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Physics LibreTexts

16.4: The Hubble Relation

When Hubble compared the radial velocities for galaxies with his distance estimates, he found a clear correlation between the radial velocities — measured from the red shifted spectral lines — and the distance. The slope of the linear correlation defines the expansion rate of the universe. This fundamental result of extra galactic astronomy is called the Hubble relation. You may see this result referred to as Hubble’s law, but it is not a law of nature like Newton’s law of gravity or the laws of thermodynamics. There is no law of physics that requires galaxies to move apart or to have motions that increase with increasing distance. Hubble’s relation is a purely observational result. However, it is a vital clue in helping us understand the universe we live in.

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Determining the Hubble constant using supernova type 1a. Click here for original source URL.


Astronomers use the term red shift as shorthand for a recession velocity thought to be caused by the expansion of the universe. Although the conceptual basis of Doppler red shifts and cosmological red shifts are quite distinct, the mathematical descriptions are identical as long as the recession is much slower than the speed of light. The Doppler shift is given by δλ / λ = v / c, where δλ is the difference between the wavelength of the observed light and the wavelength that light would have if the object was not moving. Astronomers define red shift by the symbol z, where z = δλ / λ = v / c. Red shift is therefore a pure number with no units; it is equal to the fractional wavelength shift of galaxy light or the recession velocity (v) as a fraction of the speed of light, c.

A modern version of Hubble's relation extends the linear relation between red shift and distance hundreds of times farther into space than Hubble's original work. Recession velocities as high as 30,000 km/s, or 10% of the speed of light, are easily measured for faint galaxies. The largest distance measure is 500 Mpc. In other words, we can detect galaxies that are over 1½ billion light years distant, moving away from us at 18 million mph! The two quantities that are plotted in a Hubble relation are not equally easy to measure. It is relatively simple to measure a red shift for a galaxy; only a spectrum is required. However, establishing a reliable distance can be very difficult.

In 1998, two separate teams of astronomers discovered a departure from the Hubble relation at large distances. In other words, this plot of distance versus red shift isn't a straight line. They were motivated in making their difficult observations by the fact that the expanding universe model made a predication that the expansion rate should have been faster in the past. As the galaxies all tug on each other by gravity, they will slow down or decelerate the cosmic expansion. As both these teams used supernovae as standard candles to measure large distances, they got a huge surprise. Instead of an expansion rate that has been slowing down, they found an expansion rate that is increasing or accelerating. The universe is expanding faster and faster! This acceleration is caused by a repulsive force that's not yet understood, called "dark energy."

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Doppler Shift. Click here for original source URL.