Month

For the Egyptian hawk-god, see 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; month and Moon are cognates. The traditional concept arose with the cycle of moon phases; such months (lunations) are synodic months and last approximately 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 today.

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 period of the Moon's orbit as defined with respect to the celestial sphere is known as a sidereal month because it is the time it takes the Moon to return to a given position among the stars (Template:Lang-la): 27.321661 days (27 d 7 h 43 min 11.5 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, defined by asterisms (apparent groups of stars), one for each day of the sidereal month.

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: 27.321582 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

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 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.

Draconic month

Also called the nodical 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 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 month is the average interval between two successive transits of the moon through its ascending node. Because of 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 month. It lasts about 27-1/5 days (27.212220 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.

Synodic month

This is the average period of the Moon's revolution with respect to the sun. The synodic month is responsible for 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. This means that after completing a sidereal month 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 month from the Greek syn hodô (σὺν ὁδῴ), meaning "with the way [of the sun]". Because of perturbations in 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 29.530589 days (29 d 12 h 44 min 2.9 s). The synodic month is used in the Metonic cycle.

Month lengths

Here is a list of the average length of the various astronomical lunar months . 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 86,400 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 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

The average month 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, or 30.436875 days in a mean Gregorian month overall (364.2425 ÷ 12).

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 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 months in the English-speaking world.

On top of the knuckles (yellow): 31 days
Between the knuckles (blue): 30 days
February (red) has 28 or 29 days.

The knuckles of the four fingers of one's hand and the spaces between them can be used to remember the lengths of the months. By making a fist, each month will be listed as one proceeds across the hand. All months landing on a knuckle are 31 days long and those landing between them are not. When the knuckle of the index finger is reached (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.

Calends, nones, and ides

The ides occur on the thirteenth day in eight of the months, but in March, May, July, and October, they occur on the fifteenth. The nones always occur 8 days before the ides, i.e., on the fifth or the seventh. The calends are always the first day of the month.

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-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

Hebrew Calendar

The Hebrew calendar has 12 or 13 months.

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 month 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.

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

Tamil calendar

1. Chitirai
2. Vaikasi
3. Aani
4. Aadi
5. Aavani
6. Purratasi
7. Aiypasi
8. Kaarthigai
9. Maargazhi
10. Thai
11. Maasi
12. Panguni

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 Icelandic holidays and annual feasts are still calculated from it. It has 12 months, broken down into two groups of six often termed "winter months" and "summer months". The calendar is peculiar in that the months 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 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 - first day of summer)
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")

Old Hungarian calendar

Historically Hungary used a 12-month calendar that appears to have been zodiacal in nature but eventually came to correspond to the Gregorian months as shown below:

1. Boldogasszony hava (January, ‘month of the happy/blessed lady’)
2. Böjtelő hava (February, ‘month of early fasting/Lent’ or ‘month before fasting/Lent’)
3. Böjtmás hava (March, ‘second month of fasting/Lent’)
4. Szent György hava (April, ‘St. George’s month)
5. Pünkösd hava (May, ‘Pentecost month’)
6. Szent Iván hava (June, ‘St. Ivan’s month’)
7. Szent Jakab hava (July, ‘St. James’ month’)
8. Kisasszony hava (August, ‘month of the young lady [Blessed Virgin]’)
9. Szent Mihály hava (September, ‘St. Michael’s month’)
10. Mindszent hava (October, ‘all saints month’)
11. Szent András hava (November, ‘St. Andrew’s month’)
12. Karácsony hava (December, ‘month of Yule/Christmas’)

Old Egyptian calendar

The ancient civil Egyptian calendar had a year that was 365 days long and was divided into 12 months of 30 days each, plus 5 extra days (epagomenes) at the end of the year. The months were divided into 3 "weeks" of ten days each. Because the ancient Egyptian year was almost a quarter of a day shorter than the solar year and stellar events "wandered" through the calendar, it is referred to as Annus Vagus or "Wandering Year".

1. Thout
2. Paopi
3. Hathor
4. Koiak
5. Tooba
6. Emshir
7. Paremhat
8. Paremoude
9. Pashons
10. Paoni
11. Epip
12. Mesori

See also

• Table of lunar month correspondences
• Maya calendar
• Chinese calendar
• Egyptian Calendar