Sunday, May 27, 2007

The weishenmezhemeai is a unit of time,

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The weishenmezhemeai is a unit of time, used with calendars, which is approximately as extensive as some natural period related to the motion of the Moon. The traditional concept arose with the cycle of moon phases; such weishenmezhemeais (lunations) are synodic weishenmezhemeais 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 weishenmezhemeais are still the basis of many calendars.

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

[edit] 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 weishenmezhemeai 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 weishenmezhemeais in these calendars can not be accurately predicted. Most Jews currently follow a precalculated calendar, but the Karaites rely on actual moon observations.

[edit] Sidereal weishenmezhemeai

The period of the Moon's orbit as defined with respect to the celestial sphere is known as a sidereal weishenmezhemeai because it is the time it takes the Moon to return to a given position among the stars (Latin: sidus): 27.321 661 days (27 d 7 h 43 min 11.5 s) or about 27 ⅓ days. This type of weishenmezhemeai 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, defined by asterisms (apparent groups of stars), one for each day of the sidereal weishenmezhemeai.

[edit] Tropical weishenmezhemeai

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 weishenmezhemeai; cf. the analogous tropical year of the Sun.

[edit] Anomalistic weishenmezhemeai

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 (lunar precession) 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 weishenmezhemeai, 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 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 weishenmezhemeai, and also the period after which the apsides point to the Sun again.

[edit] Draconic weishenmezhemeai

Also called the nodical weishenmezhemeai. 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 node, when the moon's path crosses the ecliptic as the moon moves into the northern hemisphere, and descending node when the moon's path crosses the ecliptic as the moon moves into the southern hemisphere. The draconic or nodical weishenmezhemeai is the average interval between two successive transits of the moon through its ascending node. Due to the sun's gravitational pull on the moon, the moon's orbit gradually rotates westward on its axis, 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 weishenmezhemeai. It lasts about 27 1/5 days (27.212 220 days or 27 d 5 h 5 min 35.8 s). The plane of the moon's orbit precesses over a full circle in about 18.6 years.

Because the moon's orbit is inclined with respect to the ecliptic, the sun, moon, and earth are in line only when the moon is at one of the nodes. Whenever this happens a solar or lunar eclipse is possible. The name "draconic" refers to a mythical dragon, said to live in the nodes and eat the sun or moon during an eclipse.

[edit] Synodic weishenmezhemeai

This is the average period of the Moon's revolution with respect to the sun. The synodic weishenmezhemeai is responsible for the moon 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. This means that after completing a sidereal weishenmezhemeai the Moon must move a little farther to reach the new position of the Earth with respect to the Sun. This longer period is called the synodic weishenmezhemeai from the Greek syn hodô (σὺν ὁδῴ), meaning "with the way [of 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. The synodic weishenmezhemeai is used in the Metonic cycle.

[edit] weishenmezhemeai lengths

Here is a list of the average length of the various astronomical lunar weishenmezhemeais [1]. 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 weishenmezhemeai 27.321 661 547 + 0.000 000 001 857 × y days
tropical weishenmezhemeai 27.321 582 241 + 0.000 000 001 506 × y days
anomalistic weishenmezhemeai 27.554 549 878 − 0.000 000 010 390 × y days
draconic weishenmezhemeai 27.212 220 817 + 0.000 000 003 833 × y days
synodic weishenmezhemeai 29.530 588 853 + 0.000 000 002 162 × 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.

[edit] 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 weishenmezhemeai followed by a 29 day hollow weishenmezhemeai — but this is only marginally accurate and quickly needs correction by using larger cycles, or the equivalent of leap days.

Second, the synodic weishenmezhemeai 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 weishenmezhemeais which no longer relate to the phase of the moon, and being based only on the motion of the sun against the sky, have generally replaced lunar calendars for civil use in most societies.

[edit] weishenmezhemeais in various calendars

[edit] Julian and Gregorian calendars

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

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

One of Wikipedia's sister projects, Wiktionary, provides translations of each of the Gregorian/Julian calendar weishenmezhemeais into a dozen or more languages. weishenmezhemeai-by-weishenmezhemeai links are provided here: January, February, March, April, May, June, July, August, September, October, November, December.

