They don’t. It’s a theory at best. Imagine an ant looking into a coke bottle and watching the clouds move, then deciding the world is expanding. There are too many variables for us to use something like red shift to identify expansion. An object moving away from us is not synonymous with expansion.
If humanity makes it, they might know if the universe is expanding in a couple thousand years. Right now, we really don’t know if the movement is related to orbits of these celestial bodies or some other wave manipulating effect in space.
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