Exoplanet Discovery Calculator

Most exoplanets cannot be resolved as separate points of light from their host stars, so astronomers infer them through periodic effects. Transit photometry detects a temporary decrease in starlight when a planet crosses the stellar disk. Radial-velocity observations detect the star's repeated motion toward and away from the observer as star and planet orbit their common center of mass. This calculator compares ideal signal scales for both methods. Orbital semi-major axis is estimated with Kepler's third law using stellar mass in solar masses and period in years. When planet mass is small compared with stellar mass, the convenient relationship is axis cubed equals stellar mass times period squared, with axis in astronomical units. Very massive companions require adding companion mass to the system mass, but that correction is negligible for ordinary planets in this screening model. Transit depth is the square of planet radius divided by stellar radius, expressed as a percentage. An Earth-radius planet crossing a Sun-radius star blocks only about 0.0084 percent of the light, while a Jupiter-size planet blocks roughly one percent. The model assumes a fully overlapping, uniformly bright stellar disk. Real light curves are shaped by limb darkening, grazing geometry, star spots, blended background stars, exposure time, and instrument response. Geometric transit probability is approximated by stellar radius plus planet radius divided by semi-major axis. Close-in planets are much more likely to align for a transit than planets on wide orbits. This probability describes random orbital orientations before observations; it is not the chance that a noisy dataset will detect an already transiting planet. Eccentricity and argument of periastron can change the geometric probability. The radial-velocity semi-amplitude uses a circular, edge-on, low-planet-mass approximation. It grows with planet mass, increases for shorter orbital periods, and decreases for more massive stars. Actual amplitude is multiplied by orbital inclination's sine and affected by eccentricity. Stellar activity, oscillations, rotating spots, spectral type, cadence, and spectrograph precision determine whether that amplitude is measurable. Use solar masses and radii for the star, Earth masses and radii for the planet, and days for period. Outputs are best for education, target comparison, and quick plausibility checks. Candidate validation requires repeated observations, uncertainty analysis, false-positive assessment, and usually independent methods. Professional modeling should fit the complete light curve or velocity time series and include inclination, eccentricity, limb darkening, contamination, correlated noise, and parameter uncertainties.