Final answer:
Edwin Hubble proved that galaxies lie far beyond the Milky Way by showing a relationship between a galaxy's distance and its recession velocity. Using the 2.5-meter telescope to measure distances and velocities, he discovered that the universe is expanding, which was crucial for the acceptance of the Big Bang Theory.
Step-by-step explanation:
Edwin Hubble proved that galaxies lie far beyond the Milky Way by utilizing the capabilities of powerful telescopes, such as the 2.5-meter telescope at Mount Wilson Observatory. By the late 1920s, collaborating with Milton Humason, Hubble photographed the spectra of faint galaxies to obtain more accurate estimates of their distances. Their observations uncovered a direct correlation between the distance to a galaxy and its recession velocity, which is the speed at which the galaxy is moving away from us. This relationship, known as Hubble's Law, was instrumental in demonstrating that the universe was expanding, contradicting the prevailing belief at the time that the Milky Way contained all celestial bodies.
The realization of other galaxies' existence was a turning point in the perception of the cosmos, as many astronomers held the view until the 1920s that the universe consisted solely of the Milky Way. Hubble's discovery expanded our understanding of the universe and set the stage for the acceptance of the Big Bang Theory, further supported by observations of the Doppler shifts in light wavelengths from these distant galaxies.