Many body problems with contact forces, like grains of sand on a beach, are quite hard to solve satisfactorily with a computer. Is there a similar problem with galaxies where the stars are in gravitational contact, and could that be a factor in the problem with the galactic rotation curves not turning out as expected?
Grains of sand are still pretty tricky to model as convincing-looking sand. And as much as we use grains of sand as a metaphor for the number of stars in a galaxy, stars and sand can be a pretty poor comparison if you take the metaphor too far. Galaxies may appear to be solid objects in our skies, with tightly packed clusters of stars, but in fact, galaxies contain huge amounts of empty space. The problem is that for most galaxies, we don’t have the observing power required to distinguish the individual stars, and so the stellar multitudes blur their light together.
If we start to look around within our own galaxy – for instance around our own solar system – we can get a handle on just how much empty space we’re dealing with. Our Sun lives about two thirds of the way out from the center of our galaxy, so while we’re certainly not in the densest part of a galaxy, we’re by no means in a particularly vacant neighborhood either. The nearest stars to us, Alpha Centauri and Proxima Centauri, are 4 light years away. And looking at the diagram, you can see that that 4 light year distance is about as closely packed as the stars get in our neck of the galactic woods.
Now, Alpha Centauri raises an interesting point – Alpha Centauri is actually two stars. This is not uncommon in a galaxy. The two stars orbit each other as a binary system, and those two stars together travel around the galaxy’s core. However, the two stars are really not very close to each other at all. The two stars in Alpha Centauri are typically somewhere between 1 million miles and three million miles apart. That’s enough space to fit at least half our solar system between the two stars. At their narrowest, the two stars are separated by the distance between the Sun and Saturn.
Source: Jillian Scudder, PhD, Forbes – http://www.forbes.com/sites/jillianscudder/2016/10/16/astroquizzical-stars-touching/#6b0e19612184