Hubble’s Law

Hubble’s law also known as Hubble-Lamaitre law is the observation that galaxies are moving away from the 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 been determined by their redshift, a shift of the light they emit toward the red end of the 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 evidence most often cited in support of the Big Bang model. The motion of astronomical objects due solely to this expansion is known as the Hubble flow. 

It is often expressed by the equation  , with   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 speed of separation v, i.e. the derivative of proper distance with respect to cosmological time coordinate.

Hubble constant 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, and its value is about 70 (km/s)/Mpc. However, the SI unit of   is simply s−1, and the SI unit for the reciprocal of   is simply the second. The reciprocal of   is known as the Hubble time.

The Hubble constant can also be interpreted as the relative rate of expansion. In this form  = 7%/Gyr, meaning that at the current rate of expansion it takes a billion years for an unbound structure to grow by 7%.

As techniques of measuring hubble constant have improved, the estimated measurement uncertainties have shrunk, but the range of measured values has not, to the point that the disagreement is now statistically significant (this discrepancy is called Hubble tension).

In February 2020, the Megamaser Cosmology Project published independent results that confirmed the distance ladder results and differed from the early-universe results at a statistical significance level of 95%. In July 2020, measurements of the cosmic background predict that the Universe should be expanding more slowly than is currently observed.

Although widely attributed to Edwin Hubble, the notion of the universe expanding at a calculable rate was first derived from 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 that were the case. 

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 for the proportionality constant.

This constant, when Edwin Hubble confirmed the existence 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. Though the Hubble constant   is roughly constant in the velocity-distance space at any given moment in time, the Hubble parameter  , 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.

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