Exoplanet Radial Velocity Wobble

System Parameters

Planet mass 1.00 M♃

Orbital distance 0.10 AU

Star mass 1.00 M☉

Eccentricity 0.00

Radial Velocity

RV semi-amplitude K

–

Current RV

–

Orbital period

–

Doppler state

–

Blueshifted — star approaching Earth
Redshifted — star receding
Planet, orbiting the barycenter

How the radial-velocity method works

A star and its planet both orbit their common center of mass (barycenter), not each other. The planet swings around in a wide orbit; the much heavier star swings around in a tiny mirror orbit of its own. As the star wobbles toward and away from Earth, its light is Doppler-shifted: blueshifted while approaching, redshifted while receding. Spectrographs like HARPS measure that shift directly as a periodic velocity signal — the star never needs to be resolved as more than a point of light.

Ms·rs = Mp·rp           (barycenter balance)
P² = 4π²a³ / (G(Ms+Mp))  (Kepler's third law)
K  = (2πG/P)^(1/3) · Mp·sin i / (Ms+Mp)^(2/3) · 1/√(1−e²)

Planet mass — a heavier planet pulls the star through a wider, faster wobble, raising the RV semi-amplitude K.
Orbital distance — sets the orbital period via Kepler's third law; closer planets orbit (and wobble the star) faster.
Star mass — a heavier star barely moves for the same planet, shrinking both its orbit and its Doppler signal.
Eccentricity — stretches the orbit into an ellipse; the star whips fastest near closest approach (periapsis), producing a sharp spike in the RV curve instead of a smooth sine wave.

This is the method that found 51 Pegasi b in 1995 — the first exoplanet confirmed around a Sun-like star — and it remains the primary way to measure a planet's true mass once the transit method has found its size.

t = 0.0 s

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.