z3bi/MWC

## MWC
11.0     FUNCTIONS OF LATITUDE AND SEASONS FOR FAJR AND ISHA

In the calculations shown here, “abs” means absolute value.
“LT” means latitude in degrees (+ for North and – for South).
“DYY” means day number of the year: For Northern Hemisphere start from December 21 (DYY=0 for December 21, and counting forward, DYY=11 for January 1 and so on).
            For Southern Hemisphere start from June 21 (DYY=0 for June 21, and counting forward)

11.1          Fajr – Function of Latitude and seasons

For Subh-Sadiq, Constants A, B, C, D are calculated as follows:
            A = 75 + 28.65 / 55.0 * abs(LT);                       B = 75 + 19.44 / 55.0 * abs(LT);
            C = 75+ 32.74 / 55.0 * abs(LT);                        D = 75 + 48.1 / 55.0 * abs(LT);
   if ( $DYY < 91)
            A = A + ( B - A )/ 91.0 * DYY; //  '91 DAYS SPAN
        else if ( DYY < 137)
            A = B + ( C - B ) / 46.0 * ( DYY - 91 ); //  '46 DAYS SPAN
        else if ( DYY< 183 )
            A = C + ( D - C ) / 46.0 * ( DYY - 137 ); // '46 DAYS SPAN
        else if ( DYY < 229 )
            A = D + ( C - D ) / 46.0 * ( DYY - 183 ); //  '46 DAYS SPAN
        else if ( DYY < 275 )
            A = C + ( B - C ) / 46.0 * ( DYY - 229 ); // '46 DAYS SPAN
       else if ( DYY >= 275 )
            A = B + ( A - B ) / 91.0 * ( DYY - 275 ); //  ' 91 DAYS SPAN

11.2          Isha – Function of Latitude and seasons

For Shafaq (General – combination of White and red Shafaq for high latitudes
Constants A, B, C, D are calculated as follows:
            A = 75  + 25.6 / 55.0 * abs(LT);                  B = 75  + 2.05 / 55.0 * abs(LT);
            C = 75  - 9.21 / 55.0 * abs(LT);                   D = 75  + 6.14 / 55.0 * abs(LT);
   if ( $DYY < 91)
            A = A + ( B - A )/ 91.0 * DYY; //  '91 DAYS SPAN
        else if ( DYY < 137)
            A = B + ( C - B ) / 46.0 * ( DYY - 91 ); //  '46 DAYS SPAN
        else if ( DYY< 183 )
            A = C + ( D - C ) / 46.0 * ( DYY - 137 ); // '46 DAYS SPAN
        else if ( DYY < 229 )
            A = D + ( C - D ) / 46.0 * ( DYY - 183 ); //  '46 DAYS SPAN
        else if ( DYY < 275 )
            A = C + ( B - C ) / 46.0 * ( DYY - 229 ); // '46 DAYS SPAN
       else if ( DYY >= 275 )
            A = B + ( A - B ) / 91.0 * ( DYY - 275 ); //  ' 91 DAYS SPAN
In the equations above, in Sections 11.1 and 11.2, there is a number 75, that is the base time in minutes after sunset, which is exactly equal to the time for disappearance of White Shafaq observed at 18 degrees at equator. "A" is 75 minutes plus additional time in minutes that varies with latitude and seasons.  Furthermore, the variables B, C, D are values in minutes also and are functions of latitude and seasons.

Instead of using any fixed degrees to calculate Fajr & Isha for all seasons, it makes more sense to use a function of latitude and seasons which are determined by observations keeping in mind the hardship for higher latitudes.


12.0                          CONCLUSIONS

Among the Fuqaha’ there is a consensus that Fajr al‑Mustatir/Imsak begins at Subh Sadiq/Fajr Thani, and Isha begins when Shafaq disappears.  From the discussions presented here it is quite obvious that, Subh Sadiq and end of Shafaq cannot be tied to the astronomical twilight (18° sun's depression).

