Final answer:
Edwin Hubble discovered that the more distant a galaxy is from us, the faster it is moving away, which supported the theory of a universally expanding universe and the Big Bang theory.
Step-by-step explanation:
Edwin Hubble showed that, with the exception of our nearest neighbors, the more distant a galaxy is from us, the faster it is moving away from us.
By observing the redshift in the hydrogen spectra of these galaxies, which is proportional to their distance, Hubble concluded that there is a cosmological red shift due to the expansion of space itself. This meant that photons experience a stretching of their wavelength as they travel through expanding space, leading to the observed redshift.
This observation is a cornerstone of the Big Bang theory, indicating that the universe is expanding and that distant galaxies move faster away from us as their distance increases. This universal expansion suggests that what we observe as a redshift for galaxies moving away from us would be a blueshift if they were moving towards us.