Questions: Doppler Effect Applications in Astronomy

Question 1

A spectral line normally observed at 500 nm appears at 520 nm in a distant galaxy's spectrum. Is this galaxy approaching or receding? Estimate its recession velocity.

Model answer: The line shifted to a longer wavelength — a redshift — so the galaxy is receding. Using Δλ/λ = v/c: Δλ = 20 nm, λ = 500 nm, so v/c = 20/500 = 0.04, giving v ≈ 0.04c ≈ 12,000 km/s.

Red = longer wavelength = receding. The classical Doppler approximation Δλ/λ ≈ v/c works for velocities well below c. At v = 0.04c the relativistic correction is small (~0.1%) and can be ignored at introductory level.

Question 2

Why is the cosmological redshift of distant galaxies not simply caused by the galaxies moving through space?

Model answer: Cosmological redshift is caused by the expansion of space itself — the fabric of space stretches while photons travel through it, increasing their wavelengths. The galaxies are not necessarily moving through space at high velocities; space between them is expanding, carrying them apart. This is why galaxies can appear to recede faster than light without violating special relativity.

The distinction matters because ordinary Doppler redshift from motion through space has different implications than cosmological redshift from space expansion. The two are described by different mathematical frameworks: special relativity handles the former; general relativity and the Friedmann equations handle the latter.

Question 3

Why must relativistic Doppler formulas be used for quasars and distant galaxies, while the classical formula works for nearby stars?

Model answer: Classical Doppler assumes velocities much smaller than c. For nearby stars, radial velocities are typically tens to hundreds of km/s — tiny fractions of c — so the classical approximation is accurate. Distant quasars can have recession velocities that are significant fractions of c, where relativistic time dilation changes the observed frequency by amounts that cannot be ignored.

The relativistic Doppler formula reduces to the classical formula in the limit v << c. At v = 0.1c, the difference between classical and relativistic predictions is about 0.5% — small but measurable. At v = 0.5c, the difference is 13%, which would produce significant errors in velocity estimates.