Learn9702Paper 4 · A Level Structured QuestionsAstronomy and cosmologyHubble's law and the Big Bang

Astronomy and 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 $c$ , $\dfrac{\Delta\lambda}\lambda\approx\dfrac{\Delta f}f\approx\dfrac vc$ , giving the recession speed. Hubble's law: a galaxy's recession speed is proportional to its distance, $v=H_0d$ , with $H_0\approx2.3\times10^{-18}$ 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 $\dfrac1{H_0}\approx14$ 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 $\dfrac{\Delta\lambda}\lambda\approx\dfrac vc$ .
State and use Hubble's law $v=H_0d$ .
Explain how redshift shows the universe is expanding.
Estimate the age of the universe from $H_0$ .

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

$z=\frac{\Delta\lambda}\lambda\approx\frac vc$ . $v=H_0d$ . Age ≈ $\frac1{H_0}$ .

1. Redshift

Galaxies: recession speed against distance

A straight line through the origin.

H_0=70

km s

^{-1}

Mpc

^{-1}=2.3\times10^{-18}

^{-1}

Worked exampleA receding galaxy

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

Goal: $v$ and $d$ .
Strategy: Redshift, then Hubble.

$z=\frac7{656}=0.0107$
Fractional shift.
$v=0.0107\times3\times10^8=3.2\times10^6\text{ m s}^{-1}$
$v\approx zc$ .
$d=\frac{3200}{70}=46\text{ Mpc}$
In km s $^{-1}$ .

Answer

3200

km s

^{-1}

;

46

Mpc.

✓ Check

z\ll1

, so

v\approx zc

is valid ✓.

2. Hubble's law and age

Absorption lines shift towards red for a receding galaxy

The pattern is the same, just shifted. The fractional shift gives the speed.

Age of the universe

$t=\frac dv$
Time for a galaxy to reach distance $d$ at constant $v$ .
$=\frac1{H_0}$
$v=H_0d$ ; the same for every galaxy.
$\frac1{2.3\times10^{-18}}=4.3\times10^{17}\text{ s}\approx14\text{ Gyr}$
Evaluate.

Common misconceptionEarth at the centre Every observer sees the same pattern: space itself expands.

Summary

$z\approx v/c$ .
$v=H_0d$ ; age ≈ $1/H_0$ .

Redshift: Fractional wavelength increase.

HistoryHubble, Humason and Lemaître. Georges Lemaître, a Belgian priest and physicist, predicted an expanding universe in

1927

and estimated the expansion rate. In

1929

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\%

of the static on an old analogue TV tuned between channels came from the cosmic microwave background: light released

380\,000

years after the Big Bang, stretched by expansion from visible light to microwaves.

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