How do we know that galaxies are moving away from the center of the universe?
Galaxies are moving away from each other.,
There is no center of universe. THe red shift in the spectrum shows the galaxies are red shifted.That is indication that they are moving naway from each other.
The universe has no centre to move away from.
If the universe had a centre, we would have a point of reference by which we could measure the speed of galaxies.
The theory of relativity effectively states that there is no point of reference. We can only measure the relative speeds of a galaxy with respect to another galaxy.
Galaxies are moving in all directions, but there is no point where we can say all galaxies are moving away from.
The concepts of centre or edge are meaningless when it comes to the universe. We live in a region we call the visible universe. It contains all of the objects which light has had time to reach us. What lies outside of this region we will never know.