               1.      Observations and instrumental measurements both do not support this claim.
               2.      Prayer schedules prepared on the basis of 18°/15° create undue hardship and result in a large "exempt" zone for higher latitudes.
               3.      Islam's universality and 'ease' require a broader interpretation of Fajr and Shafaq.

The conclusions of the research by Moonsighting.com can be stated as follows:

o       From equator to 55°, the 18° depression angle calculations are compared with the values given by the functions of latitude and seasons and most favorable values are used, which means; For Fajr, the later of the two and for Isha the earlier of the two.

o       At latitudes between 55° and 60°, the rule of Sab'u Lail (1/7th of the night) is used, because other methods give times that become hardship for those areas.  This has been permitted by Hakim ul Ummat Ashraf Ali Thanwi (Imdadul Fatawa, vol 2, p98, 12/12/1322 Hijri) and also by Allamah Shami in Durre Mukhtar.  Mufti Shafi Usmani said: "This statement is presented via assumption, that in those countries where Subah Sadiq cannot be clearly distinguished (e.g., Northern Europe in the summer months) it is permissible to act upon this advice".  Therefore, two things are calculated for Fajr; one is Tabayyan (when morning light in the sky has spread) and the other is last 1/7th of the night.  Fajr time is later of the two.  Similarly, two things are calculated for Isha; disappearance of Shafaq and first 1/7th of the night.  Isha time is earlier of the two.


o       At latitudes more than 60°, hardship prevails and at latitudes more than 65°, the sun does not set/rise for a number of days every year. All Muslim scholars agree that whenever there is perpetual day or perpetual night for 24 hours or more, the prayer times during the affected days should be approximated. This is because the Messenger (SAW) said: "There will come a time when there will be a day like a year, a day like a month, and a day like a week…"  The people asked him (SAW) if during the day like a year; should they offer each prayer only once.  He (SAW) replied: "You should approximate the times" [Sahih Muslim].  Therefore, for such situations, a suggestion by Fuqaha' is to calculate on the basis of "Aqrabul-Ayyam" or "Aqrabul-Bilad". Some Fuqaha'  suggest to use Makkah times for all five prayers. Another jurisprudence (Fatwa) by by Dar al-Ifta, stipulated by Sheikh Mohammed Rashid Ridha, citing Sheikh Mohammed Abdou, the former Grand Mufti of Egypt dated 08/08/2010 is as follows:

Any location where the duration of fasting exceeds 18 hours or is less than 6 hours should refer itself to the times valid for the closest “balanced” location in order to determine the moment of breaking the fast. It is certainly not logical, nor sensible nor reasonable to “jump” from 18 hours to 14 hours and 54 minutes – the longest day in Makkah.

An example of such a location is Hammerfest, Norway, a town of 7000 inhabitants, claiming to be the northernmost town in the world. The Muslim population of Norway is about 300,000 and that of Hammerfest is around 250.  Hammerfest is situated at 70.65° N and 23.68° E.

Now take Oslo (latitude = about 60°) and using the rule of Sab'u Lail, we calculate the longest day to be 19 hours 38 minutes and the shortest day to be 7 hours and 43 minutes. Of course, we are beyond the 18 hour limit fixed by the Fatwa, but since the inhabitants of Oslo seem to admit to these timings without difficulty, we will retain 60° as the latitude based on "Aqrabul-Bilad" concept.

      Therefore, at latitudes more than 60°, first we calculate the interval from sunrise to sunset and being a little conservative assume it to be the day length (which is an interval from Fajr to Maghrib). If day length is more than 18 hours or less than 6 hours, then we slide down to 60° and calculate Fajr & Isha using the rule of Sab'u Lail. But then we keep whatever values are obtained at this new latitude, even if they are more than 18 hours. This will thus respect both the jurisprudence and the practices of Muslims in cities around 60 degrees latitude.

All knowledge comes from Allah (SWT).  If I have written things that are right, they come from Him by His blessings on me.  If I made a mistake, I seek forgiveness from Allah (SWT) and I beg that the readers will forgive me too.

