When a source of waves moves relative to an observer, the observed frequency and wavelength change. This is the Doppler effect.• source moving away: wavelength increases, frequency decreases: red shift
• source moving towards the observer: wavelength decreases: blue shift
Astronomers measure the shift of known absorption lines (for example hydrogen lines) in a star's or galaxy's spectrum. For speeds much less than the speed of light (v << c):z = Δf / f = v / c Δλ / λ = −v / c where z is the red shift, v the speed along the line of sight, and the minus sign shows that when frequency increases the wavelength decreases. In calculations use the size of the shift: z = v/c = Δλ/λ.Worked example: a hydrogen line with laboratory wavelength 656.3 nm is observed at 662.9 nm in a galaxy's spectrum.
Δλ = 662.9 − 656.3 = 6.6 nm (an increase, so red shift: the galaxy is receding)
v = c × Δλ / λ = 3.00 × 108 × 6.6 / 656.3 = 3.0 × 106 m s-1Binary stars: in a spectroscopic binary the two stars orbit each other. Viewed edge-on, each star moves alternately towards and away from us, so its spectral lines are alternately blue shifted and red shifted. The lines split and merge periodically, and the time between repeats gives the orbital period. Viewed face-on (orbital plane perpendicular to the line of sight) there is no Doppler shift.
• source moving towards the observer: wavelength decreases: blue shift
Astronomers measure the shift of known absorption lines (for example hydrogen lines) in a star's or galaxy's spectrum. For speeds much less than the speed of light (v << c):Δλ = 662.9 − 656.3 = 6.6 nm (an increase, so red shift: the galaxy is receding)
v = c × Δλ / λ = 3.00 × 108 × 6.6 / 656.3 = 3.0 × 106 m s-1Binary stars: in a spectroscopic binary the two stars orbit each other. Viewed edge-on, each star moves alternately towards and away from us, so its spectral lines are alternately blue shifted and red shifted. The lines split and merge periodically, and the time between repeats gives the orbital period. Viewed face-on (orbital plane perpendicular to the line of sight) there is no Doppler shift.