Lunar month

Animation of the Moon as it cycles through its phases, as seen from the Northern Hemisphere. The apparent wobbling of the Moon is known as libration.

In lunar calendars, a lunar month is the time between two successive syzygies (new moons or full moons). The use of the lunar month varies by which culture has utilized the method, the main difference being when the "new" month begins.

This article deals with the definitions of a 'month' that are mainly of significance in astronomy. For other definitions, including a description of a month in the calendars of different cultures around the world, see: month.

Variations

In Shona, Middle-Eastern and European traditions, the month starts when the young crescent moon becomes first 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 moon could no longer be seen just before sunrise. Others use calculation, of varying degrees of sophistication, e.g., the Hebrew calendar or the ecclesiastical lunar calendar. Yet others run from full moon to full moon. Calendars count integer days, so months may be 29 or 30 days in length, in some regular or irregular sequence. In India the month from conjunction to conjunction is divided into thirty parts known as tithis. The date is named after the tithi ruling at sunrise. As the tithi is shorter than the day the date sometimes jumps.

Terminology

There are several types of lunar month. Usually the term lunar month refers to the synodic month, because it is the cycle of visible moon phases. Most of the following types of months (but not the distinction between sidereal and tropical months) were first recognized in Babylonian lunar astronomy.

Sidereal month

The period of the Moon's orbit as defined with respect to the celestial sphere (of the fixed stars, nowadays 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 11.5 s).[1] 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.

Synodic month

This is the average period of the Moon's revolution with respect to the line joining the Sun and Earth. The synodic month is the period of the Moon's phases, because the Moon's appearance depends on the position of the Moon with respect to the Sun as seen from the Earth.

While the Moon is orbiting the Earth, the Earth is progressing in its orbit around the Sun. After completing a sidereal month the Moon must move a little further to reach the new position having the same angular distance from the Sun. This longer period is called the synodic month (Greek: συνοδικός, sunodikos, meaning "pertaining to a synod, i.e., a meeting" [in this case of the Sun and the Moon]).

Since the Earth's orbit around the Sun is elliptical and not circular, the angular rate of Earth's progression around the Sun varies during the year. The angular rate is faster nearer periapsis and slower near apoapsis. The same is so for the Moon's orbit around the Earth. Because of these variations in angular rate, the actual time between lunations may range from about 29.18 to about 29.93 days. The long-term average duration is 29.530587981 days[2] (29 d 12 h 44 min 2.8016 s). The synodic month is used to calculate eclipse cycles.

A synodic month is longer than a sidereal month because the Earth-Moon system is orbiting the Sun in the same direction as the Moon is orbiting the Earth. Therefore, the Sun appears to move with respect to the stars, and it takes about 2.2 days longer for the Moon to return to the same apparent position with respect to the Sun.

Tropical month

It is customary to specify positions of celestial bodies with respect to the vernal 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 zero than to the same point amidst the fixed stars: 27.321582 days (27 d 7 h 43 min 4.7 s). This slightly shorter period is known as tropical month; cf. the analogous tropical year of the Sun.

Anomalistic month

The Moon's orbit approximates 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 (lunar precession) in about 3,233 days (8.85 years). It takes the Moon longer to return to the same apsis because it moved ahead during one revolution. This longer period is called the anomalistic month, 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, and therefore 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, and also the period after which the apsides point to the Sun again.

An anomalistic month is longer than a sidereal month because the perigee moves in the same direction as the Moon is orbiting the Earth, one revolution in nine years. Therefore, the Moon takes a little longer to return to perigee than to return to the same star.

Draconic month

Sometimes written 'draconitic' month,[3] and also called the nodical month.[4] The orbit of the moon lies in a plane that is tilted with respect to the plane of the ecliptic at an inclination of about 5.3°. The line of intersection of these planes passes through the two points where the moon's orbit crosses the plane of the ecliptic: the ascending node, when the moon's path crosses the ecliptic as the moon moves into the northern celestial hemisphere and descending node when the moon's path crosses the ecliptic as the moon moves into the southern celestial hemisphere. 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 couple, the plane of the moon's orbit gradually rotates westward, which means the nodes gradually rotate around the earth. As a result, the time it takes the moon to return to the same node is shorter than a sidereal month. It lasts 27.212220 days (27 d 5 h 5 min 35.8 s). The plane of the moon's orbit precesses 360° in about 6,793 days (18.6 years).

A solar or lunar eclipse is possible only when the moon is at or near the point where its orbit crosses the ecliptic plane i.e. it is at or near one of the nodes. The name "draconic" refers to a mythical dragon, said to live in the nodes and eat the sun or moon during an eclipse.[3]

A draconic month is shorter than a sidereal month because the nodes move in the opposite direction to that in which the Moon is orbiting the Earth, one revolution in 18.6 years. Therefore, the Moon returns to the same node slightly earlier than it returns to the same star.

Cycle lengths

Regardless of the culture, all lunar months approximate the mean length of the synodic month, or how long it takes on average to pass through each phase (new, half, full moon) and back again. It takes 29–30[5] days. The moon completes its orbit around the earth in 27.3 days (the sidereal month), but due to the Earth's motion around the sun it has not finished a full (synodic) cycle until it reaches the point in its orbit where the sun is in the same position.[6]

Here is a list of the average length of the various astronomical lunar months.[7] These are not constant, so a first-order (linear) approximation of the secular change is provided:

Valid for the epoch J2000.0 (1 January 2000 12:00 TT):

Month type Length in days
anomalistic 27.554549878 − 0.000000010390 × Y
sidereal 27.321661547 + 0.000000001857 × Y
tropical 27.321582241 + 0.000000001506 × Y
draconic 27.212220817 + 0.000000003833 × Y
synodic 29.530588853 + 0.000000002162 × Y

Note: In this table, time is expressed in Ephemeris Time (more precisely Terrestrial Time) with days of 86,400 SI seconds. Y is years since the epoch (2000), expressed in Julian years of 365.25 days. For calendric calculations, one would probably use days measured in the time scale of Universal Time, which follows the somewhat unpredictable rotation of the Earth, and progressively accumulates a difference with ephemeris time called ΔT.

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. [8]

See also

References

  1. ↑ Lang, Kenneth (2012). Astrophysical Data: Planets and Stars. Springer. p. 57.
  2. ↑ CRC Handbook of Chemistry and Physics, page F-258
  3. 1 2 Linton, Christopher M. (2004). From Eudoxus to Einstein: a history of mathematical astronomy. Cambridge University Press. p. 7. In medieval times, the part of the Moon's orbit south of the ecliptic was known as the 'dragon' (which devoured the Moon during eclipses) and from this we get the terminology 'dragon's head' for the ascending node and 'dragon's tail' for the descending node. … The periods between successive nodes has, over time, been termed the dracontic, draconic and draconitic month, the words deriving from the Greek for 'dragon'.
  4. ↑ Lockyer, Sir Norman (1870). Elements of Astronomy: Accompanied with Numerous Illustrations, a Colored Representations of the Solar, Stellar, and Nebular Spectra, and Celestial Charts of the Northern and Southern Hemisphere. American Book Company. p. 223. Retrieved 10 February 2014. The nodical month is the time in which the Moon accomplishes a revolution with respect to her nodes, the line of which is also movable.
  5. ↑ Espenak, Fred. "Length of the Synodic Month: 2001 to 2100". Retrieved 2014-04-04.
  6. ↑ Fraser Cain (October 24, 2008). "Lunar Month". Universe Today. Retrieved 18 April 2012.
  7. ↑ Derived from ELP2000-85: 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
  8. ↑ "NASA - Eclipses and the Moon's Orbit".
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