Stellar Radial Velocity (Doppler Spectroscopy) Calculator
Calculate a star's radial velocity from observed spectral line shift.
Determine if a star is approaching (blueshift) or receding (redshift).
Doppler spectroscopy measures how fast a star is moving toward or away from us by detecting tiny shifts in the wavelengths of its spectral lines.
The Doppler formula:
v_r = (Δλ / λ₀) × c = ((λ_obs - λ_rest) / λ_rest) × c
Where:
- v_r = radial velocity (positive = receding, negative = approaching)
- λ_rest = rest (lab) wavelength
- λ_obs = observed wavelength
- c = 299,792.458 km/s
Blueshift vs redshift:
- λ_obs < λ_rest → star is approaching (blueshift, Δλ negative)
- λ_obs > λ_rest → star is receding (redshift, Δλ positive)
Common spectral lines used:
- H-alpha: λ₀ = 656.28 nm (hydrogen)
- H-beta: λ₀ = 486.13 nm (hydrogen)
- Ca II K: λ₀ = 393.37 nm (calcium)
- Ca II H: λ₀ = 396.85 nm (calcium)
- Na D doublet: λ₀ ≈ 589 nm (sodium)
Exoplanet detection: This technique can detect exoplanets by the wobble they induce in their host star. Jupiter causes the Sun to wobble at about 12.5 m/s. Earth’s effect on the Sun is only about 0.09 m/s — at the limit of current instruments. The HARPS spectrograph can measure velocities to ~1 m/s precision. The radial velocity method was used to discover the first confirmed exoplanet around a Sun-like star in 1995 (51 Pegasi b).
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