Hubble’s Law and the expansion of the universe
In the first two decades of the 20th century, astronomers began to measure the velocities of nearby galaxies in our line of sight using the Doppler shift (see chapter 3). The majority of these velocities were away from us, i.e. the galaxies are receding from us. A few galaxies, such as the Andromeda Galaxy, M31, are moving towards us. Edwin Hubble was also trying to estimate the distances of the galaxies, using Cepheid variable stars (see chapter 4).
In 1929 Hubble announced, based on the distances of 18 galaxies, that the more distant a galaxy, the faster it is moving away from us:
velocity / distance = constant.
This constant is called the Hubble constant, or H0 (see chapter 9). Hubble’s Law is often called the redshift–distance law, because the recession velocities of galaxies are measured by the shifting of their spectral lines towards the red end of the visible spectrum. This turned out to be just what would be expected in an expanding universe, the simplest possible model for the universe in Einstein’s General Theory of Relativity (see chapter 6).
For very high velocities (i.e. galaxies receding at a substantial fraction of the speed of light) the full and more complicated version of the redshift formula is used. Here the true distance to and velocity of the object being observed depends on the model of the universe in use.
The redshift z does give a relatively simple indication of how the scale of the universe has changed. If Rnow is the scale factor (one measure of distance between two galaxies) in the present day and Rthen the scale factor at the time when light left the galaxy being observed, then in this case the two are related by
1 + z = Rnow / Rthen
(1 + z) is then the factor by which the universe has expanded in the time taken for the light to travel from the galaxy to the telescope looking at it.
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