Question

How do we know that galaxies are moving away from the center of the universe?

Answer 1

And in fact, the farther away a galaxy is the faster it is moving away from us. The galaxies seem to be receding from us because the entire universe is getting larger. The space in between the galaxies is stretching! And the farther away a galaxy is the more space there is to stretch so the faster the galaxy appears to move away from us.

Over the past half-century astronomers have observed many other facts about the universe that all point to the fact that the universe is expanding.