Exoplanet Discovery Calculator

This calculator utilizes foundational astrophysical equations to simulate how an orbiting planet interacts with its host star. For transit photometry, the percentage dimming of the star's light is calculated using the ratio of the planetary area to the stellar area: dimmer = 100 * (A_planet / A_star), where A = pi * r^2. For orbital mechanics and the radial velocity method, Kepler's Third Law is applied to find the orbital period using the equation period = 2 * pi * sqrt(orbRad^3 / (G * m_sum)), where G is the gravitational constant. Additionally, relativistic Doppler shifts and stellar wobble velocities are computed to map out the gravitational tug-of-war between the star and its planet.

Let us walk through a sample calculation for a rocky exoplanet orbiting a Sun-like star. Assume a stellar radius (r_star) of 696,340,000 meters and a planetary radius (r_planet) of 6,371,000 meters. First, we determine the stellar area: A_star = pi * (6.9634e8)^2. Next, we determine the planetary area: A_planet = pi * (6.371e6)^2. The transit dimmer percentage is calculated as 100 * (A_planet / A_star), yielding a tiny light drop of approximately 0.0084 percent during a transit event. If we factor in a stellar mass of 2e30 kg, a planetary mass of 6e24 kg, and an orbital radius (orbRad) of 1.5e11 meters, Kepler's equation computes an orbital period of roughly 31.5 million seconds (or 365 days), illustrating how these physical properties interconnect.

When entering data into the calculator, ensure all physical units remain consistent, preferably using SI units such as meters for radii and kilograms for masses. Keep in mind that transit depth calculations assume a perfectly aligned orbit where the planet crosses directly across the stellar disk center. For radial velocity estimates, remember that inclination angles can alter the observed wobble amplitude from the true spatial velocity.