Every point in the Universe is the center. If you off a ladder the earth is actually moving towards you while you remain at rest. But if you were observing the earth you would fall towards it. This is because the universe is expanding. Most people think of the universe as like a balloon being filled with air, this is not the nature of the universe. Therefore every single point in the universe is itself expanding.
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Yeah. I actually just made a post on universe expansion being a possible connection. But you bring up excellent points, more in depth!