Radial velocity

15 chapters, each an animated explainer with its physics and sources. Every drawing says whether it is an illustration, a model from stored values, or real data, and by how much it is exaggerated. Only the transit chapter is something SetuHQ itself does.

Chapter 4 of 15

Radial velocity

A planet and its star both orbit their shared centre of mass, the barycentre. The star's small orbit makes its light shift back and forth: the radial-velocity curve. Its amplitude K gives the planet's minimum mass, m sin i.

Model from stored values
Top-down view with the observer at the bottom. A star and its planet orbit their barycentre, always on a straight line through it, at the same period and opposite phase; the star's motion is exaggerated and labelled. Eccentric orbits speed up near periastron (Kepler's equation). Beside it, the radial-velocity curve is drawn live and a strip of spectral lines shifts blue and red in step.

The numbers

K = (2πG/P)^⅓ · Mp sin i / (M★ + Mp)^⅔ / √(1 − e²) (Gaudi & Winn 2007). The star's orbit is a★ = a · Mp/(M★ + Mp); the planet's is a · M★/(M★ + Mp). Eccentric orbits follow Kepler's equation, M = E − e sin E. Masses use the IAU nominal GM values (Prša et al. 2016).

QuantityValueFrom
51 Peg b: K from our formula56.7 m/sexoplanet.eu P = 4.2307966 d, m sin i = 0.46 MJ, M★ = 1.03 M☉, e = 0.0069 [calc]
51 Peg b: K published55.77 m/sexoplanet.eu; about 56 m/s
Difference+1.6%ours vs published; the catalogue mixes values from different papers
Jupiter–Sun K12.5 m/sP = 11.862 yr, e = 0.049, IAU nominal masses [calc]
Jupiter–Sun barycentre1.07 R☉ from the Sun's centrejust outside the surface [calc]
Earth–Sun K8.9 cm/s[calc]
Earth–Sun barycentre449 km from the Sun's centredeep inside the Sun [calc]
pi Men c: K from our formula1.20 m/sexoplanet.eu stored K = 1.21 m/s; Huang et al. 2018 values (4.82 M⊕) give 1.57 m/s [calc]
Best spectrograph stability< 25 cm/s in a nightESPRESSO (Pepe et al. 2021)

Why Earth twins are hard

An Earth twin moves its Sun-like star by about 9 cm/s. ESPRESSO holds better than 25 cm/s within a night and about 50 cm/s over months (Pepe et al. 2021). The star's own surface (granulation, oscillations, spots) adds RV noise of order m/s (Fischer et al. 2016), larger than the signal itself.

Illustration
A close-up of a Sun-like star's surface: granulation cells rise (blueshifted) and sink (redshifted), with tracked markers. Beside it, an Earth twin's radial-velocity signal of about 9 centimetres per second over two years, with each point scattered by the chosen noise level, showing the signal buried in the star's own motion.

1,329 of the 8,049 planets with a stored distance in exoplanet.eu were found by radial velocity (the first method listed). Show them on the Galaxy map ›

peak 124 (2022)

19882026

Planets found by radial velocity per year, 1988–2026: 1,329 in all; the most in one year was 124 in 2022. Source: exoplanet.eu, fetched 2026-10-18.
Planets in this chapter51 Peg b ›HD 80606 b ›pi Men c ›
Sources

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