The Determination of Salat Times

of the location are known. However, the theoretical determination of prayer times is a lengthy process. Much of this tedium may be alleviated by using...

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การคํานวณทางดาราศาสตรสําหรับเวลาอิสลามิกและทิศกิบลัต ASRTONOMUCAL CALCULATION OF ISLAMIC TIMES AND QILAT DIRECTION

นิแวเตะ หะยีวามิง1

Niweateh Hajewaming1 1

Department of Science, Faculty of Science and Technology, Prince of Songkla University, Pattani Campus, Pattani, 96000. Email: [email protected]

บทคัดยอ: มุสลิมตองปฏิบัติละหมาดวันละหาเวลา และในขณะละหมาดตองผินหนาสูทิศเมืองมักกะฮของ ประเทศซาอุดีอราเบียเรียกวาทิศกิบลัต เวลาละหมาดทั้งหาเวลานี้จะอางอิงปรากฏการณทางดาราศาสตร กลาวคือ เวลาซุฮรี เริ่มเมื่อดวงอาทิตยคลอยจากเหนือศรีษะ เวลาอัสรีเริ่มเมื่อเงาของวัตถุเริ่มยาวเทากับวัตถุ บวกกับเงาตอนเที่ยงของวัตถุ เวลามักริบเริ่มเมื่อดวงอาทิตยลับขอบฟา เวลาอีชาเริ่มเมื่อทองฟาเริ่มมืดสนิท และเวลาซุบฮเริ่มเมื่อมีแสงรุงอรุณ เวลาเหลานี้สามารถคํานวณไดโดยอาศัยหลักวิชาดาราศาสตรทรงกลม งานวิจัยนี้ไดสรางสมการการคํานวณเวลาละหมาดทั้งหาเวลาและเวลาอิมซักกับชูรุกอีกสองเวลา พรอมกับได สรางสมการหาทิศกิบลัต จากสมการที่สรางขึ้นมาแสดงวาเวลาละหมาดขึ้นกับคาลองติจูด ละติจูดของแตละ ตําบล และขึ้นกับคาสมการของเวลากับดิคลิเนชั่นของดวงอาทิตยในแตละวัน Abstract: For Muslims it is obligatory to perform five prayers throughout the day and the night. Muslim must be faced to Mecca city of Saudi Arabia, while pray. The most of Islamic prayer times correspondence with astronomical phenomena such as , The time of Zuhr starts when sun passes its zenith, Asri begins when the length of the shadow of a vertical rod is equal to the length of the rod plus its shadow at noon. Maghrib begins immediately after sunset, Isha begins when the sky is completely dark and Subh begins before sunrise. The equations of prayer times and two another times Imsuk and Shuruk may be derived from Spherical Astronomy also equation of Qiblat direction be derived. The Islamic daily prayer times vary with declination of the sun and Equation of Time, it does also depend on longitude and latitude of places. Introduction: The five Islamic daily prayers show in figure1 are named Subh, Zuhr, Asr, Maghrib and Isha. The timing of these five prayers varies from place to place and from day to day. It is obligatory for Muslims to perform these prayers at the correct time. The prayer times for any given location on earth may be determined mathematically if the latitude and longitude of the location are known. However, the theoretical determination of prayer times is a lengthy process. Much of this tedium may be alleviated by using computer programs. Definition of prayer times[1, 2]: Subh starts with the dawn or morning twilight. Subh ends just before sun rise. Zuhr begins after midday when the trailing limb of the sun has passed the meridian. Zuhr ends at the start of Asr time, The timing of Asr depends on the length of the shadow cast by an object. According to the Shafi school of jurisprudence, Asr begins when the length of the shadow of an object exceeds the length of the object. According to the Hanafi school of jurisprudence, Asr begins when the length of the shadow exceeds twice the length of the object. In both cases, the minimum length of shadow(which occurs when the sun passes the meridian) is subtracted from the length of the shadow before comparing it with the length of the object. Maghrib begins at sunset and ends at the start of Isha, and Isha starts after dusk when the evening twilight disappears. 33rd Congress on Science and Technology of Thailand

