The radial component of the wobble scales with sin i for circular orbits. Face-on systems (i near 0) show almost no line-of-sight motion; only edge-on geometries let sin i ≈ 1.

Is eccentricity included?

No — this page uses e = 0. Eccentric orbits add harmonic content and change the effective K.

Exoplanet Radial Velocity

K from masses & P; sinusoidal V_r(t); M sin i.

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About this model

In the two-body problem the star and planet orbit their barycenter. For a circular orbit the star’s line-of-sight velocity is sinusoidal with semi-amplitude K = (M_p/M_tot) √(G M_tot/a) sin i, with a fixed by Kepler’s third law from M_tot and P. Spectroscopy measures Doppler shifts; without knowing inclination i, radial-velocity surveys constrain M_p sin i rather than M_p alone. Stellar activity (“jitter”) and multiple planets add complexity beyond this single-planet, zero-eccentricity model.

Who it's for: Pairs with the transit simulator and spectral Doppler page.

Key terms

radial velocity
Doppler wobble
semi-amplitude
M sin i
Kepler’s third law

How it works

A planet and star orbit their common center of mass. The star’s line-of-sight speed varies with the orbital phase; for a circular orbit the radial velocity is sinusoidal with semi-amplitude K. Larger planet mass, shorter period (smaller a), and higher sin i increase K. Spectrographs measure Doppler shifts of stellar lines; the minimum planet mass is M sin i when inclination is unknown. This page neglects eccentricity and stellar jitter.

Key equations

a³ = G M_tot P² / (4π²) · K = (M_p/M_tot) √(G M_tot/a) sin i

V_r(t) = K sin(2πt/P + φ)

Frequently asked questions

Why M sin i?: The radial component of the wobble scales with sin i for circular orbits. Face-on systems (i near 0) show almost no line-of-sight motion; only edge-on geometries let sin i ≈ 1.
Is eccentricity included?: No — this page uses e = 0. Eccentric orbits add harmonic content and change the effective K.

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