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2. Calendar Database and Algorithms for Calculation and Conversion: Christian’s and Muslim’s Calendars in our Region Authors: Biljana Samardžija, Dušan Marčeta, Slaviša Milisavljević, Stevo Šegan Department of Astronomy Faculty of Mathematics Belgrade University The fifth SEEDI International Conference Digitization of cultural and scientific heritage, May 19-20, 2010, Sarajevo, BiH

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4. 4 Content:  Astronomical Bases of Calendars  Basic Models for Making Calendar  Map of Calendars  Some Facts and Important Events in the History of Calendars  History of Islamic Calendar  How to Calculate Prayer Schedule – Vaktija  Program

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6. 6 Astronomical Bases of Calendars The principal astronomical cycles: The principal astronomical cycles:  Day (based on the rotation of the Earth on its axis)  Year (based on the revolution of the Earth around the Sun)  Month (based on the revolution of the Moon around the Earth)

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8. 8 Astronomical Bases of Calendars The newest astronomical practice accepts the next attitudes and phrases: The newest astronomical practice accepts the next attitudes and phrases:  Tropical year (currently 365.242190 days) is defined as the mean interval between vernal equinoxes; it corresponds to the cycle of the seasons  Synodic month (currently 29.5305889 days), the mean interval between conjunctions of the Moon and Sun, corresponds to the cycle of lunar phases  19 tropical years is close to an integral number (235) of synodic months

9. 9 The Basic Models for Making Calendars  Solar calendar is designed to maintain synchrony with the tropical year – days are intercalated to increase length of calendar year  Lunar calendar, such as the Islamic calendar, follows the lunar phase cycle without regard for the tropical year – months systematically shift  Lunisolar calendar has a sequence of months based on the lunar phase cycle, but every few years a whole month is intercalated

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11. 11 Throughout the History…

12. 12 A few facts about Muslim calendar...(1)  Purely lunar calendar - months correspond to the lunar phase cycle  The cycle of twelve lunar months regresses through the seasons over a period of about 33 years  For religious purposes, Muslims begin the months with the first visibility of the lunar crescent after conjunction - important for establishing the beginning and end of Ramadan  For civil purposes is often used a tabulated calendar that approximates the lunar phase cycle

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14. 14  The seven-day week, each day begins at sunset  Day 1 begins at sunset on Saturday and ends at sunset on Sunday  Day 6, which is called Jum'a (Friday in Gregorian calendar), is the day for congregational prayers  New month may be declared thirty days after the beginning of the preceding month  Eleven leap years in the thirty-year cycle A few facts about Muslim calendar...(2)

15. 15 Months of Tabular Islamic Calendar 1. Muharram** 30 7. Rajab** 30 2. Safar 29 8. Sha'ban 29 3. Rabi'a I 30 9. Ramadan*** 30 4. Rabi'a II 29 10. Shawwal 29 5. Jumada I 30 11. Dhu al-Q'adah** 30 6. Jumada II 29 12. Dhu al-Hijjah** 29  In a leap year, Dhu al-Hijjah has 30 days  ** Holy months  *** Month of fasting  Years 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, and 29 are leap years

16. 16  Years of twelve lunar months are reckoned from the Era of the Hijra, commemorating the migration of the Prophet and his followers from Mecca to Medina  Astronomical Hijra epoch - 1 A.H. (Anno Higerae) Muharram 1, is generally taken by astronomers (Neugebauer, 1975) to be Thursday, +622 July 15 (Julian calendar) - Chronological tables (e.g., Mayr and Spuler, 1961; Freeman-Grenville, 1963)  Civil epoch - Friday, July 16 The History of Islamic Calendar (1)

17. 17  Lunisolar calendar - intercalary month added from time to time to keep the pilgrimage within the season  A lunar calendar without intercalation was introduced in 9 AH (for Latin Anno Hegirae, “in the year of the Hijrah”) by the Prophet in the Qur'an (Sura IX, verse 36-37)  Number and position of intercalary months between 1-10. AH (622-632 AD) is uncertain - the dates may be wrong for one, two or three lunar months  Caliph 'Umar I was establishing the Hijra Era in 17 A.H. The History of Islamic Calendar (2)

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19. 19  It is not known how the initial date was determined, but calculations show that the astronomical New Moon (i.e., conjunction) occurred on +622 July 14 at 04:44 UT (assuming AT = 1.0 hour), so that sighting of the crescent most likely occurred on the evening of July 16.  The earliest known visibility tables are by al-Khwarizmi, a ninth- century astronomer of Baghdad (King, 1987), were based on the Indian criterion that the Moon will be visible if the local hour angle of the Moon at sunset is equal to or less than 78 degrees  The oldest existing example of the use of Hijra calendar in one papyrus from Egypt in the year 22 AH (642 / 43.) The History of Islamic Calendar (3)

20. 20 Conversion between Calendars JD0 = 1948440 (16 July 622) L = JD - JD0 + 10632 N = [(L - 1)/10631] L = L - 10631 × N + 354 J = [(10985 - L)/5316] × [(50 × L)/17719] + [L/5670] × [(43 × L)/15238] L = L - [(30 - J)/15] × [(17719 × J)/50] - [J/16] × [(15238 × J)/43] + 29 M = [(24 × L)/709] D = L - [(709 × M)/24] G = 30 × N + J - 30 D = L - [(709 × M)/24] G = 30 × N + J - 30 G = 30 × N + J - 30

21. 21 How to Calculate Prayer Times  Calendar which specifies the beginning of prayer times and their duration is called Vaktia  There are five prayer times which are calculated according to relative position of the Sun to the horizon: Fajr (dawn) Fajr (dawn) Shorook (sunrise) Shorook (sunrise) Zuhr (noon) Zuhr (noon) Asr (afternoon) Asr (afternoon) Maghrib (sunset) Maghrib (sunset) Isha (night) Isha (night)

22. 22 How to Calculate Prayer Times Calendar and prayer times calculation

23. 23 Reference:  Schaefer, B.E. (1988). "Visibility of the Lunar Crescent" Q. Jour. R.A.S. 29, 511-523.  Ilyas, M. (1984). A Modern Guide to Astronomical Calculations of Islamic Calendar Times and Qibla Kuala Lumpur.  Harvey, O.L. (1983). Calendar Conversions by Way of the Julian Day Number Philadelphia.  Fotheringham, J.K. (1934). "The Calendar" in The Nautical Almanac 1935 London.  Fliegel, H.F. and Van Flandern, T.C. (1968). "A Machine Algorithm for Processing Calendar Dates" Communications of the Association of Computing Machines 11, 657.