It is important to clarify that Edwin Hubble did not use the Doppler effect directly to prove that the universe is expanding. Instead, he utilized the relationship between the Doppler shift and the recessional velocity of galaxies to support the idea of an expanding universe. Hubble's observations and subsequent analysis contributed to the development of the concept of the expanding universe.
In the 1920s, Hubble conducted extensive observations of galaxies using the 100-inch Hooker telescope at Mount Wilson Observatory. He focused on studying a particular class of variable stars called Cepheid variables, which have a well-known relationship between their intrinsic luminosity and pulsation period. By measuring the period and apparent brightness of Cepheid variables in distant galaxies, Hubble determined their distances from Earth using the known intrinsic luminosity of these stars.
Hubble noticed a remarkable correlation between the distances of galaxies and their measured recessional velocities. He found that galaxies farther away from us exhibited larger recessional velocities. This relationship became known as Hubble's Law. Hubble interpreted this correlation as evidence that the universe itself is expanding, with galaxies moving away from us in a manner akin to the stretching of space.
The connection between the Doppler effect and the change in wavelength of light from different positions comes into play here. The Doppler effect describes how the wavelength of light changes when the source of light or the observer is in motion relative to each other. When an object emitting light moves away from an observer, the wavelengths of the light waves become stretched or "redshifted." Conversely, when an object approaches an observer, the wavelengths become compressed or "blueshifted."
Hubble connected the concept of the Doppler effect to the observed redshifts in the spectra of distant galaxies. He found that the spectral lines of these galaxies were shifted towards longer (redder) wavelengths compared to their laboratory measurements. This redshift indicated that the galaxies were moving away from us, consistent with an expanding universe.
By quantifying the relationship between the observed redshift (which corresponds to the recessional velocity) and the distance to galaxies, Hubble provided evidence for the expansion of the universe. Hubble's Law, combined with subsequent developments in cosmology and the discovery of the cosmic microwave background radiation, led to the formulation of the Big Bang theory, which suggests that the universe originated from a dense and hot initial state and has been expanding ever since.