Radial Velocity Method: Detecting Exoplanets by Stellar Wobble

Orbital Parameters

Planet mass 1.00 M_J

Orbital period 10.0 d

Eccentricity 0.00

Inclination 90°

Doppler Readouts

RV semi-amplitude K

— m/s

Current radial velocity

— m/s

Minimum mass (M_p sin i)

— M_J

← blueshiftredshift →

Radial Velocity Curve

How it works

A planet doesn't just orbit its star — the star orbits the system's common center of mass (barycenter) too, with a much smaller radius. As the star wobbles toward and away from Earth, its light is Doppler-shifted: blueshifted while approaching, redshifted while receding. This is the radial velocity method, the technique that found the first confirmed exoplanet around a sun-like star (51 Pegasi b, 1995).

Kepler's equation:  E − e·sin(E) = M(t),  M(t) = 2π t / P
True anomaly:       ν = 2·atan2(√(1+e)·sin(E/2), √(1−e)·cos(E/2))
RV semi-amplitude:  K = (2πG/P)^(1/3) · Mp·sin(i) / (M★+Mp)^(2/3) / √(1−e²)
Radial velocity:    v_r(t) = K · [cos(ν(t)) + e]

Planet mass — heavier planets tug the star harder, raising K in direct proportion.
Orbital period — shorter periods mean a tighter, faster orbit and a larger K (K ∝ P^-1/3).
Eccentricity — stretches the ellipse and skews the RV curve into a sharp spike near periastron instead of a smooth sinusoid.
Inclination i — the tilt of the orbital plane relative to the sky. i = 90° is edge-on (we see the full velocity swing); i → 0° is face-on (the star's motion is entirely sideways, no Doppler signal). Because only Mp·sin(i) is measurable this way, radial velocity alone gives a minimum mass — the true mass could be higher if the orbit is more face-on.

Positions in the 3D view are rescaled for visibility and playback is time-compressed so any period completes in a few seconds — but the velocity readouts and the RV curve use the real formula above with the period, mass and eccentricity you set.

Star (wobbles) Planet (unseen) Barycenter

👁 Observer looks along +Z

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