Month

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In Egyptian mythology, Month is an alternate spelling for Menthu.

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 (lunations) 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.

Contents 1 Astronomical background 1.1 Sidereal month 1.2 Tropical month 1.3 Anomalistic month 1.4 Draconic month 1.5 Synodic month 1.6 Month lengths 2 Calendrical consequences 3 Months in various calendars 3.1 Julian and Gregorian calendars 3.2 French Republican calendar 3.3 Islamic calendar 3.4 Hebrew Calendar 3.5 Hindu Calendar 3.6 Iranian/Persian calendar 3.7 Icelandic/Old Norse calendar 4 Notes 5 See also

Astronomical background

The motion of the Moon in its orbit is very complicated and its period is not constant. Moreover, many cultures (most notably those using the ancient Hebrew (Jewish) calendar and the Islamic calendar) start a month with the first appearance of the thin crescent of the new moon after sunset over the western horizon. The date and time of this actual observation depends on the exact geographical longitude as well as latitude, atmospheric conditions, the visual acuity of the observers, etc. Therefore the beginning and lengths of months in these calendars can not be accurately predicted. Most Jews currently follow a precalculated calendar, but the Karaites rely on actual moon observations.

Sidereal month

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): 27.321 661 days (27 d 7 h 43 min 11.5 s) or about 27 ⅓ days. This type of "month" has appeared among cultures in the Middle East, India, and China in the following way: they divided the sky in 27 or 28 lunar mansions, characterized by asterisms (apparent groups of stars), one for each day that the Moon follows its track among the stars.

Tropical month

It is customary to specify positions of celestial bodies with respect to the vernal equinox. Because of precession, 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: 27.321 582 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

Like all orbits, the Moon's 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 the anomalistic month, and has an average length of 27.554 551 days (27 d 13 h 18 min 33.2 s), or 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 (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.

Draconic month

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 nodes. 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, nodical, or draconitic month. It lasts 27.212 220 days (27 d 5 h 5 min 35.8 s), or 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 at one of the nodes. At this time a solar or lunar eclipse is possible. The "draconic/draconitic" month refers to the mythological dragon that lives in the nodes and regularly eats the Sun or Moon during an eclipse.

Synodic month

The cause of 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 the Sun, it takes the Moon extra time (after completing a sidereal month, i. e. a full circle) to catch up and return to the same position with respect to the Sun. This longer period is called the synodic month (from Greek syn hodô or σὺν ὁδῴ, meaning "with the way", i. e. the Moon travelling with the Sun). Because of the perturbations of the orbits of the Earth and Moon, the actual time between lunations may range from about 29.27 to about 29.83 days. The long-term average duration is 29.530 588 days (29 d 12 h 44 min 2.8 s), or about 29 ½ days.

Month lengths

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

Valid for the epoch J2000.0 (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

Note: time expressed in Ephemeris Time (more precisely Terrestrial Time) with days of 86400 SI seconds. y is years since the epoch (2000), expressed in Julian years of 365.25 days. Note that for calendrical 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.

Calendrical consequences

For more details on this topic, see lunar calendar and lunisolar calendar.

At the simplest level, all lunar calendars are based on the approximation that 2 lunations last 59 days: a 30 day full month followed by a 29 day hollow month — but this is only marginally accurate and quickly needs correction by using larger cycles, or the equivalent of leap days.

Second, the synodic month does not fit easily into the year, which makes constructing accurate, rule-based lunisolar calendars difficult. The most common solution to this problem is the Metonic cycle, which takes advantage of the fact that 235 lunations are approximately 19 tropical years (which add up to not quite 6940 days). However, a Metonic calendar (such as the Hebrew calendar) will drift against the seasons by about 1 day every 200 years.

The problems of creating reliable lunar calendars may explain why solar calendars, having months which no longer relate to the phase of the moon, and being based only on the more predictable motion of the sun against the sky, have generally replaced lunar calendars for civil use in most societies.

Months in various calendars

Julian and Gregorian calendars

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

1. January, 31 days
2. February, 28 days, 29 in leap years, or 30 on certain occasions in related calendars
3. March, 31 days
4. April, 30 days
5. May, 31 days
6. June, 30 days
7. July, 31 days
8. August, 31 days
9. September, 30 days
10. October, 31 days
11. November, 30 days
12. December, 31 days

For the rationale behind the unusual day lengths, see February and August.

Template:Selfref

Months existing in the Roman calendar in the past include:

• Mercedonius, an occasional month after February to realign the calendar.
• Quintilis, renamed to July in honor of Julius Caesar.
• Sextilis, renamed to August in honor of Caesar Augustus.

The famous mnemonic Thirty days hath September is the most common way of teaching the lengths of the months.

You can also use the knuckles of the four fingers of your hand and the spaces between them to remember the lengths of the months. First make a fist, then begin listing each month as you proceed across your hand. All months landing on a knuckle are 31 days long and those landing between them are not (it's up to you to figure out February). When you reach the knuckle of your little finger (July), go back to the first knuckle and continue with August.

