In the 1910s Vesto Slipher found that the spectral lines of most galaxies are redshifted: they are moving away from us. In 1929 Edwin Hubble combined those speeds with distances from Cepheids and found a simple pattern (Georges Lemaître had predicted it two years earlier): the farther a galaxy, the faster it recedes, in proportion.
Why it works
The rule is $v = H_0 d$, the Hubble–Lemaître law. $H_0$, the Hubble constant, is measured at about $70$ km/s per megaparsec (recent measurements range from about 67 to 73). Why proportional? Imagine space itself stretching evenly, like a sheet of rubber with dots on it, or raisin bread rising. If every distance grows by $1\%$ in some time, a galaxy $100$ Mpc away moves $1$ Mpc farther while one $200$ Mpc away moves $2$ Mpc: twice the distance, twice the speed. And the same is true seen from any dot. So the law is exactly what uniform expansion of the universe looks like from inside it. (For galaxies far away, the redshift is best understood as light's wavelength stretching along with space.)
Key idea
Hubble–Lemaître law: $v = H_0 d$, with $H_0 \approx 70$ km/s/Mpc. Galaxies recede faster the farther away they are, because the universe is expanding, everywhere at once.
Worked examples
Worked example: Speed from distance
How fast does a galaxy $100$ Mpc away recede, with $H_0 = 70$ km/s/Mpc?
- $v = 70 \times 100 = 7000$ km/s.
Answer: $7000$ km/s.
Worked example: Distance from a redshift
A galaxy's lines are shifted by $z = \Delta\lambda/\lambda = 0.02$. How far is it?
- For small $z$, $v = cz = 3.00 \times 10^{5} \times 0.02 = 6000$ km/s.
- $d = \frac{v}{H_0} = \frac{6000}{70} = 86$ Mpc, about 280 million light-years.
Answer: About $86$ Mpc.
Common mistake
Since nearly every galaxy is moving away from us, it can seem that we must be at the center of everything. But in a uniformly expanding universe, every observer sees the same thing: all the other galaxies receding, faster when farther. There is no center. Check with the raisin bread: pick any raisin, and all the others move away from it as the dough rises.