A planet blocks part of the star's light. Build the folded light curve, fit the planet radius and find out when noise hides the dip.
Collect a few transits, then press Fit.
The science
Transit depth. A dark disc of radius Rp in front of a star of radius Rs removes a fraction of the light. For a uniformly bright disc the depth is (Rp/Rs)2: Jupiter in front of the Sun is about 1 %, Earth about 84 ppm.
Limb darkening. The star is dimmer near its edge because we look at cooler, higher layers there. The quadratic law used here is I(μ)/I(1) = 1 - u1(1-μ) - u2(1-μ)2 with μ = sqrt(1 - r2). A central transit blocks the brighter centre, so the dip is deeper than p²; a grazing one is shallower and rounder. Mean intensity is I(1)(1 - u1/3 - u2/6).
Light curve. Flux is 1 - ∫ I dAblocked / ∫ I dA. Here the star is split into 300 thin annuli and the blocked area inside each is the exact circle-circle lens overlap. It is a numerical integral, not the fast analytic Mandel-Agol series.
Geometry. Kepler III: a3 = G M P2 / 4π2. Circular orbit, cos i = b Rs/a, projected separation z = (a/Rs) sqrt(sin2φ + cos2i cos2φ). Total duration T14 = (P/π) asin[(Rs/a) sqrt((1+p)2-b2)/sin i].
Detection. With N in-transit points of scatter σ, SNR = depth · sqrt(N) / σ. Surveys often require about 7 (typical threshold, not a hard law). Folding k transits improves SNR by sqrt(k). The Monte-Carlo button repeats the whole survey 200 times and compares the scatter of fitted radii with the Fisher-information prediction σp = σ / sqrt(Σ(∂F/∂p)2).
Simplifications. Circular orbit, one planet, dark planet disc, no stellar spots, no planet light, white Gaussian noise, no atmosphere, period known. Presets use typical, rounded values chosen for illustration, not catalogue fits. The telescope is a generic segmented-mirror space observatory; it is a decoration, the physics does not depend on its aperture.
Time warp. Long periods would make a real-time transit last a blink, so the clock runs slowly during transit and fast between transits.