How do you find a planet you cannot see, around a star light-years away? You watch the star’s brightness and wait. When a planet crosses in front, it blocks a sliver of light — a tiny, repeating DIP. Most of the thousands of known exoplanets were caught this way. Slide the planet’s size and watch the star wink.
When a planet of radius Rᶲ transits a star of radius Rₓ, it hides a fraction of the disc equal to the ratio of their AREAS: the dip in brightness is exactly (Rᶲ/Rₓ)². Jupiter across the Sun dims it ~1%; Earth only ~0.008% (84 parts per million) — which is why finding Earth-twins needs space telescopes. A fail-loud self-check throws unless the computed dip equals (Rᶲ/Rₓ)² and a Jupiter-sized planet gives ~1% while an Earth-sized one gives <0.01%.
Assumes a uniform stellar disc and an edge-on orbit that actually crosses; real light-curves add limb-darkening, grazing transits, and noise, and give only a LOWER bound on planet count (non-transiting worlds are missed). The area-ratio dip is exact.