# Hubble's Law

Hubble’s law is an observed relationship between the distance to far-off objects in the universe and the speed with which they are moving away from us. These observations tell us that the universe is expanding, and allow us to estimate the age of the universe.

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**Experimental Basis**

The distance to certain objects in the universe (such as type 1a supernovae) may be determined using standard candle methods. The speed at which these objects are moving towards or away from us may be determined by analyzing the radiation from them in terms of the Doppler effect.

It turns out that all distant galaxies are moving away from us, and that the speed at which they are receding is approximately proportional to their distance. The constant of proportionality between recessional velocity \((v)\) and distance \((d)\) is known as Hubble's constant \(H_0:\)

\[v = H_0d.\]

This graph is for illustrative purposes only and does not represent real data.

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**Implications**

The first and obvious implication of Hubble's law is that the universe is expanding.

The second is that for distant galaxies we can use Hubble's law to estimate their distance when there is no other method available.

The third is that, since very distant galaxies still nearly fit a linear relationship, despite the fact that the light reaching us left them a long time into the past, the universe has been expanding at a nearly constant rate for most of its lifte time.

Finally, if we assume that the Big Bang theory of the universe's origins is correct, and all matter has expanded from almost a single position a finite length of time ago, we can use Hubble's law to estimate that time--the age of the universe. We can do this by dividing the distance to very distant objects by the speed at which they are receding, to calculate how long they have been moving away from us: \(t = \frac{d}{v}.\) This age, \(t,\) is also given by \(t = \frac{1}{H_0}.\)

The graph below shows the distance and recessional velocity of a number of distant galaxies. Assuming the universe started with a "Big Bang" in which all of these galaxies were crammed into a small area of space, and that they have all been moving apart at a constant speed since then, estimate the age of the universe in years.

Note: 1 megaparsec is \(\num{3.09e22}\) years.