IGCSE Physics / Cosmology
Calculating the speed of a galaxy revision notes
Edexcel International GCSE Physics (4PH1), chapter 28: Cosmology, specification point 8.16P. Free lesson.
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A galaxy’s speed can be calculated from how much a known spectral line shifts to a longer wavelength. The red-shift equation links this change to the speed of light.
What the wavelengths mean
Compare the same line in a laboratory spectrum and a galaxy’s spectrum. The laboratory gives the reference wavelength, λ₀. The galaxy gives the observed wavelength, λ. The difference is the change in wavelength, Δλ. Δλ = λ − λ₀ A line shifted to a longer wavelength shows that the galaxy is moving away.
How to use the red-shift equation
The equation connects the wavelength shift to the galaxy’s speed. It is on the equation list. The denominator is the reference wavelength from the laboratory, not the observed wavelength. Δλ/λ₀ = v/c Δλ is the change in wavelength, in nm or m. λ₀ is the laboratory reference wavelength; λ is the observed wavelength from the galaxy. v is the galaxy’s speed in m/s. c is the speed of light, 3 × 10⁸ m/s.
How to calculate a galaxy’s speed
Find the wavelength change first, then use the reference wavelength in the fraction. This gives the galaxy’s speed in metres per second.
How to find an observed wavelength
When the speed is given, rearrange the same equation to find the change in wavelength. For a galaxy moving away, the observed wavelength is longer, so add the change to the reference wavelength.