25.2.2 Doppler Redshift

• Recall 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 moves 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)

Step 1:            Write down the known quantities

Emitted frequency, f = 4.570 × 10¹⁴ Hz

Shift in frequency, Δf = (4.547 – 4.570) × 10¹⁴ = –2.3 × 10¹² Hz

Speed of light, c = 3.0 × 10⁸ m s^–1

Step 2:            Write down the Doppler redshift equation

Step 3:            Rearrange for speed v, and calculate

Step 4:            Write a concluding sentence

The observed frequency is less than the emitted frequency (the light from a laboratory source), therefore, the source is receding, or moving away, from the Earth at 1.5 × 10⁶ m s^–1

• After the discovery of Doppler redshift, astronomers began to realise that almost all the galaxies in the universe are receding
• This lead 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

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 as the rubber stretches when the balloon is inflated, space itself is stretching out between galaxies
  • Just like the dots, the galaxies move away from each other, however, they themselves do not move