2D Lunar Eclipse: Umbra & Penumbra Shadow Geometry

Eclipse Timeline

Time from opposition +00:00

Orbit Geometry

Ecliptic latitude of Moon +0.30°

Moon distance (apparent size) Average

Scenario preset

Live Readouts

TOTAL LUNAR ECLIPSE

Umbra coverage

100%

Magnitude

1.42

Moon-shadow-axis distance (d)

0.05 units

How it works

Earth's shadow at the Moon's orbital distance is modelled as two concentric discs — a dark umbra (radius R_u) and a wider, fainter penumbra (radius R_p). The Moon's disc (radius r) sweeps past them at perpendicular distance d, built from its ecliptic latitude (out-of-plane tilt) and its position along the orbit:

d = hypot(latitude-offset, along-orbit offset)
overlap area = circleOverlap(r, R, d)   (two-circle intersection)
magnitude = (R_u + r − d) / (2r)

Total when d ≤ R_u − r (the Moon fully inside the umbra), partial when the umbra circle and Moon disc merely overlap, penumbral when only the wider penumbra circle is touched, and no eclipse once d exceeds R_p + r. This is the exact geometry the 3D version's shadow cones reduce to in cross-section — same constants, same formulas, flattened to a plane you can read directly.

Penumbra Umbra Moon