# Hubble's law

The Hubble–Lemaître Law, also known as Hubble's Law,[1] is the observation in physical cosmology that:

1. Objects observed in deep space—extragalactic space, 10 megaparsecs (Mpc) or more—are found to have a redshift, interpreted as a relative velocity away from Earth;
2. This Doppler shift-measured velocity of various galaxies receding from the Earth is approximately proportional to their distance from the Earth for galaxies up to a few hundred megaparsecs away.[2][3]

Hubble–Lemaître is considered the first observational basis for the expansion of the universe and today serves as one of the pieces of evidence most often cited in support of the Big Bang model.[4][5]The motion of astronomical objects due solely to this expansion is known as the Hubble flow.[6]

Although widely attributed to Edwin Hubble,[7][8][9] the notion of the universe expanding at a calculable rate was first derived from the general relativity equations in 1922 by Alexander Friedmann. Friedmann published a set of equations, now known as the Friedmann equations, showing that the universe might expand, and presenting the expansion speed if this was the case.[10] Then Georges Lemaître, in a 1927 article, independently derived that the universe might be expanding, observed the proportionality between recessional velocity of and distance to distant bodies, and suggested an estimated value of the proportionality constant, which when corrected by Hubble became known as the Hubble constant.[4][11][12][13] Though the Hubble constant ${\displaystyle H_{0}}$ is roughly constant in the velocity-distance space at any given moment in time, the Hubble parameter ${\displaystyle H}$, which the Hubble constant is the current value of, varies with time, so the term 'constant' is sometimes thought of as somewhat of a misnomer.[14] Moreover, two years later Edwin Hubble confirmed the existence of cosmic expansion, and determined a more accurate value for the constant that now bears his name.[15]Hubble inferred the recession velocity of the objects from their redshifts, many of which were earlier measured and related to velocity by Vesto Slipher in 1917.[16][17][18][19]

The law is often expressed by the equation v = H0D, with H0 the constant of proportionality—Hubble constant—between the "proper distance" D to a galaxy, which can change over time, unlike the comoving distance, and its velocity v, i.e. the derivative of proper distance with respect to cosmological time coordinate. (See uses of the proper distance for some discussion of the subtleties of this definition of 'velocity'.) Also, the SI unit of H0 is s−1, but it is most frequently quoted in (km/s)/Mpc, thus giving the speed in km/s of a galaxy 1 megaparsec (3.09×1019 km) away. The Hubble constant is about 70 (km/s)/Mpc. The reciprocal of H0 is the Hubble time.

## Discovery

Three steps to the Hubble constant.[20]

A decade before Hubble made his observations, a number of physicists and mathematicians had established a consistent theory of an expanding universe by using Einstein's field equations of general relativity. Applying the most general principles to the nature of the universe yielded a dynamic solution that conflicted with the then-prevailing notion of a static universe.

### Slipher's observations

In 1912, Vesto Slipher measured the first Doppler shift of a "spiral nebula" (spiral nebula is the obsolete term for spiral galaxies), and soon discovered that almost all such nebulae were receding from Earth. He did not grasp the cosmological implications of this fact, and indeed at the time it was highly controversial whether or not these nebulae were "island universes" outside our Milky Way.[21][22]

### FLRW equations

In 1922, Alexander Friedmann derived his Friedmann equations from Einstein's field equations, showing that the universe might expand at a rate calculable by the equations.[23] The parameter used by Friedmann is known today as the scale factor which can be considered as a scale invariant form of the proportionality constant of Hubble's law. Georges Lemaître independently found a similar solution in 1927. The Friedmann equations are derived by inserting the metric for a homogeneous and isotropic universe into Einstein's field equations for a fluid with a given density and pressure. This idea of an expanding spacetime would eventually lead to the Big Bang and Steady State theories of cosmology.

### Lemaître's Equation

In 1927, two years before Hubble published his own article, the Belgian priest and astronomer Georges Lemaître was the first to publish research deriving what is now known as Hubble's Law. According to the Canadian astronomer Sidney van den Bergh, "The 1927 discovery of the expansion of the universe by Lemaître was published in French in a low-impact journal. In the 1931 high-impact English translation of this article a critical equation was changed by omitting reference to what is now known as the Hubble constant."[24] It is now known that the alterations in the translated paper were carried out by Lemaitre himself.[12][25]

### Shape of the universe

Before the advent of modern cosmology, there was considerable talk about the size and shape of the universe. In 1920, the Shapley-Curtis debate took place between Harlow Shapley and Heber D. Curtis over this issue. Shapley argued for a small universe the size of the Milky Way galaxy and Curtis argued that the universe was much larger. The issue was resolved in the coming decade with Hubble's improved observations.

