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Learn7408Paper 3B · Option: AstrophysicsCosmologyHubble's law and the Big Bang
Cosmology · Subtopic 3 of 3

Hubble's Law and the Big Bang

Spectral lines from distant galaxies are shifted to longer wavelengths: redshift. For speeds much less than cc, Δλλ≈Δff≈vc\dfrac{\Delta\lambda}\lambda\approx\dfrac{\Delta f}f\approx\dfrac vc, giving the recession speed. Hubble's law: a galaxy's recession speed is proportional to its distance, v=H0dv=H_0d, with H0≈2.3×10−18H_0\approx2.3\times10^{-18} s⁻¹. Every galaxy moving away from every other means the universe is expanding; running it backwards points to a hot, dense beginning: the Big Bang, about 1H0≈14\dfrac1{H_0}\approx14 billion years ago.

Cambridge 9702 Paper 4Edexcel YPH11 WPH15AQA 7408 Paper 3B≈ 35 minRevision 6 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Explain redshift and use Δλλ≈vc\dfrac{\Delta\lambda}\lambda\approx\dfrac vc.
  • State and use Hubble's law v=H0dv=H_0d.
  • Explain how redshift shows the universe is expanding.
  • Estimate the age of the universe from H0H_0.
Pause and think

Almost every galaxy is moving away from us. Does that put the Milky Way at the centre of the universe?

Section 2 of 14

Core idea

Start hereRaisins in rising dough

In rising bread dough, every raisin moves away from every other, and raisins further apart separate faster. Galaxies do the same: the further away, the faster they recede. Run the film backwards and everything was once together.

The big idea

z=Δλλ≈vcz=\frac{\Delta\lambda}\lambda\approx\frac vc. v=H0dv=H_0d. Age ≈ 1H0\frac1{H_0}.

1. Redshift

Galaxies: recession speed against distance
10020030040050050001000015000200002500030000350000distance (Mpc)speed (km/s)gradient H₀ ≈ 70 km/s/Mpc
A straight line through the origin. H0=70H_0=70 km s−1^{-1} Mpc−1=2.3×10−18^{-1}=2.3\times10^{-18} s−1^{-1}.
Worked exampleA receding galaxy

H-alpha 656 nm observed at 663 nm; H0=70H_0=70 km s−1^{-1} Mpc−1^{-1}.

Goal
vv and dd.
Strategy
Redshift, then Hubble.
  1. z=7656=0.0107z=\frac7{656}=0.0107
    Fractional shift.
  2. v=0.0107×3×108=3.2×106 m s−1v=0.0107\times3\times10^8=3.2\times10^6\text{ m s}^{-1}
    v≈zcv\approx zc.
  3. d=320070=46 Mpcd=\frac{3200}{70}=46\text{ Mpc}
    In km s−1^{-1}.
Answer32003200 km s−1^{-1}; 4646 Mpc.
✓ Checkz≪1z\ll1, so v≈zcv\approx zc is valid ✓.

2. Hubble's law and age

Absorption lines shift towards red for a receding galaxy
laboratorygalaxy: every line 6% longer (v ≈ 0.06c)
The pattern is the same, just shifted. The fractional shift gives the speed.
Age of the universe
  1. t=dvt=\frac dv
    Time for a galaxy to reach distance dd at constant vv.
  2. =1H0=\frac1{H_0}
    v=H0dv=H_0d; the same for every galaxy.
  3. 12.3×10−18=4.3×1017 s≈14 Gyr\frac1{2.3\times10^{-18}}=4.3\times10^{17}\text{ s}\approx14\text{ Gyr}
    Evaluate.
Common misconceptionEarth at the centre Every observer sees the same pattern: space itself expands.

Summary

  • z≈v/cz\approx v/c.
  • v=H0dv=H_0d; age ≈ 1/H01/H_0.
Key words
Redshift
Fractional wavelength increase.
HistoryHubble, Humason and Lemaître. Georges Lemaître, a Belgian priest and physicist, predicted an expanding universe in 19271927 and estimated the expansion rate. In 19291929 Edwin Hubble, with Milton Humason's redshift measurements, published the speed–distance relation. Lemaître called the beginning the "primeval atom"; Fred Hoyle mockingly named it the "Big Bang".
Fun factStatic on old TVs. About 1%1\% of the static on an old analogue TV tuned between channels came from the cosmic microwave background: light released 380 000380\,000 years after the Big Bang, stretched by expansion from visible light to microwaves.
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