*How we have proceeded in order to calculate the times of Fajr*

From the 19th century onwards, with the development of astronomy, Muslims habitually associate Subh Sadiq with a depression of the sun at 18° below the horizon. 18° corresponds to a precise value: it defines astronomical twilight, both at dawn and at dusk.

Later, it was discovered that, beyond certain latitudes and at certain periods of the year, the sun never attains 18° below the horizon. For example, at Cambridge in the United Kingdom (52°N), during the summer solstice around 20th June, the lowest position of the sun below the horizon is of the order of 15°. Thus, some authorities started to apply rules of 15° or 12° below the horizon for calculating the time of Subh Sadiq.

The method of the depression of the sun at 18° gives satisfactory results for the calculation of Subh Sadiq for latitudes not too far from the equator. Amongst other institutions, the University of Islamic Sciences in Karachi has adopted it. It remains a reference. But rather than introducing – more or less arbitrarily – other values for the depression of the sun at higher latitudes (such as 15° or 12°), Syed Khalid Shaukat of www.moonsighting.com has chosen a radically different method. He decided to launch an **observation** of Subh Sadiq (and of Shafaq, see paragraph for Isha below) at different places on earth over a long period and throughout the year. Based on observation, this method is scientifically much more satisfying than introducing an arbitrary value for the depression of the sun below the horizon.

The observational campaign was carried out over a period of more than ten years for places as different as Riyadh in Saudi Arabia (25°N), Tando Adam in Pakistan (26°N), Beaumont in California, USA (34°), Sidney in Australia (34°S) Wellington