Yes, galaxies do move. ... Galaxies rotate around their centers with the sections of the galaxy that are farther out from the galaxy's center rotating more slowly than the material closer to the center. Galaxies are also moving away from each other due to the expansion of the Universe brought on by the Big Bang.
Are galaxies moving randomly?
For nearby galaxies, these motions are somewhat random. For example, our Milky Way Galaxy is moving toward the Andromeda Galaxy. But on larger scales, scientists have discovered that the entire universe is expanding, causing all groupings of galaxies to move away from one another over time.
Is the Milky Way a galaxy moving?
The Milky Way as a whole is moving at a velocity of approximately 600 km per second with respect to extragalactic frames of reference. The oldest stars in the Milky Way are nearly as old as the Universe itself and thus probably formed shortly after the Dark Ages of the Big Bang.