Red-shift of light from galaxies; evidence for expanding universe; Doppler effect explained
AQA GCSE Physics 4.8 | Year 11 Higher TierThe Doppler effect describes the change in observed frequency (and wavelength) of a wave when the source of the wave and the observer are moving relative to each other. You are already familiar with this from everyday life — think of the high-pitched whine of an ambulance siren as it approaches, dropping to a lower pitch as it speeds away.
When a source moves towards an observer, the wave fronts are compressed — they arrive more frequently. This means the observed frequency is higher and the wavelength is shorter.
When a source moves away from an observer, the wave fronts are stretched — they arrive less frequently. This means the observed frequency is lower and the wavelength is longer.
This principle applies to all waves: sound, water waves, and crucially for cosmology — light.
Every element absorbs and emits light at specific, characteristic wavelengths, producing a unique pattern of dark lines in the spectrum called an absorption spectrum. When astronomers observe light from distant stars and galaxies, they find that these spectral lines appear shifted compared to the same elements measured in a laboratory on Earth.
If a galaxy is moving away from us, the Doppler effect causes the light waves to be stretched. This increases the wavelength, shifting all spectral lines towards the red end of the visible spectrum — hence the name red-shift. The greater the speed of recession, the greater the red-shift.
Conversely, if an object were moving towards us, we would observe a blue-shift — spectral lines shifted towards shorter wavelengths. The Andromeda galaxy actually shows a blue-shift because it is gravitationally approaching the Milky Way.
Astronomers use this ratio to quantify the degree of red-shift. A larger value of z means the galaxy is receding faster.
In the 1920s, Edwin Hubble made a groundbreaking discovery: the light from virtually all distant galaxies is red-shifted. Furthermore, he found a remarkable pattern — the further away a galaxy is, the greater its red-shift, meaning it is receding from us faster.
This relationship — recession speed proportional to distance — is expressed by Hubble's Law:
| Symbol | Quantity | SI Unit |
|---|---|---|
| v | Recession speed of galaxy | km s⁻¹ |
| H₀ | Hubble constant | km s⁻¹ Mpc⁻¹ |
| d | Distance to galaxy | Megaparsecs (Mpc) |
| z | Red-shift parameter | Dimensionless |
| λ₀ | Rest wavelength | m (or nm) |
| Δλ | Change in wavelength | m (or nm) |
It is important to understand that galaxies are not flying through space from a central point. Rather, space itself is expanding — like dots on the surface of an inflating balloon, every galaxy moves away from every other galaxy. There is no special centre to the universe.
If the universe is currently expanding, then working backwards in time it must have been smaller, denser, and hotter in the past. Running the expansion back to its logical conclusion leads to the idea that all matter, energy, space, and time originated from an extremely hot, dense single point approximately 13.8 billion years ago — this is the Big Bang.
Red-shift is one of the key pieces of evidence supporting the Big Bang theory. Additional evidence includes:
When astronomers compare the observed spectrum of a distant galaxy with a reference spectrum measured in the laboratory, they look for characteristic patterns. For example, hydrogen always produces absorption lines at specific wavelengths: 434 nm, 486 nm, 656 nm (in the visible range). If those same lines are observed at 470 nm, 525 nm, and 708 nm from a distant galaxy, the entire pattern has shifted to longer wavelengths — this is a red-shift.
The red-shift parameter z can also be related to recession speed for speeds much less than the speed of light:
This means that by measuring the shift in spectral lines, astronomers can calculate how fast a galaxy is moving away. Combined with Hubble's Law, they can also estimate the distance to that galaxy. This is a powerful indirect measurement technique used throughout modern cosmology.
Q1. Which of the following best describes red-shift of light from a distant galaxy?
Q2. A hydrogen spectral line has a rest wavelength of 434 nm. It is observed at 456 nm from a distant galaxy. Calculate the red-shift parameter z.
Q3. What does Hubble's Law tell us about the relationship between a galaxy's distance and its recession speed?
Q4. Using H₀ = 70 km s⁻¹ Mpc⁻¹, calculate the recession speed (in km s⁻¹) of a galaxy 560 Mpc away.
Q5. Which of the following is NOT evidence that supports the Big Bang theory?
Challenge Q1 (6 marks): A calcium absorption line has a rest wavelength of 393 nm. When observed from Galaxy X, it appears at 412 nm, and from Galaxy Y at 441 nm.
(a) Calculate the red-shift z for each galaxy.
(b) Which galaxy is further away? Justify your answer.
(c) Calculate the recession speed of each galaxy. (c = 3 × 10⁸ m s⁻¹)
Challenge Q2 (5 marks): A student measures the recession speed of three galaxies and their distances from Earth:
| Galaxy | Distance (Mpc) | Speed (km s⁻¹) |
|---|---|---|
| A | 100 | 7,000 |
| B | 250 | 17,500 |
| C | 400 | 28,000 |
(a) Use each row to calculate H₀ and comment on consistency. (b) What does the fact that all three galaxies are receding tell us about the universe?
Challenge Q3 (6 marks): A student claims: "Red-shift proves that our galaxy is at the centre of the universe, because all other galaxies are moving away from us." Evaluate this claim, explaining whether the student is correct and why. In your answer, refer to the nature of the expansion of the universe.
Challenge Q4 (4 marks): A spectral line is observed from a quasar (distant active galaxy) at a wavelength of 850 nm. The same line has a rest wavelength of 121 nm (a Lyman-alpha line in the ultraviolet). Calculate (a) the red-shift z and (b) the recession speed of the quasar. Comment on whether the approximation v = zc is valid here.