# Exoplanet Discovery Calculator (Radial Velocity)

URL: https://speedycalculator.com/calculators/physics/exoplanet/
Last updated: 2026-10-30

> The exoplanet discovery calculator finds how fast a planet makes its star wobble – the radial velocity signal astronomers measure – and the resulting Doppler shift of a spectral line, from the star's and planet's masses and the orbital radius.

## Inputs

- Star mass (M☉, kg)
- Planet
- Planet mass (M_J, M⊕, kg)
- Orbital radius (au, km, m)
- Spectral line wavelength (nm, µm, mm, m, pm, Å)

## Results

- Planet orbital speed
- Star wobble velocity
- Doppler shift of the line
- Orbital period

## Formula

```
v_p = √(G·M_*/a),  v_* = v_p·m_p/M_*,  Δλ = λ·v_*/c
```

## Explanation

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

FieldWhat to enterStar massUnits: M☉, kgPlanetChoose one: Earth-like, Jupiter-like, Hot Jupiter (51 Pegasi b), CustomPlanet massUnits: M_J, M⊕, kgOrbital radiusUnits: au, km, mSpectral line wavelengthUnits: 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)0.517.63270.7514.3971112.46821.2511.15191.510.180328.8164

## 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.

## FAQ

**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.


## Sources

- [OpenStax – Astronomy 2e](https://openstax.org/details/books/astronomy-2e)
- [NASA Exoplanet Archive](https://exoplanetarchive.ipac.caltech.edu/)