Copernicus's big thing, beyond the specific physical concept, was that it led to the philosophical concept named for him, essentially the mediocrity principle, that one should generally assume most places are more or a less alike. It's one of the key assumptions of modern physics, essentially that if you zoom out far enough everything looks the same and the same rules apply everywhere. So the stars should be evenly spaced, you'll find structure, like the Local Fluff of stars or our Galaxy, or even some truly massive things like Sloan Great Wall, but if you zoom out far enough it should be a homogeneous blob. This is an assumption rather than a provable fact, but the evidence has tended to back it as time rolls on with most of the exceptions turning out not to be.
Now an infinite Universe with a finite number of stars is a different problem. In such a scenario those finite stars either have to be in a finite volume, rendering the rest of that universe irrelevant and weird, or effectively making one star per universe. A finite number divided by infinity is as near to nothing as makes no odds, as Douglas Adams said. X/∞ = 0 for any finite X. 1/∞=0, 2/∞=0, and 999,999,999,999/∞=0.
Now why that had to be the case, and I probably glossed over it, has to do with gravity, which like brightness is an inverse-square thing.Newton was saying all objects exert force onto each other and that that force gets weaker as the grow apart, but never dies off, very much like brightness and what causes the Olber Paradox. Picture two objects, left alone they exert force on each other, no matter how far away, and begin to pull closer and closer. In time they run into each other.
Now picture 3 objects, all in a line.
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The middle one is being tugged by each other equally and won't move. But that system isn't static or 'steady state', because the two end pieces are both pulling on each other and so is the middle. Those two edge stars will begin approaching the middle one.
However If I made a really long Straight Chain of stars, this process of them collapsing would be a lot slower.
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The stars near the middle are being pulled by the edge stars about the same in each direction and the far stars are barely getting pulled on at all, but they'd still collapse eventually. If this chain was infinitely long each star would have an infinite number of stars to left and right and be pulled each way evenly. They'd never move, a infinite chain of stars would be steady state. The 2D version, an infinite plane, has the same effect. Ditto a 3D version, an infinite Universe. Only when it is infinite, and homogeneous at large scale, is a steady state solution possible. Otherwise a pre-Hubble Universe begins collapsing as soon as formed and to even exist requires someone wave a magic wand to put them all there.
It was a good question, hopefully I gave a good answer
- Albert Einstein
King of Cairhien 20-7-2
Chancellor of the Landsraad, Archduke of Is'Mod