Doppler Redshift (CIE A Level Physics)

• The Doppler effect is defined as:

The apparent change in wavelength or frequency of the radiation from a source due to its relative motion away from or toward the observer

• On Earth, the Doppler effect of sound can be easily observed when sound waves move past an observer at a notable speed
• In space, the Doppler effect of light can observed when spectra of distant stars and galaxies are observed, this is known as:
  • redshift if the object is moving away from the Earth, or
  • blueshift if the object is moving towards the Earth

• Redshift is defined as:

The fractional increase in wavelength (or decrease in frequency) due to the source and observer receding from each other

• For non-relativistic galaxies, Doppler redshift can be calculated using:

• Where:
  • Δλ = shift in wavelength (m)
  • λ = wavelength emitted from the source (m)
  • Δf = shift in frequency (Hz)
  • f = frequency emitted from the source (Hz)
  • v = speed of recession (m s^-1)
  • c = speed of light in a vacuum (m s^-1)

• After the discovery of Doppler redshift, astronomers began to realise that almost all the galaxies in the universe are receding
• This led to the idea that the space between the Earth and the galaxies must be expanding
• This expansion stretches out the light waves as they travel through space, shifting them towards the red end of the spectrum
• The more red-shifted the light from a galaxy is, the faster the galaxy is moving away from Earth

Expanding universe balloon analogy

A balloon inflating is similar to the stretching of the space between galaxies

• The expansion of the universe can be compared to dots on an inflating balloon
  • As the balloon is inflated, the dots all move away from each other
  • In the same way the rubber stretches when the balloon is inflated, space itself stretches between galaxies
  • Just like the dots, the galaxies move away from each other, however, they themselves do not move