Sidereal month

The time the Moon takes to orbit Earth once relative to the fixed stars: about 27.32 days, measured by consecutive returns to the same star background.

Synodic month: The 29.53-day cycle of lunar phases from one new moon to the next, measured relative to the Sun. About 2.2 days longer, because Earth's motion around the Sun shifts the Sun's direction during each lunar orbit.
Lunar orbit: The Moon's roughly elliptical path around Earth, inclined about 5 degrees to the ecliptic. One complete circuit of this orbit against the star background defines the sidereal month.
Ecliptic: The Sun's apparent yearly path on the celestial sphere; the Moon's orbit is tilted about 5 degrees from it. The reference great circle against which lunar periods and node motion are measured.
Babylonian astronomy: The Mesopotamian tradition that systematized lunar period relations, including the month lengths. Babylonian cuneiform records tabulate the sidereal month to seconds in the System A and B schemes.
Anomalistic month: The 27.55-day interval between successive perigee passages of the Moon. Another lunar month, longer than the sidereal one because perigee itself advances eastward.
Sidereal year: The 365.256-day period of Earth's orbit measured against the fixed stars. Earth's advance along this orbit during one lunar circuit is what lengthens the synodic month beyond it.
Celestial sphere: The imaginary sphere on which stars, Sun and Moon appear fixed and are assigned coordinates. The sidereal month is a return to a fixed point on this sphere, so it is the natural frame for it.
Hipparchus: The 2nd-century BC Greek astronomer who fixed the lunar month and year lengths from Babylonian data. His mean sidereal month value of 27 days 7 hours 43 minutes matches modern figures closely.
Draconic month: The 27.21-day interval between successive crossings of the same lunar node, governing eclipse seasons. Shorter than the sidereal month because the nodes regress westward along the orbit.
Fixed stars: Distant stars treated as an unmoving reference frame for celestial positions. They supply the backdrop that defines when one sidereal orbit ends and the next begins.

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