Ahqar, Engr. Syed Khalid Shaukat
	11.0 FUNCTIONS OF LATITUDE AND SEASONS FOR FAJR AND ISHA

	In the calculations shown here, “abs” means absolute value.
	“LT” means latitude in degrees (+ for North and – for South).
	“DYY” means day number of the year: For Northern Hemisphere start from December 21 (DYY=0 for December 21, and counting forward, DYY=11 for January 1 and so on).
	For Southern Hemisphere start from June 21 (DYY=0 for June 21, and counting forward)

	11.1 Fajr – Function of Latitude and seasons

	For Subh-Sadiq, Constants A, B, C, D are calculated as follows:
	A = 75 + 28.65 / 55.0 * abs(LT); B = 75 + 19.44 / 55.0 * abs(LT);
	C = 75+ 32.74 / 55.0 * abs(LT); D = 75 + 48.1 / 55.0 * abs(LT);
	if ( $DYY < 91)
	A = A + ( B - A )/ 91.0 * DYY; // '91 DAYS SPAN
	else if ( DYY < 137)
	A = B + ( C - B ) / 46.0 * ( DYY - 91 ); // '46 DAYS SPAN
	else if ( DYY< 183 )
	A = C + ( D - C ) / 46.0 * ( DYY - 137 ); // '46 DAYS SPAN
	else if ( DYY < 229 )
	A = D + ( C - D ) / 46.0 * ( DYY - 183 ); // '46 DAYS SPAN
	else if ( DYY < 275 )
	A = C + ( B - C ) / 46.0 * ( DYY - 229 ); // '46 DAYS SPAN
	else if ( DYY >= 275 )
	A = B + ( A - B ) / 91.0 * ( DYY - 275 ); // ' 91 DAYS SPAN

	11.2 Isha – Function of Latitude and seasons

	For Shafaq (General – combination of White and red Shafaq for high latitudes
	Constants A, B, C, D are calculated as follows:
	A = 75 + 25.6 / 55.0 * abs(LT); B = 75 + 2.05 / 55.0 * abs(LT);
	C = 75 - 9.21 / 55.0 * abs(LT); D = 75 + 6.14 / 55.0 * abs(LT);
	if ( $DYY < 91)
	A = A + ( B - A )/ 91.0 * DYY; // '91 DAYS SPAN
	else if ( DYY < 137)
	A = B + ( C - B ) / 46.0 * ( DYY - 91 ); // '46 DAYS SPAN
	else if ( DYY< 183 )
	A = C + ( D - C ) / 46.0 * ( DYY - 137 ); // '46 DAYS SPAN
	else if ( DYY < 229 )
	A = D + ( C - D ) / 46.0 * ( DYY - 183 ); // '46 DAYS SPAN
	else if ( DYY < 275 )
	A = C + ( B - C ) / 46.0 * ( DYY - 229 ); // '46 DAYS SPAN
	else if ( DYY >= 275 )
	A = B + ( A - B ) / 91.0 * ( DYY - 275 ); // ' 91 DAYS SPAN
	In the equations above, in Sections 11.1 and 11.2, there is a number 75, that is the base time in minutes after sunset, which is exactly equal to the time for disappearance of White Shafaq observed at 18 degrees at equator. "A" is 75 minutes plus additional time in minutes that varies with latitude and seasons. Furthermore, the variables B, C, D are values in minutes also and are functions of latitude and seasons.

	Instead of using any fixed degrees to calculate Fajr & Isha for all seasons, it makes more sense to use a function of latitude and seasons which are determined by observations keeping in mind the hardship for higher latitudes.


	12.0 CONCLUSIONS

	Among the Fuqaha’ there is a consensus that Fajr al‑Mustatir/Imsak begins at Subh Sadiq/Fajr Thani, and Isha begins when Shafaq disappears. From the discussions presented here it is quite obvious that, Subh Sadiq and end of Shafaq cannot be tied to the astronomical twilight (18° sun's depression).

