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?
 A: 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.
A: 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.