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Zuhr Asr

Noon

Horizon Maghrib Fajr

Isha Midnight

Figure 1 Show Daily Islamic Payer Times Calculation of Prayer Times[1, 3, 4]: To calculate the prayer times for a certain place we need to know the latitude(φ) and longitude(λ) of the location. φ and λ may be obtained from an atlas or by GPS(Geographic Positioning System). We also need to know two astronomical measures called the declination angle of the sun(φ) and the real time-mean time difference, also known as the equation of time (ED). Declination(φ)is the angular distance between a celestial object and the celestial equator. The Declination and the Right Ascension are used together to give the position of a star with reference to the celestial equator and the vernal equinox respectively. This variation of the solar declination causes the changing seasons, with their unequal periods of daylight and darkness. When the solar declination is positive, implying that the Northern Hemisphere is facing the sun, the day will be longer than night and vice-versa. The equation of time(ED). is a correction to be added to apparent solar time, as read on a sundial, to obtain mean solar time, as commonly used. This difference is a consequence of the ellipticity and tilt of the Earth's orbit, causing the irregular apparent movement of the Sun across the sky, (δ) and (ED) it’s vary according to the time of year and can be obtained accurately from The Star Almanac or calculated approximately. The most of Islamic prayer times correspondence with astronomical phenomena. The following equations of prayer times may be derived.(1) Zuhri, At the time of midday(Z), the sun center cross the meridian. For the time of Zuhri, a small correction of about 1-2 minutes need to be made to account the meridian crossing of the backward limb or semi diameter of sun. - λ Local λ E (1) )+ D Z = 12.00 + ( Zonetime 15 60 λ -λ E Zuhr = 12.00 + ( Zonetime Local ) + D + (Semidiameter of Sun) 15 60

(2)

When 12.00 it’s a theoretical midday, 12 Hr 00 Minute 00 Second Z = Meridian passage time or Real midday for any place in unit of hour λZonetime = Standard Time Zone(Longitude) such as for Thailand 105.000 E λLocal = Longitude of any place in unit of degree = Equation of Time for each day in unit of minute ED Semi diameter of Sun is any number from 1 to 2 minutes Maghrib, At the time of sun set, to calculate the instant of setting of the sun, we have first to calculate the hour angle H at the moment of rising by the cosine law of astronomical triangle PZF’ in figure2.

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90 − φ

Meridian

Z

Diurnal motion of sun

P

H φ

90 − δ

Celestial equator

δ

90 +D N

S

N’

S’

Astronomical horizon W

F

D’

Real horizon

W’

F’

Figure 2 Show astronomical triangle when sun set

Maghrib = Z + Maghrib2 = Z +

⎧− sin (0.833) - sin φ . sin δ ⎫ 1 cos -1 ⎨ ⎬ 15 cos φ . cos δ ⎩ ⎭

{

(3)

}

⎡ sin − 0.833 - 0.0347(hs )1/2 - sin φ . sin δ ⎤ 1 cos-1 ⎢ ⎥ (4) 15 cos φ . cos δ ⎣ ⎦

The actual sunrise and sunset do not occur at the time when the sun’s elevation is zero. This is due to the refraction of light by terrestrial atmosphere. A ray of light traveling in vacuum from a sun which is actually below the earth’s horizon is bent towards the earth by the heavier medium. The Horizontal Refraction angle from Astronomical or Nautical Almanac is 34 minute, and the effect of Angular Semi diameter of the sun when sun elevation start from limb of the sun not at it’s center. Angular Semi diameter value is 16 minute. Then the angles are effect to sunset and sunrise(D: Depression angle) is 34 + 16 = 50 minute or 0.833 degrees as show in equation (3). Hence actual sunrise appears slightly before astronomical sunrise and actual sunset occurs after astronomical sunset. Further, for locations which are higher than the sea level, the sun will appear in the morning slightly earlier. Corrections have therefore to be made for altitude effects. These are expressed via equation (4). When hS is height above sea level in unit of meter. Isha and Subh, Equations of Isha and Subh time may be derived as Maghrib, equation (5),(6) are Isha and Subh time. ⎧ − sin ( AIT ) - sin φ . sin δ ⎫ 1 (5) cos -1 ⎨ Isha = Z + ⎬ 15 cos φ . cos δ ⎭ ⎩ Subh = Z −

