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The term lunar month usually refers to the synodic month because it is the cycle of the visible phases of the Moon. Most of the following types of lunar month, except the distinction between the sidereal and tropical months, were first recognized in Babylonian lunar astronomy .
A synodic day (or synodic rotation period or solar day) is the period for a celestial object to rotate once in relation to the star it is orbiting, and is the basis of solar time. The synodic day is distinguished from the sidereal day , which is one complete rotation in relation to distant stars [ 1 ] and is the basis of sidereal time.
A lunar calendar is a calendar based on the monthly cycles of the Moon's phases (synodic months, lunations), in contrast to solar calendars, whose annual cycles are based on the solar year. The most widely observed purely lunar calendar is the Islamic calendar.
A month is a unit of time, used with calendars, that is approximately as long as a natural phase cycle of the Moon; the words month and Moon are cognates.The traditional concept of months arose with the cycle of Moon phases; such lunar months ("lunations") are synodic months and last approximately 29.53 days, making for roughly 12.37 such months in one Earth year.
Due to tidal locking, this equals the time that the Moon takes to complete one synodic orbit around Earth, a synodic lunar month, returning to the same lunar phase. The synodic period is about 29 + 1 ⁄ 2 Earth days, which is about 2.2 days longer than its sidereal period.
With a 780-day synodic period, 21 periods match exactly to 16,380, or 20 cycles of 819. Venus needs seven periods to match five 819-day counts, Saturn has 13 periods to fit with six 819-day counts ...
The synodic month is the time it takes the Moon to reach the same visual phase. This varies notably throughout the year, [15] but averages around 29.53 days.
The traditional lunar year of 12 synodic months is about 354 days, approximately eleven days short of the solar year. Thus, every 2 to 3 years there is a discrepancy of 22 to 33 days, or a full synodic month. For example, if the winter solstice and the new moon coincide, it takes 19 tropical years for the coincidence to recur.