Interactive orbital ray-tracing simulator demonstrating how solar and lunar eclipses occur across the 5.14° ecliptic inclination.
Eclipses are precise optical alignment events called syzygy. The fundamental mechanics depend on light ray geometry from an extended light source (the Sun) past a spherical occluder (the Moon or Earth).
Because the Sun is not a point source but an extended disk of $1.39 \times 10^6\text{ km}$, shadows cast in space have three distinct geometric regions:
The Moon completes an orbit every 29.5 days (Synodic month), passing between the Sun and Earth every New Moon. However, the Moon's orbital plane is inclined by 5.145° relative to Earth's ecliptic plane.
At 384,400 km away, a 5.14° tilt causes the shadow to pass up to 34,500 km above or below Earth. Eclipses only occur during Eclipse Seasons (~every 173.3 days) when New/Full Moon coincides with an orbital node.
The Moon's orbit is elliptical (eccentricity $e = 0.0549$). At Perigee (363,300 km), its angular diameter is $0.558^\circ$, larger than the Sun's ($0.533^\circ$), producing a Total Eclipse.
At Apogee (405,500 km), its angular diameter drops to $0.491^\circ$, smaller than the Sun, allowing a blazing annulus of sunlight ("Ring of Fire") to escape around its silhouette.
During a Total Lunar Eclipse, the Moon passes directly through Earth's gargantuan umbral cone. Even inside the umbra, the Moon does not go entirely black.
Sunlight passing through Earth's atmosphere undergoes Rayleigh scattering: shorter blue wavelengths scatter away, while long red wavelengths bend (refract) inward toward the lunar surface, projecting all of Earth's sunrises and sunsets simultaneously onto the Moon.