Redshift
The same shifts in frequency and wavelength are also observed for light coming from stars in distant galaxies.
By comparing the light from distant stars with the spectrum of light from our Sun it was noticed that the spectra from distant stars had a slightly decreased frequency and slightly increased wavelength. This indicated the stars were moving away from Earth (just as the sound of a siren moving away from you has a decreased frequency and increased wavelength).
As the light was shifted towards the red end of the spectrum (lower frequency/longer wavelength) this phenomenon was termed 'redshift'.
The upper diagram shows the absorption spectrum from a stationary galaxy with one wavelength of light and no redshift.
Redshift is also the name of the factor z indicating the relative change in wavelength due to the Doppler shift for a receding galaxy.
The Doppler equation used for sound calculations cannot be used in this situation. This is because galaxies are receding (moving away) at such high speeds that relativistic effects need to be considered in calculations.
The following equation is used to calculate redshift:
\(z=\frac{\lambda observed-\lambda rest}{\lambda rest}\)
So if a distant A cluster of billions of stars, held together by gravity. emits a characteristic spectral line of 91 nm (A high energy part of the electromagnetic spectrum associated with sunburn and skin cancer. light at the 'Lyman limit') but when observed on Earth it appears to be 640 nm (red) we can calculate the red shift using this equation:
\(z= \frac {640-91}{91}\)
There is no need to convert nanometres to metres as units cancel top and bottom.
\(z=6.03\)
For slowly moving galaxies, redshift is the ratio of the The speed of an object in a particular direction. of the galaxy to the velocity of light.
\(z= \frac{v}{c}\)