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Calendar Database and Algorithms Calendar Database and Algorithms for Calculation and Conversion: for Calculation and Conversion:

Christian’s and Muslim’s Calendars Christian’s and Muslim’s Calendars in our Regionin our Region

AutAuthhororss:: Biljana Samardžija, Dušan Marčeta, Slaviša Biljana Samardžija, Dušan Marčeta, Slaviša

Milisavljević, Stevo ŠeganMilisavljević, Stevo Šegan

Department of AstronomyFaculty of Mathematics

Belgrade University

The fifth SEEDI International Conference Digitization of The fifth SEEDI International Conference Digitization of cultural and scientific heritage, May 19-20, 2010, Sarajevo, cultural and scientific heritage, May 19-20, 2010, Sarajevo,

BiH BiH

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Content:Content:

Astronomical Bases of CalendarsAstronomical Bases of Calendars

Basic Models for Making CalendarBasic Models for Making Calendar

Map of CalendarsMap of Calendars

Some Facts and Important Events in the Some Facts and Important Events in the History of CalendarsHistory of Calendars

History of Islamic CalendarHistory of Islamic Calendar

How to Calculate Prayer Schedule – VaktijaHow to Calculate Prayer Schedule – Vaktija

Program Program

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Astronomical Bases of Calendars Astronomical Bases of Calendars

The principal astronomical cycles:The principal astronomical cycles:

DayDay (based on the rotation of the Earth (based on the rotation of the Earth on its axis)on its axis)

YearYear (based on the revolution of the (based on the revolution of the Earth around the Sun)Earth around the Sun)

MonthMonth (based on the revolution of the (based on the revolution of the Moon around the Earth)Moon around the Earth)

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Astronomical Bases of Calendars Astronomical Bases of Calendars

The newest astronomical practice accepts The newest astronomical practice accepts the next attitudes and phrases:the next attitudes and phrases:

Tropical yearTropical year ( (currently currently 365.242190365.242190 days) days)is defined as the mean interval between vernal is defined as the mean interval between vernal equinoxes; it corresponds to the cycle of the equinoxes; it corresponds to the cycle of the seasonsseasons

Synodic monthSynodic month ((currently 29.5305889currently 29.5305889 days) days), , the mean interval between conjunctions of the the mean interval between conjunctions of the Moon and Sun, corresponds to the cycle of lunar Moon and Sun, corresponds to the cycle of lunar phases phases

19 tropical years is close to an integral number19 tropical years is close to an integral number (235)(235) of synodic months of synodic months

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The Basic Models for Making The Basic Models for Making CalendarsCalendars

Solar calendarSolar calendar is designed to maintain is designed to maintain synchrony with the tropical year – days are synchrony with the tropical year – days are intercalated to increase length of calendar yearintercalated to increase length of calendar year

Lunar calendarLunar calendar, such as the Islamic calendar, , such as the Islamic calendar, follows the lunar phase cycle without regard follows the lunar phase cycle without regard for the tropical year – months systematically for the tropical year – months systematically shiftshift

Lunisolar calendarLunisolar calendar has a sequence of months has a sequence of months based on the lunar phase cycle, but every few based on the lunar phase cycle, but every few years a whole month is intercalatedyears a whole month is intercalated

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Throughout the History…Throughout the History…Roman AUC

calendar

Julian proleptic calendar

Gregorian proleptic calendar

March 1st , 1. AUC

(753 BC)

Start of AUC Calendar (Ab Urbe Condita or „from when Rome was founded“) with ten lunar months (March to December) each year.

Julian AUC

calendar

January 1st 709 AUC (45 BC)

Start of Julian calendar with the same number of days in each month we use today, except two same dates in February;

746 AUC (8 BC)

Augustus Caesar corrects the excess 366-day years by having only „normal“ 365-day years until 8 AD. Also, August now goes to the 31st, and February to the 28th. 8. p.n.e. do 4. n.e.

8 AD (761 AUC)

366-day „bissextile“ years start with two February 24ths, now every 4 years as originally intended.

End AUC

326 AD (1079 AUC)

All Christian churches adopt a unified Easter Dating Method, OEDM.

532 AD

Start of Julian AD calendar (Anno Domini or „in the year of our Lord“). Dionysius was the inventor of the Anno Domini era, which is used to number the years of both the Gregorian calendar and the Julian calendar

Gregorian calendar

October 1582

Gregorian calendar starts. Leap years are implemented by adding a Feb 29th to years evenly divisible by 4, but only in century years evenly divisible by 400.

