A solar eclipse is really a geometry problem: the Moon casts two nested cones of shadow — a narrow, fully-dark umbra and a wider, partially-dark penumbra — and whether either one reaches Earth's surface, and how, decides whether you see a total, annular, or partial eclipse (or nothing at all). This lab builds those cones from the Sun's, Moon's, and Earth's real radii and the Moon's real orbital distance range, so the "total vs. annular" split you get here comes straight out of the actual numbers, not a scripted animation.
L = R_moon · D / (R_sun − R_moon), where D is the Sun–Moon distance. With real values this comes out to about 374,300 km — almost exactly the Moon's average distance from Earth.The umbra's length and the Moon's average distance from Earth differ by only a few percent — a coincidence of the Moon's current recession rate. In roughly 600 million years the Moon will have drifted far enough that total solar eclipses become geometrically impossible from Earth, leaving only annular ones.
A 3D Sun-Earth-Moon model that builds the Moon's real umbra and penumbra shadow cones from actual radii and distances, so you can see exactly why the same Sun-Moon-Earth alignment gives a total eclipse near perigee and an annular "ring of fire" eclipse near apogee.
The umbra's cone length is fixed by similar triangles from the Sun's and Moon's radii. Whether the Moon's distance is shorter or longer than that length decides total vs. annular; the Moon's tilt off the ecliptic decides whether any eclipse happens at all.
Drag the Moon distance slider across the umbra's ~374,300 km length to flip between total and annular. Increase the ecliptic latitude slider to watch the shadow miss Earth entirely, just like most new moons.
The Moon's umbra length and its average orbital distance are within a few percent of each other — a geometric coincidence that will end in roughly 600 million years as the Moon slowly drifts farther from Earth.