Calculate exoplanet radius from transit photometry observations
Star radius in solar radii (1 R☉ = Sun's radius)
Percentage decrease in star brightness during transit
Planet Radius
1.09
Earth radii (R⊕)
Classification: Rocky/Earth-like
Jupiter Radii
0.097
R♃
Solar Radii
0.0100
R☉
Kilometers
6,960
km
Rₚ = R★ × √(depth/100) = 1.0 R☉ × √(0.01/100) = 0.0100 R☉
The transit method is the most successful technique for discovering exoplanets, responsible for finding over 75% of all confirmed exoplanets to date. It works by detecting the tiny dimming of a star's light when a planet passes in front of it, as seen from Earth. This periodic dimming event is called a transit.
When a planet transits its host star, it blocks a small fraction of the star's light proportional to the ratio of their cross-sectional areas. Since both are approximately spherical, the transit depth (the fractional decrease in brightness) is given by (Rₚ / R★)², where Rₚ is the planet radius and R★ is the star radius. By measuring the transit depth and knowing the star's radius, we can solve for the planet's radius.
NASA's Kepler and TESS missions have used this method to discover thousands of exoplanets. The technique is particularly powerful because it provides direct measurement of planet size, and when combined with other methods like radial velocity, also yields the planet's mass and density, allowing us to determine its composition (rocky vs. gaseous).
Input the host star's radius in solar radii (R☉). For reference, the Sun has R★ = 1.0 R☉. Red dwarfs typically have 0.1-0.6 R☉, Sun-like stars have 0.8-1.2 R☉, and large stars can exceed 10 R☉. Star radii are usually determined from stellar spectroscopy and models.
Input the observed transit depth as a percentage. This is the fractional decrease in the star's brightness during the transit. For example, if the star dims from 100% to 99% brightness, the transit depth is 1%. Typical values range from 0.01% (Earth-sized planets around Sun-like stars) to 3% (Jupiter-sized planets around small stars).
The calculator displays the planet's radius in multiple units (Earth radii, Jupiter radii, solar radii, kilometers) and provides a classification. Rocky/Earth-like planets have radii below 1.25 R⊕, super-Earths are 1.25-2 R⊕, mini-Neptunes are 2-6 R⊕, Neptune-like planets are 6-14 R⊕, and gas giants exceed 14 R⊕.
TRAPPIST-1 is an ultracool red dwarf star located 40 light-years away. One of its planets, TRAPPIST-1e, produces a transit depth of approximately 1.4% when it passes in front of the star. The star's radius is about 0.117 R☉. Calculate the planet's radius and determine its classification.
Depth fraction = 1.4% / 100 = 0.014
Rₚ = R★ × √(depth)
Rₚ = 0.117 R☉ × √(0.014)
Rₚ = 0.117 × 0.11832 R☉
Rₚ = 0.01384 R☉
Rₚ = 0.01384 R☉ × 109.076 R⊕/R☉
Rₚ = 1.51 R⊕
With a radius of 1.51 R⊕, TRAPPIST-1e falls into the Super-Earth category (1.25-2.0 R⊕). This planet is:
Observational Note: Because TRAPPIST-1 is a very small, cool star (only 12% the Sun's radius), even Earth-sized planets produce deep, easily detectable transits. This makes M-dwarf stars ideal targets for finding terrestrial exoplanets with current technology.
The planet's orbit must be aligned edge-on from our viewpoint for transits to occur. For a random planetary system, the probability of seeing transits is roughly (R★ / a), where a is orbital distance. Only ~0.5% of planets transit for Earth-Sun geometry, but closer-in planets transit more often.
Transit duration depends on orbital speed and geometry. For an Earth-like planet around a Sun-like star, transits last about 13 hours. Hot Jupiters in close orbits might transit for 2-4 hours, while planets in wide orbits can transit for a full day or more.
Modern telescopes like Kepler can detect brightness changes as small as 0.001% (10 parts per million). Around a Sun-like star, this corresponds to a planet about 0.3 R⊕ (Mars-sized). The smallest confirmed exoplanet, Kepler-37b, is only 0.30 R⊕ — smaller than Mercury!
Yes! By measuring transit depth at different wavelengths (transmission spectroscopy), we can detect atmospheric absorption features. Atoms and molecules in the atmosphere absorb specific colors of starlight, creating a unique spectral fingerprint that reveals composition.
Confirmation requires multiple transits at regular intervals (establishing an orbital period), radial velocity measurements to confirm mass, and ruling out false positives like eclipsing binary stars. Follow-up observations with multiple telescopes verify the planet is real.
Stars appear dimmer near their edges (limbs) than at center due to viewing angle through the atmosphere. This affects transit shape and depth by ~5-15%. Precise modeling accounts for limb darkening to extract accurate planet radii from light curves.
In principle yes, but it's incredibly difficult. A large moon (like Titan around Saturn) would cause subtle timing variations in transits (transit timing variations, or TTVs) and tiny additional dimming. No exomoons have been confirmed yet despite ongoing searches.
Simultaneous transits are rare but observable. The combined transit depth equals the sum of individual depths: (R₁² + R₂²) / R★². These events help confirm multi-planet systems and constrain orbital dynamics through timing analysis.
Related Tools
Calculate probability of love.
Calculate lunar phase.
Explore Olbers' paradox.
Calculate sun angle.
Calculate sunrise and sunset times.
Calculate synodic period.