	1. Observations and instrumental measurements both do not support this claim.
	2. Prayer schedules prepared on the basis of 18°/15° create undue hardship and result in a large "exempt" zone for higher latitudes.
	3. Islam's universality and 'ease' require a broader interpretation of Fajr and Shafaq.

	The conclusions of the research by Moonsighting.com can be stated as follows:

	o From equator to 55°, the 18° depression angle calculations are compared with the values given by the functions of latitude and seasons and most favorable values are used, which means; For Fajr, the later of the two and for Isha the earlier of the two.

	o At latitudes between 55° and 60°, the rule of Sab'u Lail (1/7th of the night) is used, because other methods give times that become hardship for those areas. This has been permitted by Hakim ul Ummat Ashraf Ali Thanwi (Imdadul Fatawa, vol 2, p98, 12/12/1322 Hijri) and also by Allamah Shami in Durre Mukhtar. Mufti Shafi Usmani said: "This statement is presented via assumption, that in those countries where Subah Sadiq cannot be clearly distinguished (e.g., Northern Europe in the summer months) it is permissible to act upon this advice". Therefore, two things are calculated for Fajr; one is Tabayyan (when morning light in the sky has spread) and the other is last 1/7th of the night. Fajr time is later of the two. Similarly, two things are calculated for Isha; disappearance of Shafaq and first 1/7th of the night. Isha time is earlier of the two.


	o At latitudes more than 60°, hardship prevails and at latitudes more than 65°, the sun does not set/rise for a number of days every year. All Muslim scholars agree that whenever there is perpetual day or perpetual night for 24 hours or more, the prayer times during the affected days should be approximated. This is because the Messenger (SAW) said: "There will come a time when there will be a day like a year, a day like a month, and a day like a week…" The people asked him (SAW) if during the day like a year; should they offer each prayer only once. He (SAW) replied: "You should approximate the times" [Sahih Muslim]. Therefore, for such situations, a suggestion by Fuqaha' is to calculate on the basis of "Aqrabul-Ayyam" or "Aqrabul-Bilad". Some Fuqaha' suggest to use Makkah times for all five prayers. Another jurisprudence (Fatwa) by by Dar al-Ifta, stipulated by Sheikh Mohammed Rashid Ridha, citing Sheikh Mohammed Abdou, the former Grand Mufti of Egypt dated 08/08/2010 is as follows:

	Any location where the duration of fasting exceeds 18 hours or is less than 6 hours should refer itself to the times valid for the closest “balanced” location in order to determine the moment of breaking the fast. It is certainly not logical, nor sensible nor reasonable to “jump” from 18 hours to 14 hours and 54 minutes – the longest day in Makkah.

	An example of such a location is Hammerfest, Norway, a town of 7000 inhabitants, claiming to be the northernmost town in the world. The Muslim population of Norway is about 300,000 and that of Hammerfest is around 250. Hammerfest is situated at 70.65° N and 23.68° E.

	Now take Oslo (latitude = about 60°) and using the rule of Sab'u Lail, we calculate the longest day to be 19 hours 38 minutes and the shortest day to be 7 hours and 43 minutes. Of course, we are beyond the 18 hour limit fixed by the Fatwa, but since the inhabitants of Oslo seem to admit to these timings without difficulty, we will retain 60° as the latitude based on "Aqrabul-Bilad" concept.

	Therefore, at latitudes more than 60°, first we calculate the interval from sunrise to sunset and being a little conservative assume it to be the day length (which is an interval from Fajr to Maghrib). If day length is more than 18 hours or less than 6 hours, then we slide down to 60° and calculate Fajr & Isha using the rule of Sab'u Lail. But then we keep whatever values are obtained at this new latitude, even if they are more than 18 hours. This will thus respect both the jurisprudence and the practices of Muslims in cities around 60 degrees latitude.

	All knowledge comes from Allah (SWT). If I have written things that are right, they come from Him by His blessings on me. If I made a mistake, I seek forgiveness from Allah (SWT) and I beg that the readers will forgive me too.

	Ahqar, Engr. Syed Khalid Shaukat