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LearnCambridge97022025–2027Paper 4 · A Level Structured QuestionsAstronomy and cosmology

Paper 4 · Module

Astronomy and cosmology

3 subtopics≈ 100 min in total

Start the module: Standard candles Open graphing calculator

Standard candles
A star's luminosity $L$ is the total power it radiates. At distance $d$ , that power spreads over a sphere of area $4\pi d^2$ , so the radiant flux intensity received is $F=\dfrac L{4\pi d^2}$ . A standard candle is an object whose luminosity is known, such as a Cepheid variable star or a type Ia supernova. Measuring its flux then gives its distance: $d=\sqrt{\dfrac L{4\pi F}}$ .
≈ 30 min
Stellar radii
Stars radiate approximately as black bodies. Wien's displacement law: the peak wavelength is inversely proportional to the surface temperature, $\lambda_{\max}T=2.9\times10^{-3}$ m K, so hotter stars look bluer. The Stefan–Boltzmann law gives the luminosity: $L=4\pi\sigma r^2T^4$ , with $\sigma=5.67\times10^{-8}$ W m⁻² K⁻⁴. Knowing $T$ (from Wien) and $L$ (from a standard candle method), you can find a star's radius.
≈ 35 min
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.
≈ 35 min