Lesson 2 of 6 · Radial velocity
Radial velocity
10 minute lesson · 3 checks along the way
Your goal for this lessonInterpret a star’s changing spectral shifts and distinguish a projected mass constraint from a full three-dimensional orbit.
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The star moves too
A planet and its star both move around their shared center of mass. The star’s motion is usually much smaller because the star is much more massive. A spectrograph spreads starlight by wavelength. As the star alternately approaches and recedes along our line of sight, its spectral lines shift. Repeated measurements can reveal a periodic velocity component caused by an orbiting companion.
measures motion toward or away from us; it does not directly plot the star’s sideways position on the sky. Instruments such as ESO’s HARPS compare many spectral features with a stable wavelength calibration. Observers also correct for the observing platform’s motion. Without those corrections, Earth’s orbital motion or instrumental drift could be mistaken for part of the star’s signal. A measured spectrum is the starting point of the analysis, not an already labeled orbit.
Projection hides part of the answer
For an isolated, well-modeled companion much less massive than its star, the orbital fit typically constrains Mp sin i when i is unknown. Here i = 90 degrees means an edge-on orbital plane, and i = 0 means face-on. An edge-on orbit supplies the largest line-of-sight reflex signal for the same physical system. A face-on orbit can have real stellar motion with no orbital radial-velocity variation.
The mass estimate also depends on the stellar mass, period, and eccentricity. An amplitude alone is insufficient. Calling Mp sin i a minimum mass is useful within the low-companion-mass approximation: sin i cannot exceed one. A constrains inclination near edge-on, while can constrain the orbit on the sky. Combining compatible measurements therefore removes information gaps that a more precise version of only one measurement might leave.
Check 1 of 3
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Work through a decision
Subtract the baseline before measuring the wobble
Consider fictional velocities of +15, +35, +15, −5, and +15 meters per second sampled at quarter-orbit intervals of a circular model. The constant is +15 meters per second. Subtract it and the residuals are 0, +20, 0, −20, and 0. The is 20 meters per second: half the 40-meter-per-second peak-to-peak change. The constant positive baseline does not mean the orbital motion always points away.
In a separate low-mass-companion fit, suppose Mp sin i equals two chosen mass units. At i = 90 degrees, sin i = 1 and Mp is two units. At i = 30 degrees, sin i = 0.5 and Mp is four units. Both can share that same projected constraint. These are teaching values, not measurements of a named planet. Keep the stellar assumptions fixed when making this comparison.
Baseline and semi-amplitude
Original instructional circular-orbit curve. The star’s systemic velocity offsets the entire curve; subtracting it leaves a ±20 m/s orbital variation. The curve supplies no planetary mass without the remaining orbital and stellar assumptions.
Open full-size diagram in a new tab: Baseline and semi-amplitudeCheck 2 of 3
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Ask whether the lines trace orbital motion
can change spectral-line profiles and mimic part of a Doppler signal. Rotating spots, evolving magnetic regions, and other stellar processes are therefore not merely background decoration. Researchers compare activity indicators, multiple wavelengths, sampling patterns, and independent observations. Agreement at a period is useful, but a plausible repeating stellar process must still be examined rather than removed by assertion.
A good next observation depends on the uncertainty. Additional spectra may distinguish a coherent orbital signal from evolving activity; sky-position measurements may constrain inclination. The 2025 Gaia-4b study combined Gaia astrometry with ground-based radial velocities, illustrating that complementarity. No single instrument automatically supplies every planetary property. Radial velocity adds a dynamical constraint to the radius information a transit can provide, while leaving atmospheric composition to other measurements.
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Put it together
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Go to the source
Explore the evidence behind this lesson. These optional readings and videos open in a new tab.
- Read: ESO: the HARPS spectrographInstrument operation and the importance of stellar-activity monitoring.
- Read: Masses from radial velocity and GaiaOriginal research on the inclination ambiguity and astrometric constraints.
- Read: Gaia wobbles with spectroscopic follow-upDated February 2025 account of complementary detections.