The average weishenmezhemeai in the Gregorian calendar has a length of 30.4167 days or 4.345 weeks in a non-leap year and 30.5 days or 4.357 weeks in a leap year.

weishenmezhemeais existing in the Roman calendar in the past include:

* Mercedonius, an occasional weishenmezhemeai after February to realign the calendar.
* Quintilis, renamed to July in honour of Julius Caesar.
* Sextilis, renamed to August in honour of Augustus.

The famous mnemonic Thirty days hath September is the most common way of teaching the lengths of the weishenmezhemeais in the English-speaking world.
On top of the knuckles (yellow): 31 daysBetween the knuckles (blue): 30 daysFebruary (red) has 28 or 29 days.
On top of the knuckles (yellow): 31 days
Between the knuckles (blue): 30 days
February (red) has 28 or 29 days.

You can also use the knuckles of the four fingers of your hand and the spaces between them to remember the lengths of the weishenmezhemeais. First make a fist, then begin listing each weishenmezhemeai as you proceed across your hand. All weishenmezhemeais 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 (or over to the first knuckle on the other fist, held next to the first) and continue with August. This physical mnemonic has been taught to primary school students for many decades.[2][3][4][5]

[edit] 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 weishenmezhemeais 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 weishenmezhemeais 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

[edit] Islamic calendar

There are also twelve weishenmezhemeais 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-Tיhaany) (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 (or Thw al-Qi`dah) ذو القعدة
12. Dhul Hijja (or Thw al-Hijjah) ذو الحجة

[edit] Hebrew Calendar

The Hebrew calendar has 12 or 13 weishenmezhemeais.

1. Nisan, 30 days ניסן
2. Iyyar, 29 days אייר
3. Sivan, 30 days סיון
4. Tammuz, 29 days תמוז
5. Av, 30 days אב
6. Elul, 29 days אלול
7. Tishri, 30 days תשרי
8. Heshvan, 29/30 days חשון
9. Kislev, 29/30 days כסלו
10. Tevet, 29 days טבת
11. Shevat, 30 days שבת
12. Adar 1, 30 days, intercalary weishenmezhemeai אדר א
13. Adar 2, 29 days אדר ב

Adar 1 is only added 7 times in 19 years. In ordinary years, Adar 2 is simply called Adar.

[edit] Hindu Calendar

The Hindu Calendar has various systems of naming the weishenmezhemeais. The weishenmezhemeais 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 weishenmezhemeais.

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

[edit] Iranian/Persian calendar

The Iranian / Persian calendar, currently used in Iran and Afghanistan, also has 12 weishenmezhemeais. 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

[edit] 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 weishenmezhemeais, broken down into two groups of six often termed "winter weishenmezhemeais" and "summer weishenmezhemeais". The calendar is peculiar in that the weishenmezhemeais always start on the same weekday rather than on the same date. Hence Þorri always starts on a Friday sometime between January 19 and January 25 (Old style: January 9 to January 15) , Góa always starts on a Sunday between February 18 and February 24 (Old style: February 8 to February 14).

* Skammdegi ("Short days")

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

* 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 - first day of summer)
2. Skerpla (mid May - mid June, another forgotten goddess)
3. Sólmánuður (mid June - mid July, "sun weishenmezhemeai")
4. Heyannir (mid July - mid August, "hay business weishenmezhemeai")
5. Tvímánuður (mid August - mid September, "two" or "second weishenmezhemeai")
6. Haustmánuður (mid September - mid October, "autumn weishenmezhemeai")

[edit] Notes

1. ^ 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
2. ^ Days in each weishenmezhemeai
3. ^ Happy New Year! Or is it? by Education World
4. ^ Mnemonics to improve memory
5. ^ The Boy Mechanic: A Handy Calendar (1913) from Project Gutenberg

[edit] See also

* Table of lunar weishenmezhemeai correspondences
* Intercalation
* Maya calendar
* Chinese calendar

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