Exoplanet Discovery Calculator

Exoplanet Discovery Calculator

Calculate exoplanet radius from transit photometry observations

Updated March 2026
R☉

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☉

What is the Transit Method?

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).

How to Use the Exoplanet Discovery Calculator

Step 1: Enter Star Radius

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.

Step 2: Enter Transit Depth

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).

Step 3: Review Results

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⊕.

Formula Details

  • Transit depth: ΔF/F = (Rₚ / R★)² where ΔF is brightness change, F is baseline brightness
  • Planet radius: Rₚ = R★ × √(depth), where depth is expressed as a fraction (not %)
  • Conversion factors: 1 R☉ = 109.076 R⊕ = 9.7313 R♃ = 696,000 km
  • This assumes the planet fully transits the star (no grazing transits) and neglects limb darkening effects

Worked Example: TRAPPIST-1e

Scenario: A Real Exoplanet System

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.

Given:

  • Star radius (R★) = 0.117 R☉
  • Transit depth = 1.4%
  • Conversion: 1 R☉ = 109.076 R⊕

Step 1: Convert Depth to Fraction

Depth fraction = 1.4% / 100 = 0.014

Step 2: Calculate Planet Radius

Rₚ = R★ × √(depth)

Rₚ = 0.117 R☉ × √(0.014)

Rₚ = 0.117 × 0.11832 R☉

Rₚ = 0.01384 R☉

Step 3: Convert to Earth Radii

Rₚ = 0.01384 R☉ × 109.076 R⊕/R☉

Rₚ = 1.51 R⊕

Step 4: Classify the Planet

With a radius of 1.51 R⊕, TRAPPIST-1e falls into the Super-Earth category (1.25-2.0 R⊕). This planet is:

  • Located in the habitable zone (right distance for liquid water)
  • Likely rocky with a solid surface, possibly with a thin atmosphere
  • Has a mass estimated at 0.692 M⊕ (from radial velocity data)
  • Receives similar radiation from its star as Earth does from the Sun
  • Considered one of the best candidates for habitability among known exoplanets

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.

Frequently Asked Questions

Why can't we see all exoplanets with the transit method?

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.

How long does a transit last?

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.

What is the smallest detectable planet?

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!

Can transit depth tell us about the planet's atmosphere?

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.

How do astronomers confirm transit detections?

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.

What is limb darkening and why does it matter?

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.

Can moons be detected with the transit method?

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.

What happens if two planets transit at once?

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.

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