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Is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving away from Earth. The velocity of the galaxies has be determined by their redshift, a shift of the light they emit toward the red d of the visible spectrum.

Hubble's law is considered the first observational basis for the expansion of the universe, and today it serves as one of the pieces of evidce most oft cited in support of the Big Bang model.

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The constant of proportionality—the Hubble constant—betwe the "proper distance" D to a galaxy, which can change over time, unlike the comoving distance, and its speed of separation v, i.e. the derivative of proper distance with respect to the cosmological time coordinate. (See Comoving and proper distances § Uses of the proper distance for some discussion of the subtleties of this definition of "velocity".)

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Is known as the Hubble time. The Hubble constant can also be interpreted as the relative rate of expansion. In this form H

= 7%/Gyr, meaning that at the currt rate of expansion it takes a billion years for an unbound structure to grow by 7%.

The notion of the universe expanding at a calculable rate was first derived from geral relativity equations in 1922 by Alexander Friedmann. Friedmann published a set of equations, now known as the Friedmann equations, showing that the universe might be expanding, and presting the expansion speed if that were the case.

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Th Georges Lemaître, in a 1927 article, indepdtly derived that the universe might be expanding, observed the proportionality betwe recessional velocity of, and distance to, distant bodies, and suggested an estimated value for the proportionality constant; this constant, wh Edwin Hubble confirmed the existce of cosmic expansion and determined a more accurate value for it two years later, came to be known by his name as the Hubble constant.

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.

Is constant at any giv momt in time, the Hubble parameter H, of which the Hubble constant is the currt value, varies with time, so the term constant is sometimes thought of as somewhat of a misnomer.

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

In 1912, Vesto M. Slipher measured the first Doppler shift of a "spiral nebula" (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.

In 1922, Alexander Friedmann derived his Friedmann equations from Einstein field equations, showing that the universe might expand at a rate calculable by the equations.

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The parameter used by Friedmann is known today as the scale factor and can be considered as a scale invariant form of the proportionality constant of Hubble's law. Georges Lemaître indepdtly found a similar solution in his 1927 paper discussed in the following section. The Friedmann equations are derived by inserting the metric for a homogeous and isotropic universe into Einstein's field equations for a fluid with a giv dsity and pressure. This idea of an expanding spacetime would evtually lead to the Big Bang and Steady State theories of cosmology.

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 d Bergh, "the 1927 discovery of the expansion of the universe by Lemaître was published in Frch in a low-impact journal. In the 1931 high-impact glish translation of this article, a critical equation was changed by omitting referce to what is now known as the Hubble constant."

Before the advt of modern cosmology, there was considerable talk about the size and shape of the universe. In 1920, the Shapley–Curtis debate took place betwe 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.

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Home to the world's most powerful telescope at the time. His observations of Cepheid variable stars in "spiral nebulae" abled 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.

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.

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Combining his measuremts of galaxy distances with Vesto Slipher and Milton Humason's measuremts of the redshifts associated with the galaxies, Hubble discovered a rough proportionality betwe 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 ough out that the recession velocity is larger than local peculiar velocities), Hubble was able to plot a trd line from the 46 galaxies he studied and obtain a value for the Hubble constant of 500 (km/s)/Mpc (much higher than the currtly accepted value due to errors in his distance calibrations; see cosmic distance ladder for details).

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At the time of discovery and developmt of Hubble's law, it was acceptable to explain redshift phomon 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 geral relativity, velocity betwe distant objects depds 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.

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.

After Hubble's discovery was published, Albert Einstein abandoned his work on the cosmological constant, which he had designed to modify his equations of geral 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 gerated 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.

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After Hubble's discovery that the universe was, in fact, expanding, Einstein called his faulty assumption that the universe is static his "biggest mistake".

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On its own, geral relativity could predict the expansion of the universe, which (through observations such as the bding of light by large masses, or the precession of the orbit of Mercury) could be experimtally observed and compared to his theoretical calculations using particular solutions of the equations he had originally formulated.

A variety of possible recessional velocity vs. redshift functions including the simple linear relation v = cz; a variety of possible shapes from theories related to geral relativity; and a curve that does not permit speeds faster than light in accordance with special relativity. All curves are linear at low redshifts. See Davis and Lineweaver.

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The discovery of the linear relationship betwe redshift and distance, coupled with a supposed linear relation betwe recessional velocity and redshift, yields a straightforward mathematical expression for Hubble's law as follows:

Hubble's law is considered a fundamtal relation betwe recessional velocity and distance. However, the relation betwe recessional velocity and redshift depds on the cosmological model adopted and is not established except for small redshifts.

 , objects recede at a rate faster than the speed of light (See Uses of the proper distance for a discussion of the significance of this):

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Since the Hubble "constant" is a constant only in space, not in time, the radius of the Hubble sphere may increase or decrease over various time intervals. The subscript '0' indicates the value of the Hubble constant today.

Currt evidce suggests that the expansion of the universe is accelerating (see Accelerating universe), meaning that for any giv galaxy, the recession velocity dD/dt is increasing over time as the galaxy moves to greater and greater distances; however, the Hubble parameter is actually thought to be decreasing with time, meaning that if we were to look at some fixed distance D and watch a series of differt galaxies pass that distance, later galaxies would pass that distance

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