Sidereal Orbital Period of the Moon

The Moon circles Earth in 27.32 days measured against the stars, yet the familiar cycle of phases takes 29.53 — the synodic month — because while the Moon orbits, Earth carries it a twelfth of the way around the Sun, and the Moon needs two extra days to catch up to the moving line between the two. Calendars follow the phases; dynamics follows the sidereal value, which is the number Kepler's third law wants.

The same 27.3217 days is also the Moon's rotation period, and that is no coincidence: tidal friction long ago braked the spin into synchronous lock, so one hemisphere faces Earth forever. Newton used this orbit for the first great test of universal gravitation — the Moon falls toward Earth 3600 times more weakly than an apple does, at sixty times the distance, exactly as an inverse-square law demands. And the period is slowly lengthening as the Moon spirals outward by 3.8 cm a year, angular momentum handed over from Earth's slowing spin.