Hubble's law

Hubble's law—formally known as the Hubble–Lemaître law—describes a key observation in physical cosmology: galaxies are receding from Earth at speeds that increase in direct proportion to their distance. In other words, the farther a galaxy lies from us, the faster it appears to move away. Astronomers typically measure a galaxy's recessional velocity by analyzing its redshift, a shift in the frequency of the light it emits.

This law is regarded as the first observational evidence for an expanding universe and is frequently cited in support of the Big Bang model. The motion of astronomical objects due solely to this expansion is called the Hubble flow. The relationship is expressed by the equation v = H₀D, where H₀ is the Hubble constant—the current value of the Hubble parameter, which itself changes over time. Because the constant is not truly constant across cosmic history, the term is sometimes considered a misnomer. The Hubble constant has units of kilometers per second per megaparsec (km/s/Mpc), meaning a galaxy one megaparsec (3.09×10¹⁹ km) away recedes at about 70 km/s. Its reciprocal gives the Hubble time, roughly 14.4 billion years. Expressed as a relative expansion rate, H₀ = 7% per gigayear, indicating that at the current rate, an unbound structure would grow by 7% over one billion years.

The discovery is credited to Edwin Hubble's 1929 work, but the idea of a calculable expansion rate first emerged from general relativity equations derived by Alexander Friedmann in 1922. His Friedmann equations showed the universe might be expanding and predicted the speed of that expansion. Before Hubble, Carl Wilhelm Wirtz used his own data in 1922 and 1924 to deduce that galaxies appearing smaller and dimmer had larger redshifts, implying more distant galaxies recede faster. In 1927, Georges Lemaître concluded the universe might be expanding by noting the proportionality between recessional velocity and distance, estimating a ratio that—after Hubble confirmed cosmic expansion and refined the value two years later—became known as the Hubble constant. Hubble inferred recession velocities from redshifts, many of which had been measured and linked to velocity by Vesto Slipher in 1917. Combining Slipher's velocities with Henrietta Swan Leavitt's intergalactic distance methods allowed Hubble to calculate a more precise expansion rate.

A decade before Hubble's observations, physicists and mathematicians had already developed a consistent theory of an expanding universe using Einstein's field equations of general relativity. Applying general principles to the universe's nature yielded a dynamic solution that contradicted the then-dominant idea of a static universe. In 1912, Slipher measured the first Doppler shift of a spiral nebula and soon found that nearly all such objects were receding from Earth, though he did not grasp the cosmological implications, and it was still debated whether these nebulae were "island universes" beyond the Milky Way.

In 1922, Friedmann derived his equations from Einstein's field equations, showing the universe could expand at a calculable rate. The parameter he used is now called the scale factor, a scale-invariant form of Hubble's law's proportionality constant. Lemaître independently found a similar solution in his 1927 paper. The Friedmann equations come from inserting the metric for a homogeneous, isotropic universe into Einstein's field equations for a fluid of given density and pressure. This expanding-spacetime concept eventually led to the Big Bang and Steady State theories.

Two years before Hubble's article, Lemaître published the first derivation of what is now Hubble's law. According to astronomer Sidney van den Bergh, Lemaître's 1927 discovery appeared in French in a low-impact journal. In the 1931 English translation—published in a high-impact journal—a critical equation was altered by omitting reference to the Hubble constant. It is now known that Lemaître himself made these changes.

Before modern cosmology, there was considerable debate about the universe's size and shape. The 1920 Shapley–Curtis debate pitted Harlow Shapley, who argued for a small universe the size of the Milky Way, against Heber D. Curtis, who argued for a much larger one. The issue was resolved in the following decade with Hubble's improved observations. Edwin Hubble conducted most of his professional work at Mount Wilson Observatory, home to the world's most powerful telescope at the time. His observations of Cepheid variable stars in spiral nebulae allowed him to calculate distances, revealing that these objects lay far outside the Milky Way.