Where it shows up
This is eclipse geometry, and the same overlap integral turns up wherever one disk slides over another. Eclipsing binary stars trace deeper versions of the very same curve. A solar eclipse is a transit with the Moon as the planet and you standing on the detector. Occultation timing, where a body passes behind a planet or asteroid, reads the sharp edges of the dip to size the occulter. NASA's Kepler and TESS (Transiting Exoplanet Survey Satellite) missions industrialised the idea, staring at hundreds of thousands of stars at once and letting software flag every recurring notch.
The knobs
- Planet radius Rp/R*: the planet-to-star size ratio. It sets the depth, which scales as the square of this value, so doubling the radius quadruples the dip.
- Impact parameter b: how high the crossing chord sits, measured in stellar radii. At the planet cuts through the bright centre; near it grazes the dim limb and the notch turns V-shaped and shallow.
- Speed: how fast the planet sweeps, and how quickly the light curve scrolls. It changes the pace, not the physics.
- Limb darkening: toggles the realistic brightness gradient. On, the star glows brighter at its centre and the floor of the dip rounds off. Off, the disk is uniform and the floor sits flat.