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The Red Shift

Possibly one of the most important uses of the Doppler Effect has been the measurement of the motion of galaxies.

The Doppler Effect predicts that radiation from sources that are towards us will be shifted towards shorter wavelengths (the blue end of the spectrum in the case of visible light) and towards longer wavelengths (the red end of the spectrum) if they are moving away from us.

See: Doppler effect

Observations of the spectra of galaxies show that the light coming from many of these is shifted significantly towards the red and this shows that they are moving away from us at high speeds, many tens of thousands of kilometres per second. This shift towards the red is called the Red Shift and is very good evidence for the expansion of the Universe and for the origin of the Universe in the Big Bang.

If the Doppler shift of lines within their spectra can be measured their speed of recession can be calculated. The speed (v) relative to the observer on the Earth is given by:

Velocity of galaxy (v) = Δλc/λ where λ is the wavelength of a line in the spectrum on Earth, Δλ is the shift in wavelength and c is the speed of light.

A diagrammatic version of the shift of two absorption lines for three galaxies together with their speeds of recession is shown in the following diagram. The comparison spectrum of an element on Earth, at rest compared with the observer, is shown above and below each galactic spectrum.

For very high speeds the simple formula cannot be used and the effects of special relativity have to be allowed for.

It is important to realise that the Doppler shift will depend on the original wavelength and so lines in the red end of the spectrum will be shifted more than those towards the violet end.


Example problems
1. Find the change in the wavelength of the light from a galaxy that is moving away from the Earth at 2000 kms-1. Assume that the emitted wavelength is 600 nm. (Speed of light in free space = 3x108 ms-1)
Using :- Δλ = λv/c = 600x10-9x2000x103/3x108 = 4 nm

2. If the wavelength of 650 nm emitted by one component of a double star is shifted by 0.05 nm compared with that of its attendant star calculate the velocity of its companion.
v = [Δλ/λ] c = 0.05x3x108/650 = 2.3x104 ms-1 = 23 kms-1
© Keith Gibbs 2013