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Astronomical Doppler shifts reveal stellar and galactic motion: blueshifts indicate motion toward us (decreasing wavelength), redshifts indicate motion away (increasing wavelength). For light waves and relativistic velocities, relativistic Doppler formulas apply. Redshift measurements of distant galaxies provide evidence for cosmic expansion.
From your study of the Doppler effect, you know that relative motion between a source and observer compresses or stretches waves: motion toward each other produces higher observed frequency (shorter wavelength), motion apart produces lower frequency (longer wavelength). Astronomy applies this same principle to light — but instead of measuring pitch changes, astronomers compare the observed wavelengths of spectral lines against their known laboratory values. Every element absorbs and emits light at precise, characteristic wavelengths — a unique atomic fingerprint. When a star or galaxy is moving relative to us, those fingerprint lines shift in wavelength by a predictable amount.
If the spectral lines of a star are shifted toward shorter, bluer wavelengths compared to laboratory values, the star is approaching — a blueshift. If they shift toward longer, redder wavelengths, the star is receding — a redshift. The fractional shift Δλ/λ is directly proportional to the radial velocity v/c, so a precise wavelength measurement converts immediately into a velocity. This is how astronomers measure the motion of stars millions of light-years away without any means of physical contact: they read the embedded velocity information in the light itself.
For nearby stars and modest velocities, the classical Doppler formula works well. But for galaxies receding at significant fractions of the speed of light, the relativistic Doppler formula must be applied. At relativistic speeds, time dilation and length contraction alter the classical prediction, and the correct formula accounts for both effects. This matters for quasars — extremely luminous active galactic nuclei — which can exhibit redshifts of z > 6, meaning the observed wavelength is more than seven times the emitted wavelength. Such objects require the relativistic treatment.
The most profound application of astronomical redshift is to cosmic expansion. Hubble observed in 1929 that nearly all galaxies beyond our local group are redshifted, and that the redshift scales with distance — more distant galaxies recede faster. This is Hubble's Law. Crucially, the cosmological redshift of distant galaxies is not simply ordinary Doppler shift from motion through space: it is caused by the expansion of space itself stretching the wavelengths of photons during their journey. The greater the distance, the longer the light has been traveling through expanding space, and the greater the stretch. Measuring these redshifts across billions of galaxies is the primary tool cosmologists use to map the large-scale structure of the universe and reconstruct its history.