French Republican calendar

This calendar was proposed during the French Revolution, and used by the French government for about twelve years from late 1793. There were twelve months of 30 days each, grouped into three ten-day weeks called décades. The five or six extra days needed to approximate the tropical year were placed after the months at the end of each year. A period of four years ending on a leap day was to be called a Franciade. It began at the autumn equinox:

• Autumn:

1. Vendémiaire
2. Brumaire
3. Frimaire

• Winter:

1. Nivôse
2. Pluviôse
3. Ventôse

• Spring:

1. Germinal
2. Floréal
3. Prairial

• Summer:

1. Messidor
2. Thermidor
3. Fructidor

Islamic calendar

There are also twelve months in the Islamic calendar. They are named as follows:

1. Muharram ul Haram (or shortened to Muharram) محرّم
2. Safar صفر
3. Rabi`-ul-Awwal (Rabi' I) ربيع الأول
4. Rabi`-ul-Akhir (or Rabi` al-THaany) (Rabi' II) ربيع الآخر أو ربيع الثاني
5. Jumaada-ul-Awwal (Jumaada I) جمادى الأول
6. Jumaada-ul-Akhir (or Jumaada al-THaany) (Jumaada II) جمادى الآخر أو جمادى الثاني
7. Rajab رجب
8. Sha'aban شعبان
9. Ramadhan رمضان
10. Shawwal شوّال
11. Dhul Qadah ذو القعدة (or Thw al-Qi`dah)
12. Dhul Hijja ذو الحجة (or Thw al-Hijjah)

For details, please see Islamic calendar.

Hebrew Calendar

The Hebrew calendar has 12 or 13 months.

1. Nisan, 30 days
2. Iyyar, 29 days
3. Sivan, 30 days
4. Tammuz, 29 days
5. Av, 30 days
6. Elul, 29 days
7. Tishri, 30 days
8. Heshvan, 29/30 days
9. Kislev, 29/30 days
10. Tevet, 29 days
11. Shevat, 30 days
12. Adar 1, 30 days, intercalary month
13. Adar 2, 29 days

Adar 1 is only added in leap years. In ordinary years, Adar 2 is simply called Adar.

Hindu Calendar

The Hindu Calendar has various systems of naming the months. The months in the lunar calendar are:

1. Chaitra
2. Vaishaakha
3. Jyaishtha
4. Aashaadha
5. Shraavana
6. Bhaadrapada
7. Aashvayuja
8. Kaartika
9. Maargashiirsha
10. Pausha
11. Maagha
12. Phaalguna

These are also the names used in the Indian national calendar for the newly redefined months.

The names in the solar calendar are just the names of the zodiac sign in which the sun travels. They are

1. Mesha
2. Vrishabha
3. Mithuna
4. Kataka
5. Simha
6. Kanyaa
7. Tulaa
8. Vrishcika
9. Dhanus
10. Makara
11. Kumbha
12. Miina

Iranian/Persian calendar

The Iranian / Persian calendar, currently used in Iran and Afghanistan, also has 12 months. The Persian names are included in the parentheses.

1. Farvardin (فروردین)‎, 31 days
2. Ordibehesht (اردیبهشت)‎, 31 days
3. Khordad (خرداد)‎, 31 days
4. Tir (تیر)‎, 31 days
5. Mordad (مرداد)‎, 31 days
6. Shahrivar (شهریور)‎, 31 days
7. Mehr (مهر)‎, 30 days
8. Aban (آبان)‎, 30 days
9. Azar (آذر)‎, 30 days
10. Dey (دی)‎, 30 days
11. Bahman (بهمن)‎, 30 days
12. Esfand (اسفند)‎, 29 days, 30 in leap years

Icelandic/Old Norse calendar

The old Icelandic calendar is not in official use anymore, but some holidays and annual feasts are still calculated according to it in Iceland. It has 12 months, broken down into two groups of six.

• Skammdegi ("Short days")

1. Gormánuður (mid October - mid November, "slaughter month" or "Gór's month")
2. Ýlir (mid November - mid December, "Yule month")
3. Mörsugur (mid December - mid January, "fat sucking month")
4. Þorri (mid January - mid February, "frozen snow month")
5. Góa (mid February - mid March, "Góa's month, see Nór")
6. Einmánuður (mid March - mid April, "lone" or "single month")

• Náttleysi ("Nightless days")

1. Harpa (mid April - mid May, Harpa is a female name, probably a forgotten goddess, first day of Harpa is celebrated as Sumardagurinn fyrsti)
2. Skerpla (mid May - mid June, another forgotten goddess)
3. Sólmánuður (mid June - mid July, "sun month")
4. Heyannir (mid July - mid August, "hay business month")
5. Tvímánuður (mid August - mid September, "two" or "second month")
6. Haustmánuður (mid September - mid October, "autumn month")

Notes

See also

Template:Wiktionary

• Table of lunar month correspondences
• Intercalation
• Maya calendar
• Chinese calendarang:Mōnaþ

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