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There are several types of lunar month. 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.
Since each lunation is approximately 29 + 1 ⁄ 2 days, [1] it is common for the months of a lunar calendar to alternate between 29 and 30 days. Since the period of 12 such lunations, a lunar year, is 354 days, 8 hours, 48 minutes, 34 seconds (354.36707 days), [1] purely lunar calendars are 11 to 12 days shorter than the solar year.
[h] However, because the Earth–Moon system moves at the same time in its orbit around the Sun, it takes slightly longer, 29.5 days, [i] [72] to return to the same lunar phase, completing a full cycle, as seen from Earth. This synodic period or synodic month is commonly known as the lunar month and is equal to the length of the solar day on ...
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.
The fact, however, that a year of twelve lunar months is ten or eleven days shorter than the solar year means that a lunar calendar drifts out of step with the seasons. Lunisolar calendars resolve this issue with a year of thirteen lunar months every few years, or by restarting the count at the first new (or full) moon after the winter solstice.
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.
The formal lunar day is therefore the time of a full lunar day-night cycle. 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.
A tropical year is approximately 365.2422 days long and a synodic month is approximately 29.5306 days long, [4] so a tropical year is approximately 365.2422 / 29.5306 ≈ 12.36826 months long. Because 0.36826 is between 1 ⁄ 3 and 1 ⁄ 2 , a typical year of 12 months needs to be supplemented with one intercalary or leap month every 2 to 3 years.
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