Hong Life CalculatorsUnderstanding the exoplanet transit calculator — concept and principle
This calculator estimates the size of a planet from how much it dims its star when it passes in front, the transit depth. It is how missions such as Kepler and TESS turn light curves into planet radii, and it is a popular classroom exercise in astronomy.
How it is calculated
δ = (Rp ÷ R★)², so Rp = R★ × √δ
- The depth δ is entered in percent or in parts per million (ppm) and converted to a fraction.
- R★ is the star's radius in solar radii; 1 solar radius = 695,700 km.
- Results are given in km, Earth radii (6,378.1 km) and Jupiter radii (71,492 km).
- The page also shows the depth an Earth-size planet would cause around the same star.
The principle
Seen from far away, both the star and the planet look like discs. While the planet is in front, it blocks a fraction of the star's light equal to the ratio of the disc areas. Areas scale with the square of the radius, so the dip equals the square of the radius ratio, and the radius ratio is the square root of the dip. The star's radius, usually known from its spectrum, then sets the scale.
Worked example
Default inputs: depth 1%, star radius 1 solar radius.
- δ = 1% = 0.01.
- Rp/R★ = √0.01 = 0.1.
- Rp = 0.1 × 695,700 km = 69,570 km.
- In Earth radii: 69,570 ÷ 6,378.1 = 10.91; in Jupiter radii: 69,570 ÷ 71,492 = 0.973.
- An Earth-size planet would make (6,378.1 ÷ 695,700)² = 84.1 ppm.
| Star radius (solar radii) | Planet radius (Earth radii) |
|---|---|
| 0.25 | 2.73 |
| 0.5 | 5.45 |
| 0.75 | 8.18 |
| 1 | 10.91 |
| 1.25 | 13.63 |
| 1.5 | 16.36 |
| 2 | 21.82 |
How to read the result
A 1% dip on a Sun-like star means a planet about the size of Jupiter. Earth-size planets around Sun-like stars produce dips under 100 ppm, which is why they need space telescopes. The same planet around a small red dwarf produces a much deeper transit. The radius alone does not tell you the mass; combine it with radial-velocity data to get density.
Common mistakes
- Entering ppm as percent: 1% is 10,000 ppm.
- Using the star's diameter instead of its radius.
- Ignoring limb darkening and grazing transits, which make the simple formula less accurate.
Frequently asked questions
How big a dip does Jupiter make on the Sun?
About 1%, since Jupiter's radius is roughly one tenth of the Sun's.
Can the transit tell the planet's mass?
No. Mass usually comes from the star's radial-velocity wobble or from transit timing variations.
Why must the orbit be nearly edge-on?
The planet only passes in front of the star if our line of sight lies close to its orbital plane.
Sources: Center for Astrophysics, Harvard & Smithsonian, exoplanet transit tutorial (A. Vanderburg) · IAU 2015 Resolution B3 (nominal solar, Earth and Jupiter radii)