Eclipse Geometry Lab

An eclipse is not a rare coincidence of light — it is a geometry problem. The Sun, Moon and Earth line up, and the Moon's shadow lands somewhere on Earth. Move the Moon in the diagram above and you can watch the shadow change shape, size and even type.

What actually has to happen

Three conditions must hold at once for a solar eclipse:

1. The Moon is between the Sun and Earth. That means it is at new moon, when its unlit side faces us.
2. It is close to a node. The Moon's orbit is tilted about 5.1° to Earth's orbital plane, so most new moons pass above or below the Sun. Only near the two points where the orbits cross — the nodes — can the three bodies line up.
3. The alignment is tight enough that the shadow reaches Earth. The Moon's shadow is a cone. If the cone's tip falls short of Earth's surface, you get an annular eclipse instead of a total one.

That third condition is why eclipses come in flavours. The Moon's distance varies between roughly 356,500 km and 406,700 km, so its apparent size swings by about 12%. When the Moon is near perigee it can just cover the Sun; near apogee it cannot, and a ring of sunlight remains.

Umbra, penumbra, and why the shadow has two parts

The Sun is not a point. It is a disc about half a degree wide in our sky, and every point on that disc casts its own tiny shadow of the Moon. The result is two nested shadow regions:

• The umbra is the cone where the Sun's disc is completely blocked. Inside it you see a total eclipse — the sky darkens, the corona appears, and stars may become visible.
• The penumbra is the wider cone where the Sun is only partly blocked. Inside it you see a partial eclipse, and the Sun looks like a crescent through a safe filter.

The umbra narrows with distance because the Moon is smaller than the Sun. At the Moon's average distance the umbra cone converges to a point roughly 373,000 km behind the Moon — just about at Earth's surface. That is a knife-edge, and it is why totality is a narrow strip, typically 100–270 km wide, while the partial-eclipse zone spans thousands of kilometres.

Reading the diagram

The canvas above is a scale-compressed schematic, not a to-scale orrery. Distances are squeezed so all three bodies fit on screen, but the angular arithmetic is real:

• Moon position moves the Moon sideways relative to the Sun–Earth line. At 0° it is perfectly centred; the further you go, the more the shadow misses Earth's disc.
• Moon distance changes the Moon's apparent size. Pull it closer and the umbra reaches Earth; push it away and the shadow tip falls short, producing an annular eclipse.
• The readout compares the Moon's angular diameter with the Sun's. If the Moon's is larger, a total eclipse is possible along the centre line; if smaller, the best you can get is annular.

The verdict panel names the eclipse type for the current geometry and explains which condition is doing the work. The export button writes a plain-text record of the exact numbers you set, so you can compare several configurations side by side.

The numbers behind the shadow

Angular diameters here use the small-angle approximation, θ ≈ 2·arctan(r / d). Over these distances the difference from the exact formula is far below the precision shown.

Why the shadow moves

Earth rotates while the Moon's shadow sweeps across it. The umbra touches down at one point, races eastward at roughly 1,700–3,000 km/h depending on latitude and eclipse geometry, and lifts off about three hours later. Anyone standing in that path sees totality for at most about 7.5 minutes; most total eclipses give two to four.

The path is curved because Earth is a sphere and the shadow cone intersects it obliquely. Near the poles the same shadow can graze the surface for much longer, which is why polar eclipses can produce unusually long totality.

Lunar eclipses are the mirror image

Swap the roles and you get a lunar eclipse: Earth sits between Sun and Moon, and the Moon passes through Earth's shadow. Earth's umbra is much wider than the Moon, so totality can last over an hour. The red colour comes from sunlight refracted through Earth's atmosphere — every sunrise and sunset on Earth projected onto the Moon at once.

Common questions