The observation that galaxies farther away from Earth move away from us faster is known as Hubble's law, which is a fundamental principle of cosmology. It is based on the empirical observation that the universe is expanding.
The key concept behind this observation is the expansion of space itself. According to the Big Bang theory, the universe originated from an extremely dense and hot state and has been expanding ever since. As space expands, it carries galaxies and other celestial objects along with it.
The rate of expansion is not uniform throughout the universe but instead follows a pattern. The farther a galaxy is from us, the more space there is between us and that galaxy. As space expands, it causes galaxies to move away from each other, and the velocity of this motion is directly proportional to their distance.
This relationship between the distance and velocity of galaxies is described by Hubble's law, which states that the recessional velocity (or apparent velocity of recession) of a galaxy is proportional to its distance:
v = H0 * d
where v is the recessional velocity, H0 is the Hubble constant (representing the rate of expansion), and d is the distance of the galaxy from us.
Therefore, galaxies that are farther away from us appear to be moving away at faster velocities simply because they are located in regions of space that are expanding faster. It is important to note that this observation does not imply that galaxies themselves are moving through space; rather, it is the expansion of space that is causing the apparent motion.