⎧ − sin ( AIT ) - sin φ . sin δ ⎫ 1 cos -1 ⎨ ⎬ 15 cos φ . cos δ ⎩ ⎭

(6)

If the earth did not have an atmosphere, the sky would become dark immediately after sunset. The earth's atmosphere causes scattering of sunlight so that light reaches the observer before sunrise and after sunset. This scattered light is called twilight. After sunset, as the depression of the sun increases the sky gets darker and darker until no scattered light reaches the observer. Conversely, in the morning light starts to appear in the sky even before sunrise. The morning twilight is called dawn whilst the evening twilight is known as dusk. In astronomy the twilight period is divided into civil, nautical and astronomical twilight corresponding to solar depressions of 6, 12 and 18 degrees respectively, as shown in figure3 Subh starts with the morning twilight (dawn) whilst Isha starts at the end of the evening twilight (dusk).

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Twilight 100

Horizon

10

Depression angle

1 0.1

S

Civil

0.01

AIT

0.001 Nautical 0.0001 1 2

Astronomical 3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Depression angle(Degrees)

Figure 3 Show graph of twilight There is some debate as to which twilight angle should be used in the calculation of Subh/Isha. Several conventions for the calculation of Subh and Isha are already in use in various countries. Subh and Isha times are usually calculated using fixed twilight angles call AIT(Astronomical-Islamic Twilight Angle) it’s vary from 15 to 21 Degrees. The methods used by some Islamic organizations are summarized in the following table[5]. Subh Organisation Isha AIT Region AIT University of Islamic 18 Sciences, Karachi

18

Pakistan, Bangladesh, India, Afghanistan, parts of Europe

Islamic Society of North 15 America (ISNA)

15

Parts of USA & Canada, UK

World Islamic League

18

17

Europe, Far East, parts of USA

Um Ul-Qura, Makkah

19

90 mins after Maghrib, Arabian Peninsula

Egyptian General Africa, Syria, Iraq, Lebanon, 19.5 17.5 Organization of Surveying Malaysia, parts of USA In locations at higher latitude, twilight may persist throughout the night during some months of the year, here alternative methods must be used to calculate Subh/Isha times. Asri prayer time also can be derived from spherical triangle when the sun altitude cast a shadow length of a vertical rod is equal to the length of the rod plus its shadow at noon. Equation(7) is Asri time. Asr = Z +

{

}

⎡ sin cot − 1 (1 + tan (φ − δ )) − sin φ . sin δ ⎤ 1 cos − 1 ⎢ ⎥ 15 cos φ . cos δ ⎣ ⎦

(7)

Qiblat Direction, the problem involves the solution of spherical triangle formed by the Place, Mecca and North pole. In figure4 show geometrical situation for determination of direction between two geographical places and equation(8) is Qiblat direction(Q) count from north to west[3, 6]. When N is Geographical North Pole, NS is any meridian, M is Mecca city 0 λM = Mecca longitude = 39.823 E, L is any place, λL= any Longitude of place 0 φM = Mecca latitude = 21.4233 N, φL = any latitude of place

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N λL B

B

- λM B

B

90 −φM

Meridian

90 −φL

M

Q L

φM

φL

equater

S Figure 4 show Qiblat direction(Q) tan Q =

sin( λ L − λ M) cos( φL ). tan( φM) − sin( φL ). cos ( λ L − λ M)

(8)

Results, Discussion and Conclusion: Zuhr, Asr and Maghrib times may be calculated unambiguously. Isha and Subh times depend on twilight and require the adoption of a suitable twilight angle. Generally, a twilight angle of 18 degrees may represent a safe upper limit although opinions and practices vary. Imsuk time is 10 minutes before Subh and Shuruk time is time at sun rise. On manual calculation of five prayer time for one place throughout the year via equation (1) to equation (8) included Imsuk, Shuruk and Qiblat direction are more than 7 x 365 = 2,555 times. In Thailand there are more than 1,000 districts. The amounts of calculation are more than 5,555,000 times, it’s impossible to do with manual calculation. By computer aided and algorithm[7] of equations of five prayer times, we can use any programming language such as Visual Basic, C, Pascal etc. to compute prayer times in any time and any where with most accuracy. Figure 5 to 9 shown graphically prayer times for Chiangmai, Bangkok and Pattani throughout the year. 12.75 12.7

