The **month** is a unit of time, used with calendars, which is approximately as long as some natural period related to the motion of the Moon. The traditional concept arose with the cycle of moon phases; such months are **synodic months** and last ~29.53 days. From excavated tally sticks, researchers have deduced that people counted days in relation to the Moon's phases as early as the paleolithic age. Synodic months are still the basis of many calendars.

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The actual period of the Moon's orbit as measured in a fixed frame of reference is known as a **sidereal month**, because it is the time it takes the Moon to return to the same position on the celestial sphere among the fixed stars (Latin: *sidus*): about 27 1/3 days on average. This type of "month" has appeared among cultures in the Middle East, India, and China in the following way: they divided the sky in 28 lunar stations, characterized by asterisms (groups of stars), one for each day that the Moon follows its track among the stars.

It is customary to specify positions of celestial bodies with respect to the vernal equinox. Because of precession, this point moves back along the ecliptic. Therefore it takes the Moon less time to return to the equinox than to the same point amidst the fixed stars. This slightly shorter period is known as **tropical** month; cf. the analogous tropical year of the Sun. This type of month is not used much.

Like all orbits, the Moon's orbit is an ellipse rather than a circle. However, the orientation (as well as the shape) of this orbit is not fixed. In particular, the position of the extreme points (the line of the apsides: perigee and apogee), makes a full circle in about nine years. It takes the Moon longer to return to the same apsis because it moved ahead during one revolution. This longer period is called **anomalistic** month, and has an average length of about 27 1/2 days. The apparent diameter of the Moon varies with this period, and therefore this type of month has some relevance for the prediction of eclipses (see saros), whose extent, duration, and appearance depend on the exact apparent diameter of the Moon.

The orbit of the Moon lies in a plane that is tilted with respect to the plane of the ecliptic: it has an inclination of about five degrees. The line of intersection of these planes defines two points on the celestial sphere: the ascending and descending node. The plane of the Moon's orbit precesses over a full circle in about 18.6 years, so the nodes move backwards over the ecliptic with the same period. Hence the time it takes the Moon to return to the same node is again shorter than a sidereal month: this is called the **draconic** month, which has an average length of about 27 1/5 days. It is important for predicting eclipses: these take place when the Sun, Earth and Moon are on a line. Now (as seen from the Earth) the Sun moves along the ecliptic, while the Moon moves along its own orbit that is inclined on the ecliptic. The three bodies are only on a line when the Moon is on the ecliptic, i.e. when it is in one of the nodes. The "draconic" month refers to the mythological dragon that lives in the nodes and regularly eats the Sun or Moon at an eclipse.

The cause of the moon phases is that from the Earth we see the part of the Moon that is illuminated by the Sun from different angles as the Moon traverses its orbit. So the appearance depends on the position of the Moon with respect to the Sun (as seen from the Earth). Because the Earth orbits Sol, it takes Luna extra time (after completing a sidereal month - 360&Deg;) to orbit around and return to the same position with respect to Sol. This longer period is called **synodic** month (from Greek *syn hodos*, with the way, i.e. the Moon travelling with the Sun), and is longer because, in order for the same S Because of the perturbations of the orbits of the Earth (Sun) and Moon, the actual time between lunations may range from about 29.27 to about 29.83 days.

Here is a list of the average length of the various astronomical lunar months [1]. These are not constant, so I provide a first-order (linear) approximation of the secular change:

Valid for the epoch J2000 (1 Jan. 2000 12:00 TT):

sidereal month: 27.321661547 + 0.000000001857*y days tropical month: 27.321582241 + 0.000000001506*y days anomalistic month: 27.554549878 - 0.000000010390*y days draconic month: 27.212220817 + 0.000000003833*y days synodic month: 29.530588853 + 0.000000002162*y days

[1] Derived from the ELP2000-85; see: M.Chapront-Touzé, J. Chapront (1991): "Lunar Tables and Programs from 4000 B.C. to A.D.8000". Willmann-Bell, Richmond VA; ISBN 0-943396-33-6

- 29 days
- 30
- 59/2
- 443/15
- 502/17
- 1447/49
- 25101/850

More importantly, in lunisolar calendars, an integral number of synodic months is fitted into some integral number of years. The average length of the tropical year divided by the average length of the synodic month, i.e. the number of synodic months in a year, is (for epoch J2000):

- 12.368266392

- 12
- 25/2
- 37/3
- 99/8
- 235/19 Metonic cycle
- 4131/334

The Gregorian calendar, like the Julian calendar before it, has twelve months:

- January, with 31 days;
- February, with 28 days or 29 in leap years;
- March, with 31 days;
- April, with 30 days;
- May, with 31 days;
- June, with 30 days;
- July, with 31 days;
- August, with 31 days;
- September, with 30 days;
- October, with 31 days;
- November, with 30 days;
- December, with 31 days.

One mnemonic for remembering the lengths of the months is to hold up your two fists with the index knuckle of your left hand against the index knuckle of your right hand. Then, starting with January from the little knuckle of your left hand, count knuckle, space, knuckle, space through the months. A knuckle represents a month of 31 days, and a space represents a short month.

Another one is:

*Thirty days hath September,**April, June, and November;**All the rest have thirty-one,**Excepting February alone,**Which hath but twenty-eight, in fine,**Till leap year make it twenty-nine.*

*See also*times from 1 megasecond to 10 megaseconds

In Egyptian mythology,