Exoplanet Discovery Calculator

Transit depth is the fractional dip in a star's observed brightness when a planet passes directly in front of it, blocking part of the starlight. It is calculated as delta = (Rp/Rs)^2, the square of the ratio between the planet's radius and the star's radius, and is usually reported as a percentage or in parts per million (ppm).

The star's brightness is proportional to its projected surface area, which scales with radius squared (pi times radius squared). A transiting planet blocks a circular area proportional to its own radius squared. The fraction of light blocked is therefore the ratio of these two areas, (Rp/Rs)^2, not simply Rp/Rs.

Earth's radius is 6,371 km and the Sun's radius is 696,000 km, giving delta = (6371/696000)^2 = 0.0000838, or 83.79 parts per million (0.008379%). This is deep enough for Kepler-class photometric precision (~20 ppm) but below the typical TESS detectability floor (~200 ppm).

A Jupiter-sized planet (about 11.2 Earth radii) transiting a Sun-like star produces delta = (11.2 x 6371 / 696000)^2 = 0.0105, or about 10,511 ppm (1.05%), easily detectable by both Kepler-class and TESS-class photometry. This is why the earliest transiting exoplanets discovered were mostly hot Jupiters.

Kepler achieved photometric precision down to roughly 20 parts per million for its brightest, quietest target stars over long observation baselines, enabling it to detect Earth-sized planets transiting Sun-like stars, a landmark achievement of the mission.

TESS observes many more, generally fainter stars over shorter baselines than Kepler, giving it a coarser practical detectability floor around 200 parts per million for typical targets. TESS compensates by surveying nearly the entire sky, favoring the discovery of larger planets or planets around smaller, cooler stars where the transit signal is deeper.

Transit depth depends only on the ratio Rp/Rs, not on the planet's absolute size. A small, Earth-sized planet orbiting a small M-dwarf star (with a radius a fraction of the Sun's) can produce a transit depth comparable to or deeper than a Jupiter-sized planet around a Sun-like star, which is why M-dwarf systems like TRAPPIST-1 are prioritized for terrestrial-planet searches.

No. The transit method only detects planets whose orbital plane is aligned edge-on as seen from Earth, so the planet actually passes in front of its star from our vantage point. For a randomly oriented orbit, the geometric transit probability is roughly Rs/a, where a is the orbital distance, meaning most planets are missed by this method alone.

The radial velocity method measures the star's wobble caused by the planet's gravitational pull. Direct imaging captures light from the planet itself. Gravitational microlensing detects the bending of background starlight. Astrometry measures tiny positional shifts of the host star. The transit method remains the most productive, having found the majority of confirmed exoplanets to date.

Yes. Enter the planet radius (in Earth radii or kilometers) and star radius (in Solar radii or kilometers) from any published exoplanet system, such as those cataloged by the NASA Exoplanet Archive, to reproduce the transit depth reported in the discovery paper and check it against Kepler and TESS detectability floors.

A transit depth below roughly 20 ppm is too shallow for even Kepler-class precision to reliably detect against the noise floor of stellar photometry. Such small planets, especially around larger stars, generally require next-generation instruments like JWST, or many stacked transits, to confirm.