1583 Revised Easter Dating Method (for Gregorian calendar) first used by Italy, REDM

Julian calendar

4099

The Gregorian calendar will need to skip a date in 4100 AD or shortly afterwards due to accumulating calendar inaccuracies, and the slowing rotation of Earth!

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A few facts about Muslim A few facts about Muslim calendar...(1)calendar...(1)

Purely lunar calendar - months correspond to the Purely lunar calendar - months correspond to the lunar phase cyclelunar phase cycle

The cycle of twelve lunar months regresses The cycle of twelve lunar months regresses through the seasons over a period of about 33 through the seasons over a period of about 33 years years

For religious purposesFor religious purposes, Muslims begin the months , Muslims begin the months with the first visibility of the lunar crescent after with the first visibility of the lunar crescent after conjunction - important for establishing the conjunction - important for establishing the beginning and end of Ramadanbeginning and end of Ramadan

For civil purposesFor civil purposes is often used a tabulated is often used a tabulated calendar that approximates the lunar phase cyclecalendar that approximates the lunar phase cycle

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The seven-day week, each day begins at sunsetThe seven-day week, each day begins at sunset

Day 1 begins at sunset on Saturday and ends at Day 1 begins at sunset on Saturday and ends at sunset on Sundaysunset on Sunday

Day 6, which is called Jum'a (Friday in Gregorian Day 6, which is called Jum'a (Friday in Gregorian calendar), is the day for congregational prayerscalendar), is the day for congregational prayers

New month may be declared thirty days after the New month may be declared thirty days after the beginning of the preceding monthbeginning of the preceding month

Eleven leap years in the thirty-year cycleEleven leap years in the thirty-year cycle

A few facts about Muslim A few facts about Muslim calendar...(2)calendar...(2)

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Months of Tabular Islamic Months of Tabular Islamic CalendarCalendar

1. 1. MuharraMuharram**m**

3030 7. Rajab**7. Rajab** 3300

2. Safar2. Safar 2929 8. Sha'ban8. Sha'ban 2299

3. Rabi'a I3. Rabi'a I 3030 9. Ramadan***9. Ramadan*** 3300

4. Rabi'a II4. Rabi'a II 2929 10. Shawwal10. Shawwal 2299

5. Jumada I5. Jumada I 3030 11. Dhu al-11. Dhu al-Q'adah**Q'adah**

3300

6. Jumada II6. Jumada II 2929 12. Dhu al-12. Dhu al-Hijjah**Hijjah**

2299

In a leap year, Dhu al-Hijjah In a leap year, Dhu al-Hijjah has 30 dayshas 30 days ** ** Holy monthsHoly months *** *** Month of fastingMonth of fasting Years 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, and Years 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, and

29 29 are leapare leap years years

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Years of twelve lunar months are reckoned from Years of twelve lunar months are reckoned from the Era of the Hijra, commemorating the the Era of the Hijra, commemorating the migrationmigration of the Prophet and his followers from of the Prophet and his followers from Mecca to MedinaMecca to Medina

Astronomical Hijra epochAstronomical Hijra epoch - 1 A.H. (Anno Higerae) - 1 A.H. (Anno Higerae) Muharram 1, is generally taken by astronomers Muharram 1, is generally taken by astronomers (Neugebauer, 1975) to be Thursday, +622 July 15 (Neugebauer, 1975) to be Thursday, +622 July 15 (Julian calendar) - Chronological tables (e.g., (Julian calendar) - Chronological tables (e.g., Mayr and Spuler, 1961; Freeman-Grenville, 1963)Mayr and Spuler, 1961; Freeman-Grenville, 1963)

Civil epochCivil epoch - Friday, July 16 - Friday, July 16

The History of Islamic The History of Islamic Calendar (1)Calendar (1)

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Lunisolar calendar - intercalary monthLunisolar calendar - intercalary month added from added from time to time to keep the pilgrimage within the time to time to keep the pilgrimage within the seasonseason

A lunar calendar without intercalation was A lunar calendar without intercalation was introduced in 9 AH (introduced in 9 AH (for Latin Anno Hegirae, “in the for Latin Anno Hegirae, “in the year of the Hijrah”)year of the Hijrah”) by the Prophet in the Qur'an by the Prophet in the Qur'an (Sura IX, verse 36-37) (Sura IX, verse 36-37)

Number and position of intercalary months Number and position of intercalary months between 1-10. AH (622-632 AD) is uncertain - the between 1-10. AH (622-632 AD) is uncertain - the dates may be wrong for one, two or three lunar dates may be wrong for one, two or three lunar monthsmonths

Caliph 'Umar I was establishing the Hijra Era in 17 Caliph 'Umar I was establishing the Hijra Era in 17 A.H.A.H.

