Synodic month

The 29.53-day cycle of lunar phases, from one new moon to the next, caused by the Moon's orbit around Earth relative to the Sun.

Sidereal month: The 27.32 days the Moon takes to return to the same position against the stars, one true orbit of Earth. About 2.2 days shorter than the synodic month because the Sun's direction shifts during the orbit.
Babylonian astronomy: The Mesopotamian tradition of recorded lunar and planetary observations that produced the earliest accurate month lengths. Babylonian tablets fixed the mean synodic month to within seconds, the base of later calendars.
Hebrew calendar: A lunisolar calendar with 12 or 13 months of 29 or 30 days, fixed by the Metonic cycle. Its months begin at computed new moons, with leap months on the 19-year pattern.
Gregorian calendar: The solar civil calendar of 365-day years with leap years, adopted across Europe from 1582. The civil West abandoned lunar month-counting, though Easter computation kept it.
New moon: The phase when the Moon lies between Earth and Sun, showing no illuminated face from Earth. Defines both endpoints of the synodic month; calendar months historically counted from it.
Meton of Athens: The fifth-century BCE Greek astronomer who computed the 19-year cycle reconciling lunar months with the solar year. His cycle is expressed entirely in whole numbers of synodic months.
Islamic calendar: A purely lunar calendar of twelve synodic months, drifting through the solar year every 33 years. Its twelve months per year are counted directly from observed lunar crescents.
Antikythera mechanism: A second-century BCE Greek geared device computing lunar phases and eclipse cycles mechanically. Its gear trains encode Metonic and Saros counts of synodic months.
Draconic month: The 27.21-day interval between successive crossings of the same node of the Moon's orbit. A third lunar period; ratios with the synodic month determine eclipse timing.
Hipparchus: The second-century BCE Greek astronomer who refined month lengths and compared Babylonian and Greek observations. Derived a synodic month length accurate to a fraction of a second from eclipse records.

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