### Cepheid variable stars outside of the Milky Way

Edwin Hubble did most of his professional astronomical observing 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” enabled him to calculate the distances to these objects. Surprisingly, these objects were discovered to be at distances which placed them well outside the Milky Way. They continued to be called “nebulae” and it was only gradually that the term “galaxies” replaced it.

### Combining redshifts with distance measurements

Fit of redshift velocities to Hubble's law.[26] Various estimates for the Hubble constant exist. The HST Key H0 Group fitted type Ia supernovae for redshifts between 0.01 and 0.1 to find that H0 = 71 ± 2 (statistical) ± 6 (systematic) km s−1Mpc−1,[27] while Sandage et al. find H0 = 62.3 ± 1.3 (statistical) ± 5 (systematic) km s−1Mpc−1.[28]

The parameters that appear in Hubble's law, velocities and distances, are not directly measured. In reality we determine, say, a supernova brightness, which provides information about its distance, and the redshift z = ∆λ/λ of its spectrum of radiation. Hubble correlated brightness and parameter z.

Combining his measurements of galaxy distances with Vesto Slipher and Milton Humason's measurements of the redshifts associated with the galaxies, Hubble discovered a rough proportionality between redshift of an object and its distance. Though there was considerable scatter (now known to be caused by peculiar velocities—the 'Hubble flow' is used to refer to the region of space far enough out that the recession velocity is larger than local peculiar velocities), Hubble was able to plot a trend line from the 46 galaxies he studied and obtain a value for the Hubble constant of 500 km/s/Mpc (much higher than the currently accepted value due to errors in his distance calibrations). (See cosmic distance ladder for details.)

At the time of discovery and development of Hubble's law, it was acceptable to explain redshift phenomenon as a Doppler shift in the context of special relativity, and use the Doppler formula to associate redshift z with velocity. Today, in the context of general relativity, velocity between distant objects depends on the choice of coordinates used, and therefore, the redshift can be equally described as a Doppler shift or a cosmological shift (or gravitational) due to the expanding space, or some combination of the two.[29]

#### Hubble Diagram

Hubble's law can be easily depicted in a "Hubble Diagram" in which the velocity (assumed approximately proportional to the redshift) of an object is plotted with respect to its distance from the observer.[30] A straight line of positive slope on this diagram is the visual depiction of Hubble's law.

### Cosmological constant abandoned

After Hubble's discovery was published, Albert Einstein abandoned his work on the cosmological constant, which he had designed to modify his equations of general relativity to allow them to produce a static solution, which he thought was the correct state of the universe. The Einstein equations in their simplest form model generally either an expanding or contracting universe, so Einstein's cosmological constant was artificially created to counter the expansion or contraction to get a perfect static and flat universe.[31] After Hubble's discovery that the universe was, in fact, expanding, Einstein called his faulty assumption that the universe is static his "biggest mistake".[31] On its own, general relativity could predict the expansion of the universe, which (through observations such as the bending of light by large masses, or the precession of the orbit of Mercury) could be experimentally observed and compared to his theoretical calculations using particular solutions of the equations he had originally formulated.

In 1931, Einstein made a trip to Mount Wilson to thank Hubble for providing the observational basis for modern cosmology.[32]

The cosmological constant has regained attention in recent decades as a hypothesis for dark energy.[33]

Other Languages
Afrikaans: Wet van Hubble
العربية: قانون هابل
asturianu: Llei de Hubble
azərbaycanca: Habbl qanunu
беларуская: Закон Хабла
български: Закон на Хъбъл
bosanski: Hubbleov zakon
español: Ley de Hubble
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hrvatski: Hubbleov zakon
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italiano: Legge di Hubble
עברית: חוק האבל
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latviešu: Habla likums
Lëtzebuergesch: Hubble-Konstant
lietuvių: Hablo dėsnis
Bahasa Melayu: Hukum Hubble
occitan: Lei de Hubble
پنجابی: ہبل دا قنون
português: Lei de Hubble
русский: Закон Хаббла
sicilianu: Liggi di Hubble
Simple English: Hubble's law
slovenčina: Hubblov zákon
slovenščina: Hubblov zakon
српски / srpski: Hablov zakon
srpskohrvatski / српскохрватски: Hablov zakon
svenska: Hubbles lag
татарча/tatarça: Habbl qanunı
Türkçe: Hubble kanunu
українська: Закон Габбла
Tiếng Việt: Định luật Hubble
West-Vlams: Wet van Hubble