Astrophysics Interactive

Doppler Shift Visualiser

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

1 + z = √((1 + β)/(1 − β)) Longitudinal special-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
Spectroscopic redshift z 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
First-order approximation for |vr| ≪ c. At 300 km s⁻¹, the exact correction is about 0.05% of the first-order wavelength shift.
Relativistic (full)
λobs = λ₀ √( (1 + β) / (1 − β) )
β = vr/c for one-dimensional relative motion in flat spacetime. Cosmological redshift requires an expanding-universe model and is not this formula.
RV precision context
σv = c / (Q √Ne⁻)
Photon-noise floor from Bouchy, Pepe & Queloz (2001): Q captures the Doppler information in the sampled spectrum and Ne⁻ is the detected photoelectron count. Stellar and instrumental systematics are additional.
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. The O₂ B feature is explicitly telluric and remains fixed in the observer frame; stellar features shift. Real pipelines combine many pixels or lines against a template rather than reading one painted stripe.

Astrophysical applications

Radial-velocity spectroscopy is one of two main methods for detecting exoplanets. A planet gravitationally tugs its host star; an edge-on Earth–Sun analogue produces a stellar semi-amplitude of about 9 cm s⁻¹. Detecting such a signal also requires modelling stellar activity, barycentric motion, tellurics, wavelength calibration, and sampling—not merely resolving a single line displacement.

Na D lines — why they matter

The displayed Na I D₂/D₁ air wavelengths, 588.995 and 589.592 nm, are an illustrative doublet anchored to the NIST Atomic Spectra Database. Line positions alone are not an RV uncertainty model: precision depends on the full spectrum's gradients, photon counts, line-spread function, wavelength solution, and stellar variability.