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Physics

24.5 - The Hubble Constant

4 min

note 1 of 7

One light-year

A light-year is the distance that light travels in one year.
One light-year is approximately 9.5 × 10¹⁵ m.

note 2 of 7

Finding recession speed from red shift

Light from a distant galaxy is red-shifted: spectral lines appear shifted to longer wavelengths because the galaxy is moving away from Earth.
A larger shift in wavelength means a faster recession speed $v$ .

Two coloured spectra with dark lines, the top labelled light from our Sun and the bottom light from a distant galaxy, with arrows showing each line shifted towards the red end.

note 3 of 7

Measuring a galaxy's distance from a supernova

A galaxy's distance is found using a supernova within it.
One specific type of supernova always reaches the same known brightness.
By comparing how bright the supernova appears from Earth with its known true brightness, astronomers calculate the distance $d$ to the galaxy.

note 4 of 7

The Hubble constant

A galaxy's recession speed is directly proportional to its distance from Earth: the further away a galaxy is, the faster it moves away.
The Hubble constant, $H_{0}$ , is the ratio of a galaxy's recession speed to its distance from Earth.

Formula for the Hubble constant

$H_{0} = \frac{v}{d}$

Where:

$H_{0}$ = Hubble constant, per second
$v$ = Recession speed, in metres per second (m/s)
$d$ = Distance to the galaxy, in metres (m)

The current accepted estimate of $H_{0}$ is about 2.2 × 10^-18 per second. Plotting the recession speed of many galaxies against their distance from Earth gives a straight line through the origin, as shown below.

A scatter graph of recession speed in metres per second against distance from Earth in metres, with twelve blue crosses rising from left to right and a straight pink line of best fit drawn through the origin.

note 5 of 7

Worked example - Calculating the Hubble constant

A galaxy is moving away from Earth at 1.5 × 10⁷ m/s and is at a distance of 6.8 × 10²⁴ m. Find the Hubble constant.

Step 1 - Formula

$H_{0} = \frac{v}{d}$

Step 2 - Substitution and calculation

$\begin{matrix} H_{0} & = \frac{1.5 \times 10^{7}}{6.8 \times 10^{24}} \\ = 2.2 \times 10^{- 18} per second \end{matrix}$

note 6 of 7

Estimating the age of the Universe

The Big Bang theory states that all matter in the Universe was once concentrated at a single point.
Assuming each galaxy has moved outwards at a constant speed since the Big Bang:

$Age of the Universe = \frac{d}{v} = \frac{1}{H_{0}}$

Using the current value of $H_{0}$ gives an age of roughly 14 billion years (about 4.5 × 10¹⁷ s).

note 7 of 7

Worked example - Estimating the age of the Universe

The Hubble constant is 2.2 × 10^-18 per second. Estimate the age of the Universe in seconds.

Step 1 - Formula

$Age = \frac{1}{H_{0}}$

Step 2 - Substitution and calculation

$Age = \frac{1}{2.2 \times 10^{- 18}} = 4.5 \times 10^{17} s$

Step 3 - Convert to years

This is about 1.4 × 10¹⁰ years, or roughly 14 billion years.

key terms

TermDefinition

Light-yearThe distance that light travels through space in one year.

Hubble constantThe ratio of a galaxy's recession speed (the speed at which it is moving away from us) to its distance from Earth.

Big Bang theoryThe theory that all the matter in the Universe was once packed into a very small, extremely hot and dense region, and that the Universe has been expanding from it ever since.

end of notes

Key points to remember

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25.1 - Variables & ControlsNext up

The Hubble constant

A galaxy's recession speed is directly proportional to its distance from Earth: the further away a galaxy is, the faster it moves away.

The Hubble constant,

H_{0}

, is the ratio of a galaxy's recession speed to its distance from Earth.

Formula for the Hubble constant

$H_{0} = \frac{v}{d}$

Where:

H_{0}

= Hubble constant, per second

v

= Recession speed, in metres per second (m/s)

d

= Distance to the galaxy, in metres (m)

The current accepted estimate of

H_{0}

is about 2.2 × 10^-18 per second. Plotting the recession speed of many galaxies against their distance from Earth gives a straight line through the origin, as shown below.

Estimating the age of the Universe

The Big Bang theory states that all matter in the Universe was once concentrated at a single point.

Assuming each galaxy has moved outwards at a constant speed since the Big Bang:

$Age of the Universe = \frac{d}{v} = \frac{1}{H_{0}}$

Using the current value of

H_{0}

gives an age of roughly 14 billion years (about 4.5 × 10¹⁷ s).