Doppler Sign Shift Cross-Scan - Observational Astrophysics: Distance, Flux, Transits, and Spectra Step by Step

A Doppler-sign-shift cross-scan flips the source's radial-velocity sign across rows, showing how the wavelength shift reverses between redshift (receding) and blueshift (approaching). The arithmetic is exact only for the stated velocities, rest wavelengths, and rows in the ideal low-speed Doppler model. Real observations add calibration, finite cadence/bandpass, noise, stellar variability, line-identification uncertainty, detector response, and measurement uncertainty.

Three exact rows show signed radial speed over light speed. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The signed radial speed sets the signed shift ratio

The checked source uses radial speed negative one and light speed six, so the normalized line shift is negative one sixth.

\Delta\lambda/\lambda=\frac{-1}{6}=-\tfrac{1}{6}

Approaching and receding cases differ by sign

The scan includes one approaching case, one receding case, and one larger receding speed with the same training light speed.

\begin{array}{c|c|c}v&c&\Delta\lambda/\lambda\\-1&6&\frac{-1}{6}\\1&6&\frac{1}{6}\\2&6&\frac{1}{3}\\\end{array}