A planet does not orbit its star. Both orbit their shared centre of mass — and because the star is far heavier, its own circle is tiny. But it is not zero.
That small circle means the star spends part of each orbit moving slightly toward us and part moving away. Motion toward us squeezes its light to shorter wavelengths, motion away stretches it — the Doppler effect, the same one that drops the pitch of a passing siren.
Split the starlight into a spectrum and its absorption lines sit at known wavelengths. Watch them slide back and forth, in step, night after night, and you are watching the star being pulled around by something you cannot see.
"Radial" means along our line of sight. Only motion toward and away is measurable this way; sideways motion leaves the spectrum untouched. That single fact is the method's great limitation.
The arithmetic
Wobble speed the star shows
K = (2πG / P)1/3 · Mp sin i / (M* + Mp)2/3 · 1/√(1−e²)
K is the half-amplitude — the peak speed in metres per second. Heavier planet, or closer in, means a bigger K.
Doppler shift actually measured
Δλ / λ = v / c
What the spectrograph sees. A 10 m/s wobble shifts a line by 3 parts in 100 million — hence instruments like HARPS and ESPRESSO.
Why the mass is a lower bound
measured = Mp · sin i
i is the orbit's tilt, which this method cannot determine. A face-on orbit (sin i ≈ 0) hides almost all of the motion, so every mass here reads "at least".
What our own planets do to the Sun
Jupiter
11.9-year period, 318 Earth masses
moves the Sun at 12.5 m/s
Earth
1-year period, 1 Earth mass
0.09 m/s — 9 cm/s
51 Pegasi b
4.2-day period, ~0.5 Jupiter masses
56 m/s — unmistakable
Walking pace versus the speed of a growing fingernail. Present-day spectrographs reach roughly 0.3 m/s, so Jupiter analogues are routine and Earth analogues remain out of reach.
What it does well
Works whatever the orbit's tilt — no lucky alignment needed
Gives mass, the one thing transits cannot
Mature: the first exoplanet around a normal star was found this way, and the technique has been refined for three decades
Where it cannot help
Only a minimum mass, until the tilt is pinned down another way
Biased toward heavy planets on short orbits — the easiest wobbles
The star's own surface churns: spots and convection produce false wobbles of several m/s, the current wall for Earth-mass detection
Landmark discovery
51 Pegasi b (1995) — the first planet found around a Sun-like star, and a Nobel Prize in 2019.
Instruments
HARPS, HIRES/Keck, ESPRESSO, CARMENES, NEID
Archive name
Radial Velocity — the value in NASA's discoverymethod field