Hubble's Law

Why Hubble's Law matters

• It launched observational cosmology. Before 1929 the universe was widely thought static and possibly no bigger than the Milky Way. A linear v–d relation across dozens of galaxies made the cosmos dynamic, vast, and evolving.
• It is the empirical backbone of the Big Bang. Run the expansion backwards and everything converges — the same extrapolation that predicts the cosmic microwave background and the light-element abundances.
• H₀ sets the cosmic clock and yardstick. The Hubble time 1/H₀ frames the age of the universe, and H₀ converts any galaxy's redshift into a distance — the workhorse of galaxy surveys.
• Its slope is a battleground. The 5-sigma disagreement between early- and late-universe values of H₀ — the Hubble tension — may be the loudest hint of new physics beyond ΛCDM.
• It calibrates dark energy. Extending the velocity-distance relation to high redshift with Type Ia supernovae revealed, in 1998, that the expansion is accelerating.

The equation and its symbols

The law is deceptively simple:

v = H₀ d

• v — recession velocity, in km/s. The rate at which a galaxy moves away from us due to cosmic expansion (the peculiar velocity from local gravity must be subtracted).
• d — proper distance to the galaxy, usually in megaparsecs (1 Mpc = 3.086 × 10¹⁹ km ≈ 3.26 million light-years).
• H₀ — the Hubble constant, the present-day expansion rate, in km/s/Mpc. The subscript "0" denotes "now"; the more general time-varying quantity H(t) is the Hubble parameter.

For nearby galaxies the recession velocity connects to the measured redshift by v ≈ cz, where z = Δλ/λ is the fractional wavelength stretch and c is the speed of light. Combining the two gives the practical distance estimator d ≈ cz / H₀. Note the units: H₀ carries dimensions of inverse time, so its reciprocal is a time and its reciprocal-times-c is a length — the Hubble length, about 4,300 Mpc (14 billion light-years).

How it works, step by step

1. Measure the redshift. A galaxy's spectrum shows familiar absorption lines — calcium H and K, hydrogen Balmer lines — shifted to longer wavelengths. The fractional shift z = Δλ/λ is read directly and precisely.
2. Measure the distance independently. Redshift alone cannot give distance, so astronomers climb the cosmic distance ladder: parallax for nearby stars, Cepheid variables (whose period fixes their luminosity via the Leavitt law) in nearby galaxies, then Type Ia supernovae as standard candles out to hundreds of Mpc.
3. Plot velocity against distance. When cz is plotted versus d, the points fall on a straight line through the origin. The slope is H₀.
4. Interpret the line. A straight line through the origin means every observer, on every galaxy, sees the same law — the hallmark of homogeneous, isotropic expansion described by the Friedmann equations. There is no centre and no edge.
5. Extrapolate in time. Uniform expansion implies a finite past: at t = 0 all separations vanish. The characteristic timescale is the Hubble time, 1/H₀ ≈ 14 Gyr, close to the true 13.8-Gyr age.

Key numbers and comparison

Quantity / probe	Value	Note
Hubble's original 1929 slope	~500 km/s/Mpc	Wrong by ~7× — his Cepheid calibration was off
Planck 2018 (CMB, early universe)	67.4 ± 0.5 km/s/Mpc	ΛCDM fit to the microwave background
SH0ES (Cepheids + Type Ia SNe)	73.0 ± 1.0 km/s/Mpc	Late-universe distance ladder
Hubble time 1/H₀ (H₀ = 70)	~14 billion years	Ballpark for the age of the universe
Hubble length c/H₀ (H₀ = 70)	~4,300 Mpc ≈ 14 Gly	Rough size of the observable horizon scale
Recession of a galaxy at 100 Mpc	~7,000 km/s (H₀ = 70)	Corresponds to z ≈ 0.023

A worked example and the history

Take the Coma cluster, roughly 100 Mpc away with a mean redshift z ≈ 0.023. Its recession velocity is v ≈ cz = 300,000 km/s × 0.023 ≈ 6,900 km/s. Dividing by distance gives H₀ ≈ 6,900 / 100 = 69 km/s/Mpc — squarely inside the modern range. Reverse the arithmetic and you have the standard way distances are estimated: a quasar at z = 0.1 sits roughly at d ≈ cz/H₀ ≈ 30,000/70 ≈ 430 Mpc.

Historically, the story runs Slipher → Lemaître → Hubble. Vesto Slipher measured the first galaxy redshifts at Lowell Observatory starting in 1912, finding most "spiral nebulae" fleeing at hundreds of km/s. In 1927 Georges Lemaître, a Belgian priest and physicist, solved Einstein's equations for an expanding universe, combined them with Slipher's velocities and Hubble's early distances, and derived v = H₀d — even estimating a coefficient near 625 km/s/Mpc. His paper appeared in a little-read French journal. In 1929 Edwin Hubble, using mostly Slipher's redshifts (with a handful of new ones from his collaborator Milton Humason) and his own Cepheid distances from Mount Wilson's 100-inch telescope, published the relation with 24 galaxies and made it famous. The 1998 discovery of cosmic acceleration by the High-z Supernova Search and the Supernova Cosmology Project extended the very same velocity-distance diagram into the high-redshift regime, revealing dark energy.

Common misconceptions

• "Galaxies are flying through space away from us." No — space itself expands between galaxies. Cosmological redshift is stretched wavelength, not a Doppler shift through a static space.
• "We are at the centre of the expansion." There is no centre. Because v ∝ d, every observer sees the same recession law; the pattern is centreless, like dots on an inflating balloon.
• "Recession faster than light is impossible." Beyond the Hubble distance, galaxies recede faster than c. This is allowed — no object moves through space faster than light; it is space growing.
• "The Hubble constant is truly constant." It is constant in space (same everywhere now) but not in time. H(t) was much larger in the past; "H₀" means its value today.
• "1/H₀ is exactly the age of the universe." Only in an empty, coasting universe. Deceleration then acceleration make the true age (13.8 Gyr) differ slightly from the Hubble time.
• "The law holds at all distances." The clean linear v = H₀d applies only nearby (low z). At high z, curvature of the expansion history and the breakdown of v = cz require the full Friedmann framework.