Hubble's Law (OCR A Level Physics)

Hubble's Law

• In 1929, the astronomer Edwin Hubble showed that the universe was expanding

  • He did this by observing that the absorption line spectra produced from the light of distant galaxies was shifted towards the red end of the spectrum

  • This doppler shift in the wavelength of the light is evidence that distant galaxies are moving away from the Earth

• Hubble also observed that light from more distant galaxies was shifted further towards the red end of the spectrum compared to closer galaxies

  • From this observation he concluded that galaxies or stars which are further away from the Earth are moving faster than galaxies which are closer

• Hubble’s law states:

   The recessional velocity, v, of a galaxy is proportional to its distance from Earth

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

v ≈ H₀d

• Where:

  • v = recessional velocity of an object, the velocity of an object moving away from an observer (km s^-1)

  • H₀ = Hubble constant, this will be provided in your examination along with the correct units (km s^-1 Mpc^-1)

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

• Alternatively, if the velocity of the receding object was measured in km s^–1 and the distance from the earth to the object was measured in km, then then unit for the Hubble constant would be s^–1

• This Hubble’s law shows:

  • The further away a star is from the Earth, the faster it is moving away from us

  • The closer a star is to the Earth, the slower it is moving away from us

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

The Hubble Constant

• By rearranging the equation for Hubble’s law, we can determine that the Hubble constant, H₀, is:

H₀ ≈ 

• v = recessional velocity of an object (km s^–1)

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

• H_o = Hubble constant (km s^–1 Mpc^–1)

• The value for the Hubble constant has been estimated using data for thousands of galaxies

• The latest estimate of the Hubble constant based on CMB observations by the Planck satellite is:

  • H₀ = 67.4 ± 0.5 km s⁻¹ Mpc⁻¹ (Planck Collaboration VI 2020)

• It is difficult to be certain about just how accurate the values for the Hubble constant are

  • This is due to the random and systematic errors involved when calculating the distance to a galaxy or star