You've heard the Doppler effect: an ambulance siren sounds higher-pitched as it comes toward you and drops lower as it drives away. The motion squeezes the sound waves together in front and stretches them out behind.
Light does the same thing. If a galaxy is moving away from us, its light waves get stretched to longer wavelengths — toward the red end of the spectrum. That's a redshift. If it's moving toward us, its light is squeezed to shorter wavelengths: a blueshift. The faster the motion, the bigger the shift.
The top strip is a lab spectrum at rest. The bottom strip is the same set of lines from a galaxy. Change the galaxy's speed and watch the whole pattern slide.
Because every element has a known pattern of lines, astronomers can recognize the pattern in a galaxy's spectrum even after it shifts, then measure how far each line moved. The size of the shift, compared with the line's original wavelength, is the redshift, written z:
Here λ₀ is the line's wavelength in the lab, Δλ is how far it moved, and c is the speed of light, about 300,000 km/s. The second equation turns a redshift into a speed — it works well as long as z is small (under about 0.1), which covers every galaxy in this unit's problems.
| Step | Worked example |
|---|---|
| Measure | A galaxy's hydrogen-alpha line (lab: 656.3 nm) appears at 671.6 nm, so Δλ = 15.3 nm |
| Redshift | z = 15.3 ÷ 656.3 ≈ 0.0233 |
| Velocity | v = 300,000 × 0.0233 ≈ 7,000 km/s, moving away from us |
Starting in 1912, Vesto Slipher measured the spectra of spiral "nebulae" and found something strange: almost all of them were redshifted, many at hundreds of kilometers per second. Once Hubble showed in 1924 that these were distant galaxies, he set out to measure their distances too. In 1929, he plotted velocity against distance and found a straight-line pattern: the farther away a galaxy is, the faster it's moving away. (Georges Lemaître had predicted the same relationship from theory two years earlier, and it's now officially called the Hubble–Lemaître law.)
The slope of that line, H₀ ("H-naught"), is the Hubble constant: how fast the universe is expanding today. Modern measurements put it at about 70 km/s per megaparsec. A megaparsec (Mpc) is a distance unit astronomers use for galaxies — about 3.26 million light-years. So a galaxy 1 Mpc away recedes at about 70 km/s, one 10 Mpc away at about 700 km/s, and so on.
Each dot is a galaxy with a measured distance and velocity. Tilt the line until it runs through the middle of the dots — its slope is the Hubble constant.
Measuring distances to galaxies is hard. Measuring redshifts is easy — you just need a spectrum. So once H₀ is known, Hubble's law becomes a distance tool. Rearranged:
The galaxy from the worked example, receding at 7,000 km/s, is about 7,000 ÷ 70 = 100 Mpc away, or roughly 330 million light-years — about the distance of the Coma Cluster. That's three steps from a single spectral line to a distance: redshift → velocity → distance.
Type in where a galaxy's hydrogen-alpha line shows up (lab value: 656.3 nm) and follow the three steps.
If nearly every galaxy is moving away from us, are we at the center of the universe? No. Picture a loaf of raisin bread rising in the oven. Every raisin moves away from every other raisin, and raisins twice as far apart separate twice as fast — no matter which raisin you pick as "home." Galaxies are the raisins, and space itself is the dough. An astronomer in any galaxy would see the same Hubble's law, so there is no center.
Run the movie backward and everything gets closer together. If galaxies have always moved apart at about today's rate, the time it took them to reach their current distances is just distance ÷ velocity — which is 1 ÷ H₀. For H₀ = 70 km/s/Mpc, that works out to about 14 billion years. Careful modern measurements give 13.8 billion years for the age of the universe — remarkably close. The expansion points back to a beginning: the Big Bang.