Drag the Moon or the teal nodes to explore eclipse geometry.
Phase
$\Delta$deg
$\beta$deg
Solar
Lunar
Nodedeg
Observable: eclipses only happen when the Moon is near a node and at New or Full phase.
Model: the Moon’s orbit is tilted ~5° from the ecliptic, so it usually passes above or below the Sun/Earth’s shadow.
Inference: eclipses are rare because two conditions must align — most New/Full Moons miss. Try setting tilt to 0° to see what would happen without tilt.
We model eclipse geometry using similar triangles for the umbra/penumbra and compute physically
motivated thresholds (in degrees) for eclipse visibility.
$\beta$ is the Moon's ecliptic latitude; when $|\beta|$ is small, the Moon is close to a node and an eclipse is
possible at New/Full.
Earth–Moon distance affects shadow size: at perigee a central solar eclipse can be total; at apogee it
can be annular.