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Galaxy redshift and Hubble's law – measure H₀, the age of the Universe and the evidence for the Big Bang

PhysicsGravitation & AstronomyAges 15–16

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Measure the redshift z = Δλ/λ₀ of absorption lines in galaxy spectra, work out the recession speed v = cz and the distance from a standard candle (a type Ia supernova), record the results and plot v against d to find the Hubble constant H₀ and the age of the Universe ≈ 1/H₀. Three more screens show expanding space stretching the wavelength of light, the black-body spectrum of the cosmic microwave background with the hydrogen–helium ratio, and the Doppler effect in the spectrum of a binary star.

Lesson: Galaxy redshift, Hubble's law and the Big Bang theory

What it shows

Light from distant galaxies is shifted to longer wavelengths. Comparing a galaxy's absorption lines with the same lines measured in a laboratory gives the redshift z = Δλ/λ₀, and for small z the recession speed is v ≈ cz. Distances come from standard candles: a type Ia supernova has a known peak luminosity, so its measured flux gives d = √(L/4πF). Plotting v against d gives a straight line through the origin, Hubble's law v = H₀d, whose slope is the Hubble constant; 1/H₀ estimates the age of the Universe. The cosmic microwave background and the hydrogen–helium ratio support the Big Bang model.

How to use

On Measure redshift, tap a galaxy in the sky, choose a Comparison line, then drag the yellow cursor onto the shifted line in the galaxy's spectrum and fine-tune it in the zoom strip or with ◀ and ▶. Press Record result and repeat for several galaxies; the graph fits H₀. Untick Realistic scatter for ideal data. Use the other tabs to watch space expand, look back in time at the CMB, and see a binary star's lines split.

Parameters you can change

  • Screen Measure redshift, Expanding universe, Big Bang evidence, Spectroscopic binary
  • Hubble constant of the model H₀ 50–100 km/s/Mpc
  • Realistic scatter (peculiar velocities, distance errors)
  • Orbital speed of star A 10–150 km/s

Questions to explore

  1. Why do the measured points not lie exactly on a straight line, and how can the effect of the scatter be reduced?
  2. How would the estimated age of the Universe change if H₀ were larger?
  3. If you stood in another galaxy, would you seem to be at the centre of the expansion? Why?

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