Double Speed Doubles the Shift Ratio - Observational Astrophysics: Distance, Flux, Transits, and Spectra Step by Step

Because the Doppler shift ratio is linear in radial speed at low velocities, doubling the speed doubles the wavelength shift. The proportionality is the v / c rule applied twice over. It holds only within the low-speed approximation and for a stated rest wavelength; real velocities come from noisy, blended, calibrated spectra, and fast sources need a relativistic correction that bends the linearity.

Changing only radial speed changes the exact signed ratio. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Only radial speed doubles

The radial speed changes to 2 meters per second while light speed stays 6.

\frac{v}{c}=\frac{2}{6}

The shift ratio becomes one third

The exact checked ratio is 1/3, so the contrast is proportional.

\Delta\lambda/\lambda=\tfrac{2}{6}=\tfrac{1}{3}