A shifting fingerprint
Hydrogen has recognisable transitions. In this model, motion shifts its line positions without changing their identity. An absorption line and an emission line undergo the same Doppler factor.
The portal / Laboratory / Doppler effect
Motion is written
in light.
A star approaches or moves away. Its spectral lines shift. Change its velocity and learn to read this shift.
Compare two hydrogen lines with their rest references. The model represents motion directly along the line of sight, in a vacuum.
Preparing…
The positions of the lines will be calculated.
Two spectra. One reference.
The same line, up close.
Reference · dashed Observed · solid
On a small screen, scroll the charts horizontally. 1 nm = 1,000 pm.
Night mode changes chart colours. Values, labels and dashed lines remain the guides for reading them.
—Observed wavelength
—Shift of the selected line
Δλ = observed λ − rest λ
—Relative shift z, without units
z = Δλ / rest λ
| Line | At rest (nm) | Observed (nm) | Shift |
|---|
What if a planet made the star wobble?
A planet and its star orbit their common centre of mass. Part of the star’s motion may then appear as alternating approach and recession.
Explore a fictional radial velocity example: amplitude of 10 m/s, period of 10 days, and a zero mean. The sine wave represents the simple case of a circular orbit; this is not a real observation.
A periodic variation is a clue to investigate: stellar activity, stellar companions and instrumental effects can also disturb spectral lines. This example determines neither a planet’s mass nor its orbital inclination.
Three guides to reading spectral lines
What the shift tells us.
Velocity along our line of sight
Radial velocity follows the line of sight: negative for approach, positive for recession. The main model assumes motion entirely in this direction; it does not represent the total velocity of an oblique motion.
A shift, not a colour
“Redshift” means “towards longer wavelengths”. An initially blue line may remain blue after a small redshift. A star’s overall colour also depends on its thermal continuum.
From shift to velocity
A proportion shared by all lines.
Observed λ / rest λ = √[(1 + β) / (1 − β)]
With β = v / c and c = 299,792,458 m/s. This relation applies here to the longitudinal relativistic case in a vacuum. The sign of v follows the convention of negative approach and positive recession.
We define z = (observed λ − rest λ) / rest λ. When velocity is small compared with the speed of light, v ≈ c × z. For the longitudinal model, the exact inverse relation is v / c = [(1 + z)² − 1] / [(1 + z)² + 1].
Try the +3,000 km/s reference to compare the approximation with the relativistic calculation. This velocity is chosen for the experiment and does not represent a particular star.
A model for understanding.
Lines, wavelengths and illustration
Two hydrogen references are used: Hα at 656.4614 nm and Hβ at 486.2721 nm in a vacuum, based on SDSS-III values. The values often quoted for air differ and must not be mixed with vacuum values.
The bands show line positions; the enlarged profiles use artificial Gaussians whose widths adapt to the zoom. Depth, width and intensity do not describe a real stellar atmosphere. The model applies no noise, rotation, radiative transfer or relativistic transformation of intensity.
The extra decimal places reveal small calculated shifts. The rounded references and the drawing do not provide a measurement standard accurate to a few metres per second.
What the Doppler calculation includes
The main calculation considers two inertial reference frames in relative motion directly along the line of sight. For the small fictional periodic signal, this calculation is applied to the instantaneous radial motion: an educational approximation at low velocities, without complete orbital geometry.
A real astronomical measurement requires further references and corrections, including the observer’s motion, atmospheric effects and stellar activity. Gravitational redshift and cosmological redshift due to the expansion of the Universe are not simulated. No distance is inferred from z here.
Scientific sources
- SDSS-III · spectra and vacuum wavelengths : Hα and Hβ references, air/vacuum conversion.
- University of California, San Diego · The Relativistic Doppler Effect : longitudinal relation and sign convention.
- NASA · How We Find and Characterize : the radial velocity method.
- ESO · HARPS : line shifts, exoplanet detection and the role of stellar activity.
Sources accessed on 19 October 2026. Text, diagrams and profiles created for this experiment.
Continue the experiment