Hubble's Law
In the 1920s, one astronomer's painstaking measurements of galaxy redshifts revealed a startling pattern: almost every galaxy we can see is rushing away from us, and the further away it is, the faster it's going. That single observation reshaped our picture of the universe.
An unexpected pattern in galaxy redshifts
Using the redshift technique from the previous lesson, astronomers in the early twentieth century began systematically measuring the recession velocities of galaxies beyond our own. At the same time, independent methods (such as the use of standard candles, covered elsewhere in this module) allowed the distances to many of these same galaxies to be estimated. When the two sets of measurements — recession velocity and distance — were compared, a strikingly simple pattern emerged: galaxies further away were, on average, receding faster, and the relationship between the two was very close to directly proportional.
This empirical relationship is now known as Hubble's law:
where $v$ is a galaxy's recession velocity (found from its redshift, using the relationships from the previous lesson), $d$ is its distance from us, and $H_0$ is a constant of proportionality called the Hubble constant. The Hubble constant is found experimentally, by plotting recession velocity against distance for many galaxies and taking the gradient of the best-fit line — it is not something that can be derived from theory alone.
What Hubble's law tells us
Taken at face value, Hubble's law says something remarkable: essentially every distant galaxy is receding from us, and the further away a galaxy is, the faster it appears to be moving away. If the Milky Way sat at some special, privileged location at the centre of everything, this might just mean we happen to be avoided by all our neighbours. But the same pattern — proportionally faster recession with distance — is observed no matter which direction in the sky we look, and (as far as we can tell) would be observed from any other galaxy doing the same measurements too. The simplest and most natural interpretation is that this isn't really about galaxies moving through space away from us specifically, but about the space between all galaxies growing over time — in other words, evidence that the universe itself is expanding. The next lesson explores this interpretation, and its important subtleties, in full.
Estimating the age of the universe
Hubble's law also offers a strikingly simple way to estimate how long the universe has been expanding for. Rearranging $v = H_0 d$ gives
Since distance is speed multiplied by time, comparing this with $d = vt$ suggests treating $\dfrac{1}{H_0}$ as a rough estimate of a timescale — specifically, the time it would have taken every galaxy to reach its current distance if it has been moving away from us at a constant recession velocity $v$ the whole time. Running the expansion backward under that assumption, everything converges back to a single point at a time roughly $\dfrac{1}{H_0}$ in the past:
This gives a rough estimate for the age of the universe, of the right order of magnitude as more careful modern determinations. But it rests on a simplifying assumption that shouldn't be glossed over: it assumes $H_0$ has stayed constant throughout cosmic history, i.e. that the rate of expansion has never changed. In reality, the expansion rate has changed over time — affected by the gravitational pull of matter within the universe and, on the largest scales, by the effects of dark energy — so $\dfrac{1}{H_0}$ should be treated as an order-of-magnitude estimate for the universe's age, not an exact calculation.
Hubble's law converts two independently measurable quantities — a galaxy's redshift and its distance — into direct evidence that the universe is expanding, and even gives a rough handle on its age, using nothing more than a straight-line graph. Few single observations in the history of physics have reshaped our picture of the universe so dramatically.
Key takeaways
- Hubble's law states $v = H_0 d$: a galaxy's recession velocity is directly proportional to its distance from us, with the Hubble constant $H_0$ as the constant of proportionality.
- $H_0$ is determined experimentally, from the gradient of a graph of recession velocity (from redshift) against distance (from independent distance measurements) for many galaxies.
- Hubble's law can be used to find a galaxy's recession velocity given its distance, or its distance given its recession velocity.
- Because the pattern (more distant galaxies receding faster) holds in every direction, the simplest interpretation is that space itself is expanding, rather than our galaxy being at a special centre.
- Assuming the expansion rate has been constant, running $d = vt$ backward gives an estimate for the age of the universe of $t_{\text{age}} \approx \dfrac{1}{H_0}$.
- This age estimate rests on a simplifying assumption — that $H_0$ hasn't changed over cosmic history — and should be treated as a rough order-of-magnitude figure, not an exact result.
- Hubble's law is the key observational evidence explored fully in the next lesson, on the expansion of the universe.