 at 14:10
• Javier - If you haven't been paying attention to the news, LUX and $Xenon_{500}$ have ruled out any rational grounds for dark matter. In addition, the Higgs Boson discovered at the LHC appears to be the Standard Model Higgs Boson, which effectively eliminates SUSY. Your 'mainstream' cosmology has no rational foundation in particle science. The equation above is 'disprovable'. So if you are a scientists, then disprove it. – user32023 Nov 29 '15 at 14:21
• Two brief comments. As far as I can tell those experiments are looking for WIMPs, which are not the only candidate for dark matter, and the LHC has most definitely not ruled out SUSY. And just because I can't disprove your theory doesn't mean it's true. – Javier Nov 29 '15 at 15:07
• I said it has 'effectively' ruled out SUSY. The odds of supersymmetry existing in some form is about the same as purple unicorns. So while I can't say for certain that purple unicorns are the source of missing mass, I would certainly be irrational for trying to base a cosmology on such a principle. – user32023 Nov 29 '15 at 15:42
• And as far as my formula goes, this is how science works: You form a theory then someone tries to disprove it. If it's disproven, that's the end of the theory. The longer something lasts without being disproven, the more authority it has as a theory. I've provided a simple formula based on an expanding universe. If you don't believe it has a place on this forum, then it should be a simple matter to disprove it and we can settle this like scientists. – user32023 Nov 29 '15 at 15:45