Many exoplanets were discovered by the tiny back-and-forth Doppler shifts they cause in their star’s light. Jupiter makes the Sun wobble by about 12.5 m/s; Earth by only 9 cm/s – which is why Earth twins are so hard to find.
How to use the Exoplanet Discovery Calculator
- Star mass
- Planet
- Planet mass
- Orbital radius
- Spectral line wavelength
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the star mass, the planet mass and its orbital radius (circular orbit seen edge-on), and a spectral line wavelength.
Inputs explained
| Field | What to enter |
|---|---|
| Star mass | Units: M☉, kg |
| Planet | Choose one: Earth-like, Jupiter-like, Hot Jupiter (51 Pegasi b), Custom |
| Planet mass | Units: M_J, M⊕, kg |
| Orbital radius | Units: au, km, m |
| Spectral line wavelength | Units: nm, µm, mm, m, pm, Å |
What each result means
- Planet orbital speed = sqrt(6.6743e-11×[Star mass]÷[a])
- Star wobble velocity = sqrt(6.6743e-11×[Star mass]÷[a])×[mp]÷[Star mass]
- Doppler shift of the line = [Spectral line wavelength]×[Star wobble velocity]÷299792458×1e12
- Orbital period = 2×pi×sqrt([a]^3÷(6.6743e-11×([Star mass] + [mp])))
Example values
How the main result changes when Star mass changes and everything else stays at the example values above:
| Star mass (M☉) | Star wobble velocity (m/s) |
|---|---|
| 0.5 | 17.6327 |
| 0.75 | 14.3971 |
| 1 | 12.4682 |
| 1.25 | 11.1519 |
| 1.5 | 10.1803 |
| 2 | 8.8164 |
Formula
v_p = √(G·M_*/a), v_* = v_p·m_p/M_*, Δλ = λ·v_*/c
Worked example
Inputs — Star mass: 1 M☉; Planet: Jupiter-like; Spectral line wavelength: 656.28 nm.
Results — Planet orbital speed = 13.06165 km/s; Star wobble velocity = 12.46823 m/s; Doppler shift of the line = 0.02729 pm; Orbital period = 4,329.021 days.
Key terms
- Radial velocity
- Speed along our line of sight.
Frequently asked questions
How small are these signals?
Modern spectrographs reach about 0.3–1 m/s precision.
Why are hot Jupiters found easily?
Massive, close planets cause large, fast wobbles.
What if the orbit is tilted?
The measured signal is reduced by sin i; this calculator assumes edge-on.
What other methods find exoplanets?
Transits, microlensing and direct imaging.