Lunar month
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.
Lunar cycles are prominent, and calculated with great precision in the ancient Hindu Panchangam calendar, widely used in the Indian subcontinent.
[2] 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.
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.
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.
[6] The average duration in modern times is 29.53059 days with up to seven hours variation about the mean in any given year.
[9][10] The duration of synodic months in ancient and medieval history is itself a topic of scholarly study.
[11] 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).
[12][5]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.
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.
[5] 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.
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.
It takes the Moon longer to return to the same apsis because it has moved ahead during one revolution.
This longer period is called the anomalistic month[15] and has an average length of 27.554551 days (27 d 13 h 18 min 33.2 s).
The apparent diameter of the Moon varies with this period, so this type has some relevance for the prediction of eclipses (see Saros), whose extent, duration, and appearance (whether total or annular) depend on the exact apparent diameter of the Moon.
The apparent diameter of the full moon varies with the full moon cycle, which is the beat period of the synodic and anomalistic month, as well as the period after which the apsides point to the Sun again.
[16] The name draconic refers to a mythical dragon, said to live in the lunar nodes and eat the Sun or Moon during an eclipse.
The draconic or nodical month is the average interval between two successive transits of the Moon through the same node.
Because of the torque exerted by the Sun's gravity on the angular momentum of the Earth–Moon system, the plane of the Moon's orbit gradually rotates westward, which means the nodes gradually rotate around Earth.
As a result, the time it takes the Moon to return to the same node is shorter than a sidereal month, lasting 27.212220 days (27 d 5 h 5 min 35.8 s).
[18] The line of nodes of the Moon's orbit precesses 360° in about 6,793 days (18.6 years).
Regardless of the culture, all lunar calendar months approximate the mean length of the synodic month, the average period the Moon takes to cycle through its phases (new, first quarter, full, last quarter) and back again: 29–30[20] days.
[21] This table lists the average lengths of five types of astronomical lunar month, derived from Chapront, Chapront-Touzé & Francou 2002.
These are not constant, so a first-order (linear) approximation of the secular change is provided.
Apart from the long term (millennial) drift in these values, all these periods vary continually around their mean values because of the complex orbital effects of the Sun and planets affecting its motion.
[22] The periods are derived from polynomial expressions for Delaunay's arguments used in lunar theory, as listed in Table 4 of Chapront, Chapront-Touzé & Francou 2002 W1 is the ecliptic longitude of the Moon w.r.t.
