Kontakt:
rita.gautschy-at-unibas.ch
Islamic Calendar
Introduction
The Islamic calendar is a lunar calendar consisting of 12 months. Hence, a year is either 354 or 355 days long. There are no intercalations to keep the lunar year synchronised with the solar year. The epoch used in the Islamic calendar is the Hijra, dates in this era are therefore denoted as Anno Hegirae AH ("in the year of the Hijra"). The beginning of this era was introduced retrospectively. In 622 CE Muhammad and his followers went from Mekka to Medina, where they installed a Muslim community - an event that is commemorated as the Hijra. From year AH 10 onward the lunar calendar consisting of 12 months was used: earlier on, probably a lunisolar calendar was employed according to Qur'an Sura 9: 36-37.
Up to recent times in many countries a new lunar month started when the lunar crescent could be observed for the first time after new moon. For the new lunar crescent to be observable, three conditions must be fulfilled:
- the lunar crescent must have a minimal width to be bright enough,
- the lunar crescent must have a minimal altitude above the horizon, otherwise extinction of Earth's atmosphere renders it invisible,
- the Sun must be far enough below the horizon.
In a lunar calendar based on observation a lunar months can either have 29 or 30 days. There is no regular pattern traceable: a lunar month of 29 days can repeat up to four times in a row, a lunar month of 30 days even up to five times [1]. Some groups - astronomers and the Ismaelites - used a calendar scheme from the 8th century onward. However, this scheme was only of little importance for the civil life. The year numbering and the month names in the scheme are the same as in the civil calendar based on observation, but the month lengths are determined by arithmetical rules, not by observation. It has a 30-year cycle with 19 years of 354 days and 11 "leap years" of 355 days. The months Muharram (1), Rabi'al-Awwal (3), Jumada l-Ula (5), Rajab (7), Ramadan (9) and Dhu l-Qa'da (11) always have 30 days and the months Safar (2), Rabi'ath-Thani (4), Jumada t-Tania (6), Sha'ban (8) and Shawwal (10) always 29 days. The month Dhu l-Hijja (12) has 29 days in normal years and 30 days in "leap years". This calendar scheme is usually used to convert Islamic dates of historical astronomical observations into Julian or Gregorian calendar dates [2]. It can deviate by one or two days from actual circumstances in the sky. The beginning of the Hijra era is computed retrospectively and fixed on July 16th, 622 CE. However, the lunar crescent was easily visible in Medina already on July 15th, 622 CE. This implies that the calendar scheme starts one day too late compared with actual observation.
Calculations
The calculation of first visibility of the lunar crescent after new Moon for times far in the past is subject to several uncertainties:
- Earth's rate of rotation decreases with time. The resulting time difference, called ΔT must be accounted for.
- Today, astronomers are still working on the problem of refining the prediciton criteria for a successful first sighting of the lunar crescent. Here Yallop's criterion is used, but only the zones A and B were considered [3].
New Moon epochs and last/first visibility of the lunar crescent before/after New Moon were calculated between 600 and 2000 AD. Concerning the lunar and solar ephemerides the longterm DE406 ephemerides of the Jet Propulsion Laboratory were used, which enable the calculation of the positions of the Sun, the Moon and of all planets between 3001 BC and 3000 AD [4]. The uncertainty in ΔT was accounted for. More details about the calculations can be found here.
Data download
If you download the following data and use them in a publication, please mention the adress of this website and the following paper as origin of the data: R. Gautschy & J. Thomann, Dating historical Arabic observations, Astronomy in Focus Volume 1, 2018 (in press).
For the sites Medina, Damascus, Bagdad, Samarra, Aleppo, Isfahan, Cordoba, Cairo, Bursa and Istanbul tables were created, containing - for a mean value of ΔT - epochs of New Moon and first or last visibility of the lunar crescent in the Julian/Gregorian Calendar and the Islamic Calendar according to observation. For better comparison with actual data and earlier work, the weekday is given too, as well as the Islamic date according to the calendar scheme that starts with July 16th, 622 CE. If there arose any difference in the date when the uncertainty of ΔT was accounted for, it is marked accordingly in the tables. In such cases one cannot say exactly on which day the last or first visibility occured.
In the following table, the downloadable data contain in the column "download data last (first)" for each site:
- The date of the last/first visibility in the Julian (after 1582, the Gregorian) Calendar,
- the time in Greenwich mean time when the lunar crescent could be observed best (to obtain local time simply add the number of hours given in the last column of the table),
- the value of ΔT in seconds,
- the value of the uncertainty of ΔT in seconds,
- the date of the last/first visibility in the Islamic Calendar (year, month, day) according to the calendar scheme,
- the weekday,
- the date of the last/first visibility in the Islamic Calendar (year, month, day) according to observation,
- the time of surise in Greenwich mean time in case of last visibility, resp. time of sunset in Greenwich mean time in case of first visibility (to obtain local time simply add the number of hours given in the last column of the table),
- the time of moonrise in Greenwich mean time in case of last visibility, resp. time of moonset in Greenwich mean time in case of first visibility (to obtain local time simply add the number of hours given in the last column of the table),
- the value of the Yallop criterion if the lunar crescent falls into zone B,
- a code if there arose a difference in the date in positive direction (+1) or in negative direction (-1) when the uncertainty of ΔT was accounted for,
- the date of (geocentric) New Moon in the Julian (after 1582, the Gregorian) Calendar,
- the time in Greenwich mean time of New Moon (to obtain local time simply add the number of hours given in the last column of the table).
| Place | download data first | download data last | correction to obtain local time in tables [hours] |
|---|---|---|---|
| Medina | here | here | +2.64 |
| Damascus | here | here | +2.42 |
| Bagdad | here | here | +2.96 |
| Samarra | here | here | +2.92 |
| Aleppo | here | here | +2.48 |
| Isfahan | here | here | +3.45 |
| Cordoba | here | here | −0.32 |
| Cairo | here | here | +2.08 |
| Bursa | here | here | +1.94 |
| Istanbul | here | here | +1.93 |
Important:
The date in the Islamic Calendar in the tables changes at midnight like the Julian/Gregorian date.
This must be taken into account when real and computed data are compared!
Bibliography
- 1 Last and first sightings of the lunar crescent.
- 2 F. Wüstenfeld, E. Mahler, B. Spuler, Wüstenfeld-Mahler'sche Vergleichungs-Tabellen zur muslimischen und iranischen Zeitrechnung, 1961.
- 3 B. D. Yallop, A Method for Predicting the First Sighting of the New Crescent Moon, NAO Technical Note No. 69, 1997.
- 4 E. M. Standish, JPL Planetary and Lunar Ephemerides, DE405/LE405, Jet Propulsion Laboratory Interoffice Memorandum 312.F, 1998.