In
lunar calendar
A lunar calendar is a calendar based on the monthly cycles of the Moon's phases ( synodic months, lunations), in contrast to solar calendars, whose annual cycles are based only directly on the solar year. The most commonly used calendar, the Gre ...
s, 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
Conjunction may refer to:
* Conjunction (grammar), a part of speech
* Logical conjunction, a mathematical operator
** Conjunction introduction, a rule of inference of propositional logic
* Conjunction (astronomy), in which two astronomical bodies ...
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 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
A panchāngam ( sa, पञ्चाङ्गम्; ) is a Hindu calendar and almanac, which follows traditional units of Hindu timekeeping, and presents important dates and their calculations in a tabulated form. It is sometimes spelled ''Pa ...
calendar, widely used in the Indian subcontinent. In India, the month from conjunction to conjunction is divided into thirty parts known as . A is between 19 and 26 hours long. The date is named after the ruling at sunrise. When the is shorter than the day, the may jump. This case is called or . Conversely a may 'stall' as well, that is – the same is associated with two consecutive days. This is known as .
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
A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A date is the designation of a single and specific day within such a system. A calendar is also a physi ...
for deeds and other written contracts by section 61(a) of the
Law of Property Act 1925
The Law of Property Act 1925c 20 is a statute of the United Kingdom Parliament. It forms part of an interrelated programme of legislation introduced by Lord Chancellor Lord Birkenhead between 1922 and 1925. The programme was intended to moderni ...
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
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 Euro ...
because it is the cycle of the visible
phases of the Moon
Concerning the lunar month of ~29.53 days as viewed from Earth, the lunar phase or Moon phase is the shape of the Moon's directly sunlit portion, which can be expressed quantitatively using areas or angles, or described qualitatively using the t ...
.
Most of the following types of lunar month, except the distinction between the sidereal and tropical months, were first recognized in
Babylonian lunar astronomy.
Sidereal month
The period of the
Moon's orbit
The Moon orbits Earth in the prograde direction and completes one revolution relative to the Vernal Equinox and the stars in about 27.32 days (a tropical month and sidereal month) and one revolution relative to the Sun in about 29.53 days (a ...
as defined with respect to the
celestial sphere
In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, ...
of apparently
fixed stars
In astronomy, fixed stars ( la, stellae fixae) is a term to name the full set of glowing points, astronomical objects actually and mainly stars, that appear not to move relative to one another against the darkness of the night sky in the backgro ...
(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
star
A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth ma ...
s ( la, sidera): 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.
Synodic month
The synodic month ( el, συνοδικός, translit=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 d 12 h 44 min and 2.9 s. 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.
While the Moon is orbiting Earth, 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, appearing to move with respect to the stars since the previous month. Therefore, the synodic month takes 2.2 days longer than the sidereal month. Thus, about 13.37 sidereal months, but about 12.37 synodic months, occur in a
Gregorian year
Gregorian may refer to:
*The thought or ideology of Pope Gregory I or Pope Gregory VII (also called ''Gregorianism'')
*Things named for Pope Gregory I:
**Gregorian chant, the central tradition of Western plainchant, a form of monophonic, unaccom ...
.
Since
Earth's orbit around the Sun is
elliptical and not
circular
Circular may refer to:
* The shape of a circle
* ''Circular'' (album), a 2006 album by Spanish singer Vega
* Circular letter (disambiguation)
** Flyer (pamphlet), a form of advertisement
* Circular reasoning, a type of logical fallacy
* Circular ...
, the
speed of Earth's progression around the Sun varies during the year. Thus, the
angular rate
In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
is faster nearer
periapsis and slower near
apoapsis
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion.
General description
There are two apsides in any ellip ...
. The same is so for the Moon's orbit around Earth. Because of these variations in angular rate, the actual time between
lunations may vary from about 29.18 to about 29.93 days. The average duration in modern times is 29.53059 days with up to seven hours variation about the mean in any given year. A more precise figure may be derived for a specific synodic month using the
lunar theory of
Chapront-Touzé and Chapront (1988):
where and is the
Julian day number
The Julian day is the continuous count of days since the beginning of the Julian period, and is used primarily by astronomers, and in software for easily calculating elapsed days between two events (e.g. food production date and sell by date).
...
(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.
Tropical month
It is customary to specify positions of celestial bodies with respect to the March
equinox. Because of Earth's
precession of the equinoxes
In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In the absence of precession, the astronomical body's orbit would show axial parallelism. In partic ...
