A galaxy is a pretty degenerate instance of the n-body problem, though. A system of one or two giant bodies orbited by a collection of tiny ones. Each tiny one

A galaxy is a pretty degenerate instance of the n-body problem, though. A system of one or two giant bodies orbited by a collection of tiny ones. Each tiny one spends most of its time in a very weakly-perturbed two-body problem, quasi-stably orbiting the giant one(s) with tiny deviations caused by all the other ones. So you have to do some statistics to see how often an assumed distribution of quasi-stable orbits results in the tiny bodies approaching each other closely enough to kick one another into meaningfully different orbits of the giant ones. This gives you a better idea of how long is "long" and how it compares to the age of the universe