Eclipse Orbital Geometry Simulator

SYZYGY & OPTICS ENGINE
Orbital Shadow Optics & Ray-Tracer
Scale: 1 : 1000 Rel
Phase: New Moon (0°)
Shadow State: Umbra Intersection
Ratio $\theta_M / \theta_S$: 1.043
Drag Moon or Earth to manipulate orbital alignment
Observer Sky Projection (From Earth)
5.14° Lunar Orbital Plane & Nodes
Total Solar Eclipse
Observer is fully within Moon's umbral shadow cone.
Event Presets
Orbital Parameters
Moon Orbital Longitude ($\lambda$) 0.0° (Syzygy)
Earth–Moon Distance ($d_{EM}$) 363,300 km (Perigee)
Orbital Inclination ($i$) 5.14° (Realistic)
Node Offset from Syzygy ($\Delta \Omega$) 0.0° (Node Line Aligned)
Observer Latitude Offset 0.0° (Direct Path)
Astronomical Telemetry
CALCULATED
Moon Angular Size
32.9'
Perigee (Large)
Sun Angular Size
31.6'
Mean: 31.95'
Eclipse Magnitude
1.041
Totality Expected
Umbral Cone Length
375,400 km
Reaches Earth
Path of Totality Width
182 km
Umbra Spot on Surface
Node Syzygy Separation
0.00°
Within Ecliptic Limit

The Physics of Eclipses: Why & How They Occur

Eclipses are precise geometric alignments governed by orbital mechanics, angular diameters, and the tilt of planetary orbits.

1. The Cosmic Coincidence & Angular Diameter

The Sun is approximately 400 times larger than the Moon, but it is also coincidentally 400 times farther away. As a result, both celestial bodies have nearly identical apparent angular diameters in our sky (~0.5° or 30 to 32 arcminutes).

$\theta = 2 \arctan\left(\frac{d}{2 D}\right) \approx \frac{d}{D}$

Because the Moon's orbit is elliptical ($e \approx 0.0549$), its distance varies between perigee (356,400 km) and apogee (406,700 km). When near apogee, the Moon is too small to cover the entire Sun, producing an Annular Eclipse (Ring of Fire).

2. The 5.14° Tilt & Eclipse Seasons

The Moon does not orbit Earth in the same plane that Earth orbits the Sun (the ecliptic). Its orbital plane is tilted by 5.14°.

Therefore, at most New and Full Moons, the Moon passes either above or below the Sun–Earth line, casting its shadow into empty space. Eclipses can only happen during an Eclipse Season (~every 173.3 days), when the Moon is near one of its two orbital intersections (the Ascending or Descending Node).

3. Umbra, Penumbra & Rayleigh Scattering

Umbra: The inner dark cone where the light source is completely blocked.
Penumbra: The lighter outer shadow where the light source is partially obscured.
Antumbra: The region beyond the umbral tip where the Moon appears entirely inside the Sun disc.

During a Total Lunar Eclipse, the Moon turns blood-red because Earth's atmosphere filters and bends sunlight through Rayleigh scattering, refracting red wavelengths into the umbral cone.