, 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
In astronomy, fixed stars ( la, stellae fixae) is a term to name the full set of glowing points, astronomical objects actually and mainly stars, that appear not to move relative to one another against the darkness of the night sky in the backgro ...
. This slightly shorter period, days (27 d 7 h 43 min 4.7 s), is known as the tropical month by analogy with Earth's
tropical year
A tropical year or solar year (or tropical period) is the time that the Sun takes to return to the same position in the sky of a celestial body of the Solar System such as the Earth, completing a full cycle of seasons; for example, the time fro ...
.
Anomalistic month
The
Moon's orbit
The Moon orbits Earth in the prograde direction and completes one revolution relative to the Vernal Equinox and the stars in about 27.32 days (a tropical month and sidereal month) and one revolution relative to the Sun in about 29.53 days (a ...
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
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion.
General description
There are two apsides in any ellip ...
:
perigee and
apogee
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion.
General description
There are two apsides in any ellip ...
), rotates once (
apsidal precession
In celestial mechanics, apsidal precession (or apsidal advance) is the precession (gradual rotation) of the line connecting the apsides (line of apsides) of an astronomical body's orbit. The apsides are the orbital points closest (periapsi ...
) in about 3,233 days (8.85 years). 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 and has an average length of days (27 d 13 h 18 min 33.2 s). The
apparent diameter
The angular diameter, angular size, apparent diameter, or apparent size is an angular distance describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it ...
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
A supermoon is a full moon or a new moon that nearly coincides with perigee—the closest that the Moon comes to the Earth in its elliptic orbit—resulting in a slightly larger-than-usual apparent size of the lunar disk as viewed from Earth. ...
, 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.
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
A draconic month or draconitic month
is also known as a nodal month or nodical month.
The name ''draconic'' refers to a mythical
dragon, said to live in the
lunar nodes and eat the Sun or Moon during an
eclipse.
A solar or lunar eclipse is possible only when the Moon is at or near either of the two points where its orbit crosses the
ecliptic plane
The ecliptic or ecliptic plane is the orbital plane of the Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic agains ...
; i.e., the satellite is at or near either of its
orbital nodes.
The orbit of the Moon lies in a plane that is
inclined
Incline, inclined, inclining, or inclination may refer to:
*Grade (slope), the tilt, steepness, or angle from horizontal of a topographic feature (hillside, meadow, etc.) or constructed element (road, railway, field, etc.)
*Slope, the tilt, steepn ...
about 5.14° with respect to the ecliptic plane. The line of intersection of these planes passes through the two points at which the Moon's orbit crosses the ecliptic plane: the ''ascending node'', where the Moon enters the
Northern Celestial Hemisphere, and the ''descending node'', where the Moon moves into the
Southern
Southern may refer to:
Businesses
* China Southern Airlines, airline based in Guangzhou, China
* Southern Airways, defunct US airline
* Southern Air, air cargo transportation company based in Norwalk, Connecticut, US
* Southern Airways Express, M ...
.
The draconic or nodical month is the average interval between two successive transits of the Moon through the same
node
In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex).
Node may refer to:
In mathematics
*Vertex (graph theory), a vertex in a mathematical graph
*Vertex (geometry), a point where two or more curves, lines, ...
. Because of the
torque exerted by the Sun's gravity on the
angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syste ...
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 days (27 d 5 h 5 min 35.8 s). The line of nodes of the Moon's orbit
precesses 360° in about 6,798 days (18.6 years).
A draconic month is shorter than a sidereal month because the nodes precess in the
opposite direction to that in which the Moon is orbiting Earth, one rotation every 18.6 years. Therefore, the Moon returns to the same node slightly earlier than it returns to meet the same reference star.
Cycle lengths
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
New is an adjective referring to something recently made, discovered, or created.
New or NEW may refer to:
Music
* New, singer of K-pop group The Boyz
Albums and EPs
* ''New'' (album), by Paul McCartney, 2013
* ''New'' (EP), by Regurgitator, ...
, first quarter,
full, last quarter) and back again: 29–30
days. The Moon completes one orbit around Earth every 27.3 days (a sidereal month), but due to
Earth's orbital motion around the Sun, the Moon does not yet finish a synodic cycle until it has reached the point in
its orbit where the Sun is in the same
relative position
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point ''P'' in space in relation to an arbitrary reference origin ''O''. Usually denoted x, r, or ...
.
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.
