Age of the Universe (Cambridge (CIE) IGCSE Physics)

The Hubble constant

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• When Edwin Hubble looked at the absorption spectra of distant galaxies, he determined a relationship between the speed of a galaxy and its distance from Earth

Comparing redshifts of galaxies

Hubble discovered that all galaxies show redshift, but the galaxies that are further away show a greater increase in redshift

• This is Hubble's law, which states

The speed of recession is proportional to the distance of the galaxy away from Earth

• 'Recession' speed means the speed at which something is moving away

• This means that the further away a galaxy is from Earth:

  • the faster it is moving away

  • the greater the increase in redshift

Relationship between redshift and galaxy distance

Hubble's law tells us the greater the distance to a galaxy, the greater the redshift, or the speed it moves away from Earth

• Hubble’s law can be expressed as an equation:

• Where:

  • H₀ = Hubble constant (per second)

  • v = recessional velocity of an object, the velocity of an object moving away from an observer (km/s)

  • d = distance between the object and the Earth (km)

• From this equation, the Hubble Constant  can be defined as:

The ratio of the speed at which the galaxy is moving away from the Earth, to its distance from the Earth

• The accepted value of the Hubble constant is  = 2.2 × 10^–18 per second

Measuring recession speed & distance

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• The Hubble constant can be determined from measurements of:

  • redshift of the light emitted by a galaxy

  • the brightness of supernovae in the galaxy

Measuring recession speeds of galaxies

• The speed of recession  of a galaxy (i.e. how fast it is moving away from the Earth) can be found from the change in wavelength of the galaxy’s starlight due to redshift

Measuring distance using supernovae

• The distance  to a galaxy can be determined using the brightness of a supernova in that galaxy

• Supernovae are exploding stars

  • Certain types of supernovae have the same peak level of brightness (absolute magnitude), meaning they can be used as standard candles

  • These supernovae are so bright that they can be used for measuring distances to the most distant galaxies

Age of the Universe

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• Hubble's law can be rearranged to give the expression:

• Since time is equal to distance divided by speed, the term represents an estimate of the age of the Universe

• Hubble's law provides further evidence for the Big Bang

• It shows that the Universe has been expanding since the beginning of time

  • If we looked at time in reverse, we would see galaxies were closer together in the past

  • This suggests that the Universe must have originated from a single point and has been expanding outwards ever since

Hubble's law graph

• Using measurements from galactic redshift and brightness of supernovae, a graph of recession velocity against distance can be plotted

Graph of galaxy recession velocity against distance

A key aspect of Hubble’s law is that the furthest galaxies appear to move away the fastest

• The gradient of the graph represents the age of the Universe

  • When the distance equals zero, this represents all the matter in the Universe being at a single point

  • This is the singularity that occurred at the moment of the Big Bang

• Astronomers have used this formula to estimate the age of the Universe is about 13.7 billion years