Stellar Spectrum: Radial Velocity from a Line Shift
Known rest wavelength λ₀ (Hα). Park a cursor on the shifted absorption line and recover v ≈ c Δλ/λ₀.
Goal
Determine the line-of-sight velocity from v = c (λ − λ₀)/λ₀. Receding is positive.
Equipment
- Zoomed stellar spectrograph
- Known Hα rest λ₀
- Wavelength cursor
Experiment
Theory
For |v| ≪ c the Doppler shift of a rest line is Δλ/λ₀ ≈ v/c. The bench hides v and any printed Δλ/λ. λ₀ is known. A live wavelength cursor on a zoomed spectrograph is the instrument — you read λ yourself.
Procedure
- The rest wavelength λ₀ of Hα is fixed and known. The star’s radial velocity is hidden. You only move the wavelength cursor.
- Park the cursor on the centre of the dark absorption line. The bench does not print v or Δλ.
- Record that λ. The notebook computes v = c (λ − λ₀)/λ₀. Repeat the hunt at least 6 times.
- Take the mean of the v column and compare with the reference.
Conclusion
The mean radial velocity agrees with the hidden redshift of Hα. Main uncertainties: parking the cursor on the line core and the discrete wavelength step.