How do you determine how quickly a distant galaxy is moving away from the earth?

Answer 1

Like sound, light waves moving away from the observer are stretched making the wavelength longer and when light comes toward us it appears to become compressed.

Since the bottom end of the spectrum is red and the top blue, an object which radiates light appears to be red shifted when it moves away from us as the light wave is stretched. It has been observed that all stars are red shifted, therefore the conclusion is that all stars are moving away from us in space.

This effect is called Doppler shift and is the reason a car engines note sounds higher as the car approaches and lower as it moves away from the listener.

Answer 2

Each star shines with its own light, and every star is different. But there are certain things that are constant, such as the spectrum lines for elements like hydrogen, helium, carbon and oxygen, and other heavier elements.

There is a phenomenon called the "Doppler efflect", named by Christian Doppler, an Austrian mathematician and physicist. (See the link below.) In the 1920's, spectral analysis of the light of distant galaxies revealed that the light spectra was shifted, and that the Doppler effect allowed astronomers to calculate the speed at which those galaxies were moving toward or away from us. With few exceptions, those galaxies are moving away, and the further away they are, the higher their velocities are.

Edwin Hubble suggested that the uniform motion away from Earth might suggest that rather than the Earth being unique in having a galactic case of terrible body odor, the universe was expanding. This took the uniqueness away from Earth or the Milky Way galaxy; hypothetical observers in ANY galaxy would perceive that everything was moving away from THEM as well. (An interesting sidenote; the Andromeda galaxy is actually getting CLOSER to the Milky Way, and will probably collide with us in about 3 billion years. Fasten your seat belts! )