Exoplanets
Radial Velocity
Detecting exoplanets by their gravitational tug on stars — Doppler shift in starlight
Radial velocity (RV) measures stellar motion along line of sight via Doppler shift in spectral lines. As a planet orbits a star, the star also moves in a small orbit around the system's center of mass. This causes periodic shift in starlight wavelengths. Detected for: massive close-in planets (large signal). 51 Pegasi b — first confirmed exoplanet (1995, Mayor and Queloz). Sensitive to planet mass × sin(i). Combined with transit (which gives radius), gives planet density and composition.
- First confirmed exoplanet51 Pegasi b, 1995 (RV detection)
- DiscoverersMayor and Queloz (Nobel 2019)
- SensitivityVelocity to <1 m/s with HARPS, ESPRESSO
- Best forMassive planets; close-in
- ProvidesMass × sin(i); orbital period
- Now combined withTransit (gives radius) → density
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Why RV matters
- Mass measurement. Direct mass (with inclination).
- Confirmed exoplanets. Original detection method.
- Planet diversity. Discovered hot Jupiters, super-Earths.
- Density via transit + RV. Composition determination.
- Spectrograph science. Drive precision instruments.
- Habitable zone. Future Earth-analog discoveries.
- Stellar physics. RV scatter from stellar activity.
Common misconceptions
- RV gives exact mass. Gives m × sin(i); minimum mass.
- RV detects all planets. Most sensitive to massive close-in.
- Higher precision needed. Yes — 10 cm/s for Earth-mass HZ.
- RV outdated. Still essential for mass determination.
- RV affected by atmosphere. Yes — extreme precision needs careful calibration.
- Doppler shift is small. 51 Peg b: 56 m/s; Earth: 0.09 m/s.
Frequently asked questions
How does RV work?
Star and planet orbit common center of mass. Star moves slightly (much smaller orbit; star much heavier). Star's motion along line of sight: detected as Doppler shift of spectral lines. Periodic over orbital period. Amplitude reveals mass × sin(inclination). Doesn't give exact mass; provides minimum mass (m sin i).
What's the velocity sensitivity needed?
For Sun-Earth: K = 0.09 m/s. For Sun-Jupiter: K = 12.5 m/s. Modern instruments (HARPS, ESPRESSO): <1 m/s. Hot Jupiters: easy (10s of m/s). Earth-mass planets in HZ around Sun-like stars: very challenging — requires extreme precision.
How does Doppler shift work?
Light from star contains spectral lines at known wavelengths. When star moves: lines shift. Toward observer: blueshift (shorter λ). Away: redshift (longer λ). Δλ/λ = v/c. Precision spectrographs measure shifts to 10⁻¹⁰ — extraordinary precision.
What's the m sin i degeneracy?
RV measures mass × sin(inclination). Without knowing inclination i, can't determine exact mass. Lower bound: m_min = m sin i. For randomly oriented orbits: typical inclination ~60° → typical actual mass ~1.15× m_min. Combined with transit (where i ≈ 90°) gives true mass.
How was 51 Pegasi b discovered?
Michel Mayor and Didier Queloz (Geneva). October 1995. Detected radial velocity variation of 51 Pegasi (Sun-like star) with 4.2-day period and 56 m/s amplitude. Indicated: 0.5 Jupiter-mass planet at 0.05 AU. First confirmed exoplanet around a main-sequence star. Surprised astronomers — hot Jupiters were unexpected. Nobel Prize 2019.
What stars work best?
Bright (Sun-like, F/G/K). Slowly rotating (sharp lines). Quiet (low magnetic activity). Low mass (more induced motion). M dwarfs: closer planets in HZ; smaller star → more reflex motion. ESPRESSO targets nearby M dwarfs. Best results from clean, well-behaved stars.
What's the future?
HARPS (~1 m/s precision). ESPRESSO (<10 cm/s). EXPRES, NEID, KPF in US. Plans to detect Earth-mass HZ planets around Sun-like stars. Also: precision spectrographs combined with high-altitude AO. Goal: <10 cm/s — sufficient for Earth analog detection. Decades of work.