Valid for the
epoch J2000.0
In astronomy, an epoch or reference epoch is a moment in time used as a reference point for some time-varying astronomical quantity. It is useful for the celestial coordinates or orbital elements of a celestial body, as they are subject to pert ...
(1 January 2000 12:00
TT):
''Note:'' In this table, time is expressed in
Ephemeris Time (more precisely
Terrestrial Time) with days of 86,400
SI seconds. ''T'' is centuries since the epoch (2000), expressed in
Julian centuries of 36,525 days. For calendrical calculations, one would probably use days measured in the time scale of
Universal Time
Universal Time (UT or UT1) is a time standard based on Earth's rotation. While originally it was mean solar time at 0° longitude, precise measurements of the Sun are difficult. Therefore, UT1 is computed from a measure of the Earth's angle with ...
, which follows the somewhat unpredictable rotation of the Earth, and progressively accumulates a difference with ephemeris time called
ΔT ("delta-T").
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.
Derivation
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. the fixed ICRS equinox: its period is the sidereal month.
If we add the
rate of precession to the sidereal angular velocity, we get the angular velocity w.r.t. the equinox of the date: its period is the tropical month, which is rarely used.
''l'' is the mean anomaly, its period is the anomalistic month.
''F'' is the argument of latitude, its period is the draconic month.
''D'' is the elongation of the Moon from the Sun, its period is the synodic month.
Derivation of a period from a
polynomial for an argument ''A'' (angle):
;
''T'' in centuries (cy) is 36,525 days from epoch J2000.0.
The angular velocity is the first derivative:
.
The period (''Q'') is the inverse of the angular velocity:
,
ignoring higher-order terms.
A
1 in "/cy ;
A
2 in "/cy
2;
so the result ''Q'' is expressed in cy/" which is a very inconvenient unit.
1 revolution (rev) is 360 × 60 × 60" = 1,296,000";
to convert the unit of the velocity to revolutions/day, divide A
1 by B
1 = 1,296,000 × 36,525 = 47,336,400,000;
C
1 = B
1 ÷ A
1
is then the period (in days/revolution) at the epoch J2000.0.
For rev/day
2 divide A
2 by B
2 = 1,296,000 × 36,525
2 = 1,728,962,010,000,000.
For
the numerical conversion factor then becomes 2 × B1 × B1 ÷ B2 = 2 × 1,296,000.
This would give a linear term in days change (of the period) per day, which is also an inconvenient unit:
for change per year multiply by a factor 365.25, and for change per century multiply by a factor 36,525.
C
2 = 2 × 1,296,000 × 36,525 × A
2 ÷ (A
1 × A
1).
Then period ''P'' in days:
.
Example for synodic month, from Delaunay's argument ''D'':
D′ = 1602961601.0312 − 2 × 6.8498 × T "/cy;
A
1 = 1602961601.0312 "/cy;
A
2 = −6.8498"/cy
2;
C
1 = 47,336,400,000 ÷ 1,602,961,601.0312 = 29.530588860986 days;
C
2 = 94,672,800,000 × −6.8498 ÷ (1,602,961,601.0312 × 1,602,961,601.0312) = −0.00000025238 days/cy.
See also
*
Lunisolar calendar
*
Chinese calendar
The traditional Chinese calendar (also known as the Agricultural Calendar ��曆; 农历; ''Nónglì''; 'farming calendar' Former Calendar ��曆; 旧历; ''Jiùlì'' Traditional Calendar ��曆; 老历; ''Lǎolì'', is a lunisolar calendar ...
*
Hebrew calendar
*
Babylonian calendar
The Babylonian calendar was a lunisolar calendar with years consisting of 12 lunar months, each beginning when a new crescent moon was first sighted low on the western horizon at sunset, plus an intercalary month inserted as needed by decree. T ...
*
Hindu calendar
The Hindu calendar, Panchanga () or Panjika is one of various lunisolar calendars that are traditionally used in the Indian subcontinent and Southeast Asia, with further regional variations for social and Hindu religious purposes. They adopt a ...
*
Islamic calendar
*
Tibetan calendar
The Tibetan calendar (), or Tibetan lunar calendar, is a lunisolar calendar, that is, the Tibetan year is composed of either 12 or 13 lunar months, each beginning and ending with a new moon. A thirteenth month is added every two or three years, ...
Notes
References
* Observer's handbook 1991, Editor Roy L. Bishop, The Royal Astronomical Society of Canada (p14)
{{DEFAULTSORT:Lunar Month
Units of time
Month
Month