Astrophysics Interactive

Doppler Shift Visualiser

Explore how stellar radial velocity shifts spectral lines — the physical basis of precision radial-velocity spectrography for exoplanet detection.

Δλ / λ = v / c Non-relativistic Doppler
Wavefront geometry
Blueshift — approaching Redshift — receding
Radial velocity 0 km s⁻¹
Rest wavelength λ₀ 589.592 nm (Na D₁)
Observed λ 589.592 nm
Wavelength shift Δλ 0.000 nm
Fractional shift Δλ/λ 0.000 × 10⁰
Effect No shift
Absorption-line spectrum — sodium D lines (Na I)
380 nm 450 nm 500 nm 550 nm 600 nm 650 nm 700 nm 750 nm
Radial velocity control
−300 km s⁻¹ v = 0 km s⁻¹ +300 km s⁻¹
← Approaching (blueshift) Receding (redshift) →
Key equations
Non-relativistic Doppler
Δλ / λ₀ = vr / c
Valid for vr ≪ c. At 300 km s⁻¹, v/c ≈ 10⁻³, so the relativistic correction is < 0.1%.
Relativistic (full)
λobs = λ₀ √( (1 + β) / (1 − β) )
β = vr/c. Used for cosmological redshifts and high-speed stellar jets.
RV precision context
σRV = (c / R) · (S/N)⁻¹ · β⁻½
R = resolving power, β = spectral filling factor. HARPS achieves ~1 m s⁻¹; ESPRESSO targets ~10 cm s⁻¹.
Live calculation
Δλ = 589.592 × (0 / 299792.458) = 0.000 nm

Physical mechanism

A stellar atmosphere radiates photons at precise rest wavelengths governed by atomic energy levels. When the star moves radially with velocity vr, the wavelengths of received photons are shifted by Δλ = λ₀ vr/c. This is the first-order Doppler effect. A receding source (positive vr) stretches photon wavelengths — redshift. An approaching source compresses them — blueshift.

Spectral lines shown

The visualiser uses the sodium D lines (Na I doublet at 588.995 and 589.592 nm) as the primary indicator, alongside representative Fe I, Mg I, Hα, and Ca II H&K lines. In a real spectrograph, hundreds of such lines are cross-correlated simultaneously to build a high-precision velocity measurement.

Astrophysical applications

Radial-velocity spectroscopy is one of two main methods for detecting exoplanets. A planet gravitationally tugs its host star; the stellar reflex velocity for an Earth-mass planet in a 1-AU orbit is only ~9 cm s⁻¹. Detecting that requires σRV < 10 cm s⁻¹, motivating ultra-stabilised spectrographs such as HARPS, ESPRESSO, and EXOhSPEC.

Na D lines — why they matter

Sodium D lines are strong, narrow, and appear in virtually every late-type stellar spectrum. Their sharpness (small intrinsic width) makes centroid measurement precise. In the solar spectrum they are among the most prominent absorption features, detected in stellar atmospheres, interstellar medium, and exoplanet atmospheres via transmission spectroscopy.