Eclipse Shadow-Cone Lab (2D)

Profile along the Moon's shadow axis with real umbra and penumbra geometry, an orbit map and live graphs.

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Presets

Playback

Live readout

Umbra length LMoon distance dUmbra radius at Earth planePenumbra radius at Earth planeShadow axis missEclipse type

What to try

1. Press Perigee: the umbra reaches past Earth, so the type is Total. 2. Press Apogee: the apex falls short and the antumbra (gold) covers Earth: Annular. 3. Press Missed (beta 5.15) and watch the whole profile slide past Earth.

Model checks

The science

The Sun and Moon are spheres of radius RS = 696,000 km and RM = 1,737 km, D = 149.6 million km apart. Similar triangles on the outer common tangent give the umbra length L = RMD / (RS - RM) (about 374,300 km). The umbra radius at distance s behind the Moon is RM(1 - s/L); a negative value means the apex has been passed and the diverging antumbra is there.

The inner tangent gives the penumbra: RP(s) = RM + s (RS + RM) / D. The shadow axis crosses the Earth plane a distance m = d sqrt(sin²beta cos²theta + sin²theta) from Earth's centre, with the Moon on the sunward side when cos theta > 0.

Honest simplifications: circular orbit of fixed radius, Earth's plane taken through its centre, rays parallel to the Sun-Earth line, no atmospheric refraction, and the type thresholds (+40 km for total, +200 km for annular) mirror the 3D lab so both pages agree. The vertical axis is exaggerated, otherwise the cones would be invisible slivers.