Eclipse Orbital Mechanics & Geometry Simulator

Explore Presets:

📐 Space & Shadow Geometry (Umbra & Penumbra Cones)

Sun (Light Source)

Umbra (100% Shadow)

Penumbra (Partial Shadow)

Earth Target Area

Moon Orbit Position: 180.0° (Syzygy)

Moon Distance: 363,300 km (Perigee)

Orbital Node Tilt (Y): 0.00° (At Node)

Observer Latitude: 0° (Equator)

🔭 Observer Sky View (From Earth Surface)

TOTALITY

📊 Real-Time Geometric Analysis

TOTAL SOLAR ECLIPSE

Solar Obscuration
100.0%
Full Umbral Totality

Moon / Sun Angular Ratio

1.042

Moon covers Sun completely

Umbra Cone Length

374,500 km

Reaches Earth Surface

Path of Totality Width

168 km

Ground Shadow Track

☀️ 1. The Geometry of Shadows

Because the Sun is an extended light source (1,392,700 km wide), shadows cast by the Moon or Earth form two distinct zones: the Umbra (a tapering dark cone of complete light blockage) and the Penumbra (a widening cone of partial blockage).

📐 2. Why Eclipses Don't Happen Monthly

The Moon's orbit around Earth is tilted by 5.14° relative to Earth's orbital plane (the ecliptic). Most new and full moons pass above or below the Sun-Earth line. Eclipses can only occur when the Moon is crossing the Nodes (where the two planes intersect).

💍 3. Total vs. Annular Eclipses

The Moon's orbit is elliptical. At perigee (~363,000 km), the Moon looks slightly larger than the Sun, creating a Total Eclipse. At apogee (~405,000 km), the Moon is too small to cover the Sun, leaving a glowing Annular Ring of Fire.

🌕 4. Lunar Eclipses & The Blood Moon

During a Lunar Eclipse, the Moon enters Earth's massive umbra. Sunlight passing through Earth's atmosphere gets scattered (Rayleigh scattering); red wavelengths bend into the shadow cone, illuminating the Moon in a copper-red glow.

Angular disks, overlap and approximate eclipse shadows

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Read the explanation

The source compares apparent Sun and Moon discs using two times arctangent of physical radius divided by distance. The Sun radius is six hundred ninety six thousand three hundred forty kilometers at one astronomical unit. The Moon radius is one thousand seven hundred thirty seven point four kilometers. At distance three hundred sixty three thousand three hundred kilometers, the Moon’s angular diameter is slightly larger. Both circles use seven pixels per arcminute of angular radius. Move the Moon out to four hundred five thousand five hundred kilometers while keeping exact central alignment. The Sun outline stays fixed. The Moon outline shrinks according to the actual source arctangent formula. This continuous geometry is before telemetry rounding. The apparent diameter ratio crosses one, changing the central overlap condition from a Moon that covers the Sun to a smaller Moon inside the Sun. The ratio decreases from about one point zero two seven four to zero point nine two zero five. The source labels central alignment total at the initial distance and annular at the final distance. We compare ideal circular apparent discs, not a geographical path forecast, atmospheric model or actual camera image. Next hold Moon distance at three hundred eighty four thousand four hundred kilometers. At exact phase one hundred eighty degrees, the centers coincide. The Moon angular radius is about fifteen point five four arcminutes; the Sun is about sixteen point zero zero. The source uses an approximate phase displacement coefficient, not a computed ephemeris. Increase the phase from one hundred eighty to one hundred eighty one degrees while holding node tilt and observer latitude at zero. The horizontal displacement equals phase offset times sixty times zero point five five. The Moon center moves thirty three arcminutes right on the same seven pixels per arcminute scale. The radii remain fixed; only relative center separation changes. Thirty three arcminutes exceeds the sum of the two angular radii, about thirty one point five four arcminutes. The discs therefore no longer intersect. This explains the source’s no-eclipse condition within this solar-zone example. The movement is an authored angular approximation, not a real elapsed-time orbital trajectory. The source also combines node tilt and observer latitude in its vertical offset. Hold phase at one hundred eighty degrees, Moon distance at three hundred eighty four thousand four hundred kilometers, and tilt at zero point three degrees. Start observer latitude at zero. The vertical displacement is eighteen arcminutes. The Sun and Moon radii stay fixed. Increase observer latitude from zero to forty five degrees. The source vertical expression is tilt times sixty minus observer latitude times zero point four. At this fixed tilt, it is eighteen minus zero point four times latitude. The Moon center returns toward the Sun center, moving from eighteen arcminutes separation to zero. The diagram uses the same quantitative angular scale. At forty five degrees the centers coincide, and the smaller Moon leaves an annular rim in this source model. The latitude coefficient is an approximation, not a calibrated parallax or a prediction that a real eclipse occurs at that location. The video teaches the page’s actual geometry and its explicit limits while retaining the original tool.