Lunar Eclipse: Umbra & Penumbra Geometry (2D)

This simulation draws the classic face-on lunar-eclipse diagram — Earth's umbra and penumbra as they appear from the Moon's distance, looking back along the Sun-Earth line — and derives both shadow radii from real physics rather than fixed numbers: Earth's true radius and the Sun's true angular size (about half a degree) fix how fast the umbra narrows and the penumbra widens with distance, giving roughly 4,580 km and 8,160 km respectively at the Moon's average orbital distance of 384,400 km. The Moon travels along a straight path at a fixed cross-track offset controlled by the orbital-plane latitude slider, exactly mirroring why most full moons don't produce an eclipse at all: the Moon's orbit is tilted about 5.14° to the plane Earth's shadow lies in, so only full moons that happen to occur near an orbital node bring the Moon's latitude down into the roughly 1.5°-wide corridor where the shadow can be reached. Moving the latitude slider toward zero sends the Moon straight through the umbra's center for a long, deep totality with a fully saturated coppery color — the same Rayleigh-scattered, refracted sunlight that reddens Earth's sunsets, bent into the shadow by the atmosphere; moving it outward shows the eclipse shrink to a shallow partial, then a penumbral-only dimming, then no eclipse whatsoever once the Moon clears the penumbra completely. The timeline slider sweeps the Moon through this crossing at its real orbital speed relative to Earth's shadow, derived from the 29.53-day synodic month, and an optional inset sketches the underlying Sun–Earth–cone geometry that produces the two shadow radii in the first place.