Detecting Exoplanets Through Transits
One of the most successful methods for discovering planets around distant stars is transit photometry. When an exoplanet crosses (or transits) in front of its host star, it temporarily blocks a small fraction of the starâs light. Sensitive telescopes measure this slight dimming, and from the depth of the brightness dip astronomers infer the planetâs size. Missions such as Kepler and TESS have found thousands of candidate exoplanets using this technique. The basic geometry is simple: the darker silhouette of the planet covers a portion of the bright stellar disk, much like a tiny eclipse.
The Transit Depth Formula
The fractional decrease in brightness during a transit, known as the transit depth, depends primarily on the ratio of the planetâs radius to the starâs radius . Under the simplest assumptionsâwhen the planet is much smaller than the star and the starâs surface brightness is uniformâthe transit depth is approximated by:
In other words, the brightness drops by the square of the ratio of planet radius to star radius. This fraction is often expressed as a percentage by multiplying by 100. A planet that is 10% the diameter of its star would block about 1% of the starlight. Real stars exhibit limb darkeningâwhere the edges appear dimmer than the centerâso precise measurements require more sophisticated models, but the simple square law captures the essence of the geometry.
Units and Conversions
Astrophysicists typically express star sizes in solar radii and planet sizes in Earth radii or Jupiter radii. One solar radius equals about 696,340 kilometers. One Earth radius equals about 6,371 kilometers. For convenience, this calculator accepts the star radius in solar radii and the planet radius in Earth radii. Internally, it converts both to meters before applying the transit depth formula. The final result is displayed both as a fraction and as a percentage.
Using the Calculator
To explore how planetary size influences transit observations, enter the radius of the host star in solar radii and the radius of the planet in Earth radii. Click the button to compute the transit depth. The calculator multiplies the squared ratio by 100 to present the brightness drop in percent. For small planets or large stars, the percentage will be tinyâfractions of a percentâwhich shows why sensitive instruments are necessary for detection. Conversely, a large planet transiting a small star may cause a noticeable dip even with modest telescopes.
Interpreting Observational Data
When astronomers monitor a starâs brightness over time, they produce a light curve. If a planet transits, the light curve reveals a repeating dip. The depth of this dip corresponds to the planet-to-star size ratio. By measuring how long the transit lasts and how frequently it repeats, astronomers deduce the planetâs orbital period and distance from the star. The transit depth alone, however, tells us little about the planetâs mass; for that, radial velocity measurements or gravitational effects on other planets are required.
Limb Darkening and Grazing Transits
Real transits are often more complex than the idealized model suggests. Stars are not uniform disksâthey are brighter at the center and dimmer near the edges due to limb darkening. This effect slightly alters the light curve shape. Additionally, if a planetâs orbit is tilted relative to our line of sight, it may only partially cross the star, producing a grazing transit. In that case, the transit depth is smaller than the simple square law predicts. Advanced models incorporate these factors to extract more accurate planetary parameters, but the basic geometry still provides a useful approximation.
Applications in Exoplanet Surveys
Large-scale surveys like Kepler and TESS continuously monitor thousands of stars for transits. By comparing the observed depth with the expected value from the starâs known radius, scientists estimate the size of each candidate planet. Follow-up observations with ground-based telescopes or other space missions refine these estimates. Transit depth also guides the search for potentially habitable worlds: Earth-sized planets transiting Sun-like stars produce dips of only about 0.01%, so detecting them requires exceptional precision.
Estimating Planetary Composition
If the planetâs mass is determined through other methods, combining it with the radius derived from transit depth yields the planetâs density. From density, researchers infer compositionârocky, icy, or gaseous. For instance, a planet with a radius similar to Earth but a much lower density might be rich in volatiles or possess a thick hydrogen-helium envelope. Thus, the humble transit depth measurement is a key step toward understanding an exoplanetâs physical nature.
Exploring System Architecture
Some stars host multiple transiting planets. By analyzing the depth and timing of each transit, astronomers unravel the architecture of these planetary systems. Resonances between orbital periods reveal gravitational interactions, and variations in transit timing can hint at additional unseen planets. The ability to model transit depth accurately is therefore crucial for interpreting these subtle signals.
Limitations and False Positives
Not every dip in brightness is caused by a transiting planet. Starspots, binary companions, and instrumental noise can mimic transit signals. Astronomers use additional dataâsuch as color-dependent light curves and radial velocity measurementsâto rule out false positives. Nevertheless, a consistent transit depth across multiple observations is a strong indicator of a planetary companion.
Final Thoughts
The transit method has revolutionized our understanding of planets beyond the Solar System. With this calculator, you can plug in star and planet sizes to see how much light is blocked during a transit. Whether youâre planning an observation campaign or simply curious about the factors that govern detectability, exploring transit depth provides valuable insight into the diversity of worlds in our galaxy.