# Hubble’s Law

Between 1922 to 1923 American astronomer Edwin Hubble carried out a survey of Cepheid variable stars in what were known at the time as “spiral nebulae”. As the period of variability of these stars is related to their intrinsic brightness, he was able to determine their distances from Earth and prove that these spiral nebulae were in fact distant galaxies, far beyond the limits of our own.

Hubble also established a linear relationship between a galaxy’s distance and the red-shift in its spectrum, which is now known as Hubble’s law.

## Redshift

This redshift is the result of the Doppler effect, which causes light from objects moving away from the observer to be shifted towards the red end of the spectrum (see relativity theory).

This suggested that distant galaxies are receding away from us and therefore that the universe is expanding. Up until the discovery of this universal red-shift it had generally been believed that the universe was static. In fact, Albert Einstein had famously introduced a “cosmological constant” to correct for the fact that his mathematical model of the universe, given by his theory of general relativity, suggest that a static universe would not be stable and must be either expanding or contracting. Einstein later referred to his failure to recognise that his equations suggested an expanding universe as his “biggest blunder”.

## The Hubble Constant

Since the recession velocity of a distant galaxy is related to its apparent red-shift, Hubble’s law can be expressed mathematically as:
v = H0D
Where v is the recession velocity of the galaxy, D is its distance from Earth and H0 is a constant of proportionality known as the Hubble constant.

It should be noted, however, that although red-shift is proportional to distance, its relationship to recessional velocity of a distant galaxy actually depends on the exact cosmological model of the expansion of the universe that is being assumed. The Hubble constant is time dependent. The Hubble constant H0 is replaced by a Hubble parameter H when considering the rate of expansion of the universe over different times or for the universe as a whole.

## Age of the Universe

The discovery that the universe is expanding led to the proposal of the big bang theory. This theory suggests that, at some point in the distant past, all of space-time itself was concentrated at a single point.

Obtaining a value for the Hubble constant therefore allowed the first rough estimates of the age of the universe to be made.

It was discovered in 1998, through observations of type Ia supernovae in extremely distant galaxies, that the rate of expansion of the universe is increasing. Prior to this discovery, it had been assumed that the expansion of the universe was slowing down. Taking this into account led to our current estimate for the age of the universe of around 13.8 billion years.