Eclipse Orbit & Shadow Geometry Simulator

Syzygy Alignment: Solar
Orbital Shadow Cone Geometry Sun → Moon → Earth
Umbra (Total Shadow) Penumbra (Partial) Earth Moon
Observer Sky Vantage Projection Obscuration: 100.0%
Totality: Solar Corona Active
Moon Orbit Phase Angle: 0.0° (New Moon) Totality (C2 → C3)
Orbital Parameters Direct Control
Primary Alignment Solar Eclipse
Lunar Distance ($d_{moon}$) 363,300 km (Perigee)
Perigee creates Total Solar; Apogee creates Annular "Ring of Fire".
Orbital Plane Node Tilt ($i$) 0.00° (Node Crossing)
Moon's 5.14° tilt causes shadows to miss Earth most new/full moons.
Observer Track Offset 0.0° (Centerline)
Distance from the centerline changes totality into partial eclipse.
Geometric Telemetry Calculated
Angular Ratio 1.034 θ Moon / θ Sun
Umbra Cone Length 375,800 km Reaches Earth? YES
Shadow Footprint 198 km Path of Totality
Eclipse Category Total Solar Duration ~ 4m 28s
Geometric Principle: In this configuration, the Moon is near perigee so its apparent angular diameter ($33.1'$) exceeds the Sun's ($31.9'$), allowing the Umbra shadow cone to reach Earth's surface and create a Total Solar Eclipse with full coronal visibility along the central track.

The Physics & Celestial Mechanics of Eclipses

An eclipse occurs during Syzygy—a straight-line gravitational alignment of three celestial bodies in space. Explore the mathematical laws governing shadow geometry and why eclipses are rare.

1. Umbra vs. Penumbra vs. Antumbra

Because the Sun is an extended light source (diameter $1,392,700\text{ km}$), celestial bodies cast three distinct shadow zones:

• Umbra: Inner cone where the Sun is 100% occluded.
• Penumbra: Outer cone with partial solar illumination.
• Antumbra: Zone extending beyond the umbra apex where the Moon is completely inside the Sun's disk, leaving a glowing annulus ("Ring of Fire").

2. The Umbral Cone Equation

The length of the Moon's umbral shadow cone $L_u$ is determined strictly by similar triangles from the solar and lunar radii:

L_u = d_{moon-sun} \times \frac{R_{moon}}{R_{sun} - R_{moon}} \approx 374,000\text{ km}

Because Earth's distance to the Moon fluctuates between $356,500\text{ km}$ and $406,700\text{ km}$, $L_u$ sometimes falls short of Earth, transforming a Total eclipse into an Annular eclipse.

3. Why Don't Eclipses Happen Every Month?

The Moon's orbit around Earth is tilted by $5.14^\circ$ relative to the Ecliptic (Earth's orbital plane around the Sun).

During most new and full moons, the Moon is above or below the ecliptic plane, casting its shadow into empty space. Eclipses can only occur when a syzygy coincides with the Moon passing through one of its two orbital nodes.