LearnLight & spectraSome maths
Doppler shift and redshift
Motion along the line of sight stretches or compresses the wavelength of light, moving spectral lines toward the red or the blue.
Why it matters
It is how we measure the radial velocity of anything — the wobble of a star with planets, the rotation of a galaxy, the expansion of the universe itself.
The maths, in layers
1 · Intuition
The fractional change in wavelength equals the fractional velocity, while v is small compared with c.
2 · The equation
z = (λ_obs − λ_rest) / λ_rest ≈ v / c
- z
- redshift, dimensionless
- λ_obs, λ_rest
- observed and laboratory wavelengths
What people usually get wrong
Cosmological redshift is a Doppler shift from galaxies rushing away.
For distant galaxies the wavelength is stretched by the expansion of space itself while the light is in transit. The arithmetic resembles a Doppler shift, but the cause is different.
Rests on
2 concepts in the full chain back to first principles.