The History of Islamic The History of Islamic Calendar (2)Calendar (2)

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It is not known how the initial date was determined, but It is not known how the initial date was determined, but calculations show that the astronomical New Moon (i.e., calculations show that the astronomical New Moon (i.e., conjunction) occurred on +622 July 14 at 04:44 UT conjunction) occurred on +622 July 14 at 04:44 UT (assuming AT = 1.0 hour), so that sighting of the crescent (assuming AT = 1.0 hour), so that sighting of the crescent most likely occurred on the evening of July 16.most likely occurred on the evening of July 16.

The earliest known visibility tables are by al-Khwarizmi, a The earliest known visibility tables are by al-Khwarizmi, a ninth-century astronomer of Baghdad (King, 1987), were ninth-century astronomer of Baghdad (King, 1987), were based on the Indian criterion that the Moon will be visible based on the Indian criterion that the Moon will be visible if the local hour angle of the Moon at sunset is if the local hour angle of the Moon at sunset is equal to or equal to or less than 78 degreesless than 78 degrees

The oldest existing example of the use of Hijra calendar The oldest existing example of the use of Hijra calendar in one papyrus from Egypt in the year 22 AH (642 / 43.)in one papyrus from Egypt in the year 22 AH (642 / 43.)

The History of Islamic The History of Islamic Calendar (3)Calendar (3)

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Conversion between CalendarsConversion 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

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How to Calculate Prayer TimesHow to Calculate Prayer Times

Calendar which specifies the beginning of prayer Calendar which specifies the beginning of prayer times and their duration is called Vaktiatimes and their duration is called Vaktia

There are five prayer times which are calculated There are five prayer times which are calculated according to relative position of the Sun to the according to relative position of the Sun to the horizon: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)

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How to Calculate Prayer TimesHow to Calculate Prayer Times

Calendar and prayer times calculation

Organization

Fajr

(Dawn)

Angle of the Sun

I sha

(Night)

Angle of the Sun

Region

Shia I thna Ashari (J afari) 16 14 In the west of central Arabia.

I slamic Society of North America (I SNA)

15 15 Parts of the USA, Canada, Parts of the UK

Muslim World League (MWL) 18 17 Europe, The Far East, Parts of the USA

Umm al-Qura, Makkah 18.5*

90 mins after Maghrib 120 mins during Ramadan

The Arabian Peninsula

Egyptian General Authority of Survey

19.5 17.5 Africa, Syria, I raq, Lebanon, Malaysia, Parts of the USA

University of I slamic Sciences, Karachi

18 18 Pakistan, Bangladesh, India, Afghanistan, Parts of Europe

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Reference:Reference: Schaefer, B.E. (1988). "Visibility of the Lunar Schaefer, B.E. (1988). "Visibility of the Lunar

Crescent" Crescent" Q. Jour. R.A.S. Q. Jour. R.A.S. 2929, 511-523. , 511-523. Ilyas, M. (1984). Ilyas, M. (1984). A Modern Guide to Astronomical A Modern Guide to Astronomical

Calculations of Islamic Calendar Times and QiblaCalculations of Islamic Calendar Times and Qibla Kuala Lumpur. Kuala Lumpur.

Harvey, O.L. (1983). Harvey, O.L. (1983). Calendar Conversions by Calendar Conversions by Way of the Julian Day NumberWay of the Julian Day Number Philadelphia. Philadelphia.

Fotheringham, J.K. (1934). "The Calendar" in Fotheringham, J.K. (1934). "The Calendar" in The The Nautical Almanac 1935 Nautical Almanac 1935 London. London.

Fliegel, H.F. and Van Flandern, T.C. (1968). "A Fliegel, H.F. and Van Flandern, T.C. (1968). "A Machine Algorithm for Processing Calendar Machine Algorithm for Processing Calendar Dates" Dates" Communications of the Association of Communications of the Association of Computing MachinesComputing Machines 1111, 657. , 657.