Exoplanet Transit

A planet on a real Keplerian orbit transits its star edge-on; the light curve is computed as the intensity-weighted geometric overlap of a quadratic limb-darkened stellar disc with the planet shadow. The depth is the square of the radius ratio, the timing pins down the period, the duration the orbit geometry, and the U-shape comes from limb darkening, exactly the four observables that make transits the discovery channel for thousands of planets. Tilt the orbital plane and the transit shrinks to a graze, then vanishes; pick a hot Jupiter for a deep, frequent dip or an Earth analogue for a tiny, slow one.