Pattani 6.83 Deg. N, 101.30 Deg. E Bangkok 14.28 Deg. N, 100.50 Deg. E Chiangmai 18.78 Deg. N, 98.78 Deg. E

Pattani Bangkok

12.65 12.6

Chiangmai

12.55

Figure 5 Show Zuhr Prayer Times

12.5 12.45 12.4 12.35 12.3 12.25

16.05

12.2

16

12.15

15.95

12.1

15.9

12.05

15.85

Pattani 6.83 Deg. N 101.30 Deg. E Bangkok 14.28 Deg. N 100.50 Deg. E Chiangmai 18.78 Deg. N 98.78 Deg. E

Pattani Bangkok Chiangmai

15.8

12

15.75

11.95 1

51

101

151

201

251

301

351

15.7 15.65 15.6 15.55 15.5 15.45 15.4

Figure 6 Show Asr Prayer Times

15.35 15.3 15.25 15.2 1

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101

151

201

251

301

5

351

19.2 19.15 19.1 19.05 19 18.95 18.9 18.85 18.8 18.75 18.7 18.65 18.6 18.55 18.5 18.45 18.4 18.35 18.3 18.25 18.2 18.15 18.1 18.05 18 17.95 17.9 17.85 17.8 17.75 17.7

Pattani 6.83 Deg. N 101.30 Deg. E Bangkok 14.28 Deg. N 100.50 Deg. E Chiangmai 18.78 Deg. N 98.78 Deg. E

Pattani Bangkok Chiangmai

Figure 7 Show Maghrib Prayer Times

1

51

101

151

201

251

20.55 20.5 20.45 20.4 20.35 20.3 20.25 20.2 20.15 20.1 20.05 20 19.95 19.9 19.85 19.8 19.75 19.7 19.65 19.6 19.55 19.5 19.45 19.4 19.35 19.3 19.25 19.2 19.15 19.1 19.05 19 18.95 18.9

301

351

Pattani 6.83 Deg. N 101.30 Deg. E Bangkok 14.28 Deg. N 100.50 Deg. E Chiangmai 18.78 Deg. N 98.78 Deg. E

Pattani Bangkok Chiangmai

Figure 8 Show Isha Prayer Times

1 5.8 5.75 5.7 5.65 5.6 5.55 5.5 5.45 5.4 5.35 5.3 5.25 5.2 5.15 5.1 5.05 5 4.95 4.9 4.85 4.8 4.75 4.7 4.65 4.6 4.55 4.5 4.45 4.4 4.35 4.3 4.25 4.2 4.15 4.1 4.05 4

51

101

151

201

251

Pattani 6.83 Deg. N 101.30 Deg. E Bangkok 14.28 Deg. N 100.50 Deg. E Chiangmai 18.78 Deg. N 98.78 Deg. E

301

351

Pattani Bangkok Chiangmai

Figure 9 Show Subh Prayer Times

1

51

101

151

201

251

301

351

References: 1. Hajewaming Niweateh, Al Falak, Islamic Academy, Bangkok(Thai), 2002. 2. Susikman Azhari, Ilmu Falak, Lazuardi, Yogyakarta(Indonesia), 2001. 3. Mohammad Ilyas;, A Modern Guide to Astronomical Calculations of Islamic Calendar, Times & Qibla, Berita Publishing Sdn Bhd., Kuala Lumpur, Malaysia, 1984. 4. Jason John Nassau, Practical Astronomy, Mc-Graw-Hill Book Company, New York, 1984. 5. Moulana Yakub Qasmi and Tariq Muneer, Prayer Times for United Kingdom & Ireland, Islamic Research Institute of Britain, Dewsbury, UK ,1989. 6. Bagvi, Malik Bashir Ahmed: Determination of the Direction of Qibla and the Islamic Timings, Ashraful-Madaris, Karachi, 1970. 7. Jean Meeus, Astronomical Algorithms; 2nd ed, Willmann -Bell Inc; Richmond, USA, 1991. Keywords: Islamic time, Spherical Triangle, The sun.

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