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

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

Live graphs

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.