Subsection 2.4 · Chapter 2

Hubble’s Law& the ExpandingUniverse

At the end of the last lesson we found almost every galaxy racing away from us. Edwin Hubble explained why. By measuring galaxies' distances with pulsating Cepheid stars, and their speeds from the redshift of their light, he uncovered a stunningly simple rule — the farther a galaxy, the faster it flees — and read from it both the age of the Universe and the expansion of space itself, the long echo of the Big Bang.

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Distance and Speed

At the end of the last lesson (§2.3) we left a loose thread: almost every galaxy in the sky is rushing away from us. That single fact rewrote our picture of the cosmos — but pinning it down meant measuring two stubbornly difficult things for every galaxy: exactly how far away it is, and exactly how fast it is moving. Edwin Hubble, working at California's Mount Wilson Observatory in the 1920s with the largest telescope on Earth, found a way to measure both — and from enough galaxies, a breathtakingly simple pattern falls out.

Start with distance — and it sounds impossible, because we cannot stretch a tape measure across space. The trick is a standard candle: an object whose true brightness we know in advance. A lamp of known wattage looks dimmer the farther off it is, in a precise way — four times farther away makes it one-quarter as bright — so comparing how bright something truly is with how bright it merely looks gives its distance at once. The whole problem becomes: how do you know a star's true brightness without already knowing how far away it is?

The answer came from Henrietta Leavitt, an astronomer at Harvard, who in 1912 studied a class of pulsating stars called Cepheids — giant stars that swell and shrink in a steady rhythm, brightening and dimming over days to weeks. Studying Cepheids in a nearby satellite galaxy, the Small Magellanic Cloud, Leavitt found something remarkable: the slower a Cepheid pulses, the brighter it truly is, and the relationship is exact. So you simply time a Cepheid's blink, and its period tells you its true luminosity — its real wattage. It is a candle that announces its own brightness. Drag the slider in the figure below to time a Cepheid and watch its true brightness, and its distance, follow.

A PULSING CEPHEIDBRIGHTNESS OVER TIME31 daysLEAVITT’S LAW · 191225102040601k10k50kPULSATION PERIOD (days)TRUE BRIGHTNESS (× Sun)Andromeda’s Cepheid
31 days
2 days · faint & near60 days · brilliant & far
1 · Pulsation period
31 days
what we time
2 · True brightness
22,100× the Sun
from Leavitt's law
3 · Distance
2.5 Mly
from how faint it looks
Andromeda’s Cepheid. Near 31 days you reach the kind of star Hubble timed in Andromeda in 1925. It lies 2.5 million light-years off — far beyond the Milky Way’s 100,000-light-year span — so Andromeda is a galaxy all its own.
Fig. 2.4.aA Cepheid is a cosmic yardstick. Drag the slider (or use ← / →) to pick a Cepheid’s pulsation period. Henrietta Leavitt’s 1912 law turns that period into the star’s true luminosity; comparing that to how faint it looks gives its distance. Near 31 days you land on the Cepheid Edwin Hubble found in Andromeda — 2.5 million light-years off, proof it is a galaxy all its own.

Hubble pointed the great 100-inch telescope at the faint smudge then known as the Andromeda Nebula and found Cepheids inside it. Reading their periods gave their true brightness; their faintness gave the distance — and the answer was staggering. Even Hubble's rough first estimate in 1925 (about 900,000 light-years, which we now know was an underestimate) placed Andromeda far outside our own Milky Way, whose disk is only some 100,000 light-years across. Andromeda was not a cloud within our galaxy at all, but a separate galaxy of its own — an "island universe," in the language of the day. Modern measurements put it at 2.5 million light-years. At a stroke, the known universe grew from a single galaxy to a sky strewn with billions of them (§2.2).

The second number — how fast a galaxy moves — is hidden in its light. Recall from §0.4 that the colour of light is set by its wavelength, the tiny distance between one wave crest and the next, and that starlight spread into a spectrum is crossed by dark lines at fixed wavelengths — the chemical fingerprints of the elements in the star. Those lines are the key.

You already know the effect by ear. When a train or ambulance races past, its pitch drops the instant it passes: rushing toward you, its sound waves are squeezed shorter and the pitch rises; rushing away, they are stretched longer and the pitch falls. This is the Doppler effect, and light does the same. A galaxy moving away has its light waves stretched to longer wavelengths — shifted toward the red end of the spectrum — and the faster it recedes, the bigger the shift. Astronomers call it the galaxy's redshift. Find the fingerprint lines in a galaxy's spectrum, measure how far they have slid toward red, and you have its speed. Slide the control in the figure below to send a galaxy racing away and watch its spectrum redden.

AT REST · IN THE LABORATORYAS WE RECEIVE IT · REDSHIFTED THE LIGHT WAVE, STRETCHEDemittedreceived400 nm500 nm600 nm700 nm
z = 0.040
at rest · no shiftracing away · strongly redshifted
Redshift z
0.040
the measured stretch
Recession speed
11,752 km/s
≈ 3.9% of light
The Hα line
656 → 683 nm
shifted toward red
Fig. 2.4.bReceding galaxies turn red. Drag (or use ← / →) to send the galaxy racing away. Every dark line in its spectrum slides toward the red end, and the light wave is stretched longer — the cosmological redshift. The bigger the shift, the faster the galaxy recedes; measuring it gives the speed. A passing train’s whistle is the intuition, but here it is space itself stretching the light as it travels.

One subtlety matters, and we will return to it: a galaxy's redshift is not really the train-whistle Doppler effect. The galaxies are not so much speeding through space as being carried apart by space — which stretches every light wave crossing it. The train is a good first picture; the truth is stranger, and it is exactly where this lesson is headed.

The Expanding Universe

By 1929 Hubble had both numbers — distance and speed — for a few dozen galaxies, and he did the obvious thing: he plotted one against the other. The result is one of the most consequential graphs ever drawn. The points did not scatter at random; they fell along a straight line through the origin. The farther a galaxy, the faster it recedes — and not vaguely, but in exact proportion: a galaxy twice as far away flees twice as fast. This is Hubble's law. Tilt the line yourself in the figure below to find the slope that fits the galaxies, and read off what that slope implies.

015030045060003,5007,00010,50014,000DISTANCE (million light-years)RECESSION SPEED (km/s)slope = H₀
H₀ = 21 km/s/Mly
shallow · old universesteep · young universe
Hubble constant 21 km/s/Mly
implied age (1 / H₀) 14.3 billion years
Best fit. Out to hundreds of millions of light-years, the straight line is unmistakable. The slope, about 21 km/s for every million light-years, gives an age near 14 billion years — close to the true 13.8 billion. Switch to Hubble's 1929 data (press 1) to see how little he had to go on.
Fig. 2.4.cDistance against speed — a straight line. Each dot is a galaxy: its distance across, its recession speed up. Drag the line’s slope (← / →) to fit the cloud — that slope is the Hubble constant, and its inverse, 1 / H₀, is a rough age for the Universe. Near 21 km/s per million light-years the line threads the data and the age lands at about 14 billion years. Press 1 / 2 to compare Hubble’s sparse 1929 data with a modern survey.

The steepness of that line — how much extra speed you gain for each extra step of distance — is the Hubble constant, written H₀. Its value is about 21 kilometres per second for every million light-years: a galaxy a million light-years away recedes at roughly 21 km/s, one two million light-years off at twice that, and so on outward. (Pinning the exact figure down is famously hard — today's best measurements disagree by a few percent, an open puzzle astronomers call the Hubble tension.) Hubble was not quite first to the idea: the Belgian priest-astronomer Georges Lemaître had derived the same expanding universe two years earlier, in 1927, and Vesto Slipher had measured many of the redshifts Hubble leaned on. But it was Hubble's graph that made the law undeniable, and his name it carries.

The Hubble constant hides a clock. If the galaxies have been drifting apart at a steady rate, then running the film backward they were all crammed together at one moment in the past — and the constant tells you how long ago. That number, one divided by H₀, comes out to about 14 billion years. It is only a rough figure — the expansion has not, in truth, been perfectly steady — yet it lands remarkably close to the carefully measured age of the Universe, 13.8 billion years. The slope of a line on a graph of galaxies turns out to be the age of everything.

Now the question that trips everyone: if every galaxy flies away from us, are we at the centre? No — and seeing why is the deepest idea in this lesson. The galaxies are not racing through space from some central point; rather, space itself is expanding, swelling everywhere at once and carrying the galaxies along like raisins in rising bread. We met this picture as a balloon back in §0.3, before we had redshift or recession to give it meaning; the figure below draws the same expansion as a stretching grid, with each galaxy's speed shown as an arrow.

HOME
space ×1.00
younger · denserolder · more spread out
Home — galaxy 10 of 20
From home, the arrows fan out and lengthen with distance: the galaxy twice as far recedes twice as fast — Hubble’s law, read straight off the picture. Move home to any other galaxy and the same law holds, so none is the centre. Run the slider back and every galaxy piles onto every other — the hot, dense Big Bang.
Fig. 2.4.dExpansion has no centre. Drag (or use ← / →) to inflate the Universe — each arrow is a galaxy’s recession speed. Watch the lengths: a galaxy twice as far from home grows an arrow twice as long — speed in exact proportion to distance, Hubble’s law made visible. Click any galaxy (or press ↑ / ↓) to move home onto it; every arrow redraws, yet that proportion never breaks — so no galaxy is the centre.

As space stretches, every galaxy moves away from every other and the farthest apart separate fastest — Hubble's law once more — yet none sits at the centre: stand on any galaxy and the view is identical, everyone else fleeing, you apparently at the middle. Every observer in the cosmos sees their own Hubble's law. Two cautions: the grid's flat sheet stands in for three-dimensional space, and the galaxies themselves — bound tight by their own gravity — do not swell; only the empty space between them grows.

Wind that expansion backward far enough and you reach Lemaître's conclusion: if space has grown for 14 billion years, then long ago it was unimaginably small, hot, and dense — everything pressed together before it began to expand. We met that fiery beginning at the start of the course (§0.2) and read its afterglow in the cosmic microwave background (§1.4); Hubble's law is the evidence for it, written across the sky. The flight of the galaxies is no explosion in space, hurling matter from a centre — it is the swelling of space itself, the expansion that began with the Big Bang and is under way tonight, in every direction you can look.


With Hubble's law we close the Galactic Age: we have found not only what galaxies are and how they form, but that the whole sky of them is in motion, expanding from a common origin. From here the course turns inward — from the galaxies to the engines that light them: the stars.