In lunar calendars, a lunar month is the time between two successive syzygies of the same type: new moons or full moons. The precise definition varies, especially for the beginning of the month.
Variations In Shona, Middle Eastern, and European traditions, the month starts when the young crescent moon first becomes visible, at evening, after conjunction with the Sun one or two days before that evening (e.g., in the Islamic calendar). In ancient Egypt, the lunar month began on the day when the waning moon could no longer be seen just before sunrise. Others run from full moon to full moon. Yet others use calculation, of varying degrees of sophistication, for example, the Hebrew calendar, the Chinese calendar, or the ecclesiastical lunar calendar. Calendars count integer days, so months may be 29 or 30 days in length, in some regular or irregular sequence. Lunar cycles are prominent, and calculated with great precision in the ancient Hindu Panchangam calendar, widely used in the Indian subcontinent. In Indonesia, the month from conjunction to conjunction is divided into thirty parts known as tithi. A tithi is between 19 and 26 hours long. The date is named after the tithi ruling at sunrise. When the tithi is shorter than the day, the tithi may jump. This case is called kṣaya or lopa. Conversely a tithi may 'stall' as well, that is – the same tithi is associated with two consecutive days. This is known as vriddhi. In English common law, a "lunar month" traditionally meant exactly 28 days or four weeks, thus a contract for 12 months ran for exactly 48 weeks. In the United Kingdom, the lunar month was formally replaced by the calendar month for deeds and other written contracts by section 61(a) of the Law of Property Act 1925 and for post-1850 legislation by the Interpretation Act 1978 (Schedule 1 read with sections 5 and 23 and with Schedule 2 paragraph 4(1)(a)) and its predecessors.
Types
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.
Synodic month
The synodic month (Greek: συνοδικός, romanized: synodikós, meaning "pertaining to a synod, i.e., a meeting"; in this case, of the Sun and the Moon), also lunation, is the average period of the Moon's orbit with respect to the line joining the Sun and Earth: 29 (Earth) days, 12 hours, 44 minutes and 2.9 seconds. This is the period of the lunar phases, because the Moon's appearance depends on the position of the Moon with respect to the Sun as seen from Earth. Due to tidal locking, the same hemisphere of the Moon always faces the Earth and thus the length of a lunar day (sunrise to sunrise on the Moon) equals the time that the Moon takes to complete one orbit around Earth, returning to the same lunar phase. While the Moon is orbiting Earth, Earth is progressing in its orbit around the Sun. After completing its § Sidereal month, the Moon must move a little further to reach the new position having the same angular distance from the Sun, appearing to move with respect to the stars since the previous month. Consequently, at 27 days, 7 hours, 43 minutes and 11.5 seconds, the sidereal month is about 2.2 days shorter than the synodic month. Thus, about 13.37 sidereal months, but about 12.37 synodic months, occur in a Gregorian year. Since Earth's orbit around the Sun is elliptical and not circular, the speed of Earth's progression around the Sun varies during the year. Thus, the angular velocity is faster nearer periapsis and slower near apoapsis. The same is true (to an even larger extent) for the Moon's orbit around Earth. Because of these two variations in angular rate, the actual time between lunations may vary from about 29.274 days (or 29 d 6 h 35 min) to about 29.829 days (or 29 d 19 h 54 min). The average duration in modern times (mean synodic month) is 29.53059 days or 29 d 12 h 44 min 3 s, with up to seven hours variation about the mean in any given year. A more precise figure of the average duration may be derived for a specific date using the lunar theory of Chapront-Touzé and Chapront (1988): 29.5305888531 + 0.00000021621T − 3.64×10−10T2 where T = (JD − 2451545.0)/36525 and JD is the Julian day number (and JD = 2451545 corresponds to 1 January AD 2000). The duration of synodic months in ancient and medieval history is itself a topic of scholarly study.
Sidereal month The period of the Moon's orbit as defined with respect to the celestial sphere of apparently fixed stars (the International Celestial Reference Frame; ICRF) is known as a sidereal month because it is the time it takes the Moon to return to a similar position among the stars (Latin: sidera): 27.321661 days (27 d 7 h 43 min 11.6 s).This type of month has been observed among cultures in the Middle East, India, and China in the following way: they divided the sky into 27 or 28 lunar mansions, one for each day of the month, identified by the prominent star(s) in them.
Tropical month Just as the tropical year is based on the amount of time between perceived rotations of the sun around the earth (based on the Greek word τροπή meaning "turn"), the tropical month is the average time between corresponding equinoxes. It is also the average time between successive moments when the moon crosses from the southern celestial hemisphere to the northern (or vice versa), or successive crossing of a given right ascension or ecliptic longitude. The moon rises at the North Pole once every tropical month, and likewise at the South Pole. It is customary to specify positions of celestial bodies with respect to the First Point of Aries (Sun's location at the March equinox). Because of Earth's precession of the equinoxes, this point moves back slowly along the ecliptic. Therefore, it takes the Moon less time to return to an ecliptic longitude of 0° than to the same point amid the fixed stars. This slightly shorter period, 27.321582 days (27 d 7 h 43 min 4.7 s), is commonly known as the tropical month by analogy with Earth's tropical year.
Anomalistic month
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