Measure stellar wobble from planet gravity—compute RV semi-amplitude and period from Doppler shifts
The radial velocity (RV) method was the first technique to successfully detect exoplanets orbiting Sun-like stars. It works by measuring the tiny Doppler shift in a star's spectrum as it wobbles in response to an orbiting planet's gravitational pull. When the star moves toward us, its light is blueshifted; when it moves away, it's redshifted. By tracking these shifts over time, astronomers can infer the presence, mass, and orbit of unseen planets.
The amplitude K of the radial velocity curve depends on the planet's mass M_p, orbital period P, eccentricity e, and orbital inclination i. For circular orbits around a Sun-like star:
K ≈ 28.4 (M_p/M_Jup) (P/year)-1/3 sin(i) m/s
A Jupiter-mass planet in a 10-day orbit produces K ≈ 200 m/s, while an Earth-mass planet at 1 AU produces only K ≈ 0.09 m/s—requiring exquisite precision to detect. Modern spectrographs achieve precision below 1 m/s, enabling detection of Neptune-mass and super-Earth planets.
Eccentric orbits produce asymmetric RV curves with sharper peaks when the planet is at periastron (closest approach) and slower variations at apastron. The shape of the curve encodes both the eccentricity e and the argument of periastron ω, providing detailed information about the orbit's geometry beyond what transit photometry alone can reveal.
RV measurements alone yield only M_p sin(i)—a lower limit on the planet's mass. For randomly oriented orbits, the true mass could be larger if the orbit is inclined relative to our line of sight. When transit observations are available, they constrain i ≈ 90°, breaking this degeneracy and providing the true mass. This synergy between RV and transit methods has characterized thousands of exoplanets.
To detect periodic signals in noisy RV data, astronomers use the Lomb-Scargle periodogram, which identifies the periods that best fit the observations. The periodogram shows power as a function of trial period—peaks indicate candidate orbital periods. For unevenly sampled data typical of ground-based surveys, Lomb-Scargle is superior to Fourier analysis. False alarm probabilities quantify detection significance.
In 1995, Michel Mayor and Didier Queloz announced the discovery of 51 Pegasi b using the RV method—the first exoplanet found orbiting a Sun-like star. This "hot Jupiter" in a 4.2-day orbit defied theoretical expectations and sparked the exoplanet revolution. The RV method has since discovered over 1000 exoplanets and remains crucial for measuring planetary masses and characterizing multi-planet systems. Mayor and Queloz received the 2019 Nobel Prize in Physics for this breakthrough.