Hubble's Law (OCR A Level Physics)

• 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

   Step 1: List the known quantities

• • d = 20 light years
  • H_o = 2.2 x 10^-18 s^-1

   Step 2: Convert 20 light-years to m

• • From the data booklet: 1 ly ≈ 9.5 x 10¹⁵ m
  • So, 20 ly = 20 x (9.5 x 10¹⁵) = 1.9 x 10¹⁷ m

   Step 3: Substitute values into Hubble's Law

• • From the data booklet: v ≈ H₀d 
  • So, v ≈ (2.2 x 10^-18 s^-1) x (1.9 x 10¹⁷ m) = 0.418 m s^-1

   Step 4: Confirm your answer

• • The velocity of the galaxy as it moves away from Earth 0.42 m s^-1

• 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

  Step 1: From the data booklet

Hubble’s Law: v ≈ H₀d

   Step 2: Determine the Hubble constant, H₀, from the graph

• • y–axis = v = 20, 000
  • x–axis = d = 305
  • gradient = H₀

   Step 3: Calculate the gradient of the graph

• • H₀ = = 66 km s^–1 Mpc^–1

   Step 4: Confirm your answer

• • The Hubble Constant = 66 km s^–1 Mpc^–1