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What was the exact method by which Hubble discovered the red-shift of distant galaxies?
How did he determine the distance to these galaxies?
Hubble used a technique called the period-luminosity relationship to determine the distances to these galaxies. This technique involves observing variable stars, known as Cepheid variables, and using their pulsation period to determine their intrinsic brightness. By comparing this intrinsic brightness to their observed brightness, Hubble was able to calculate their distance using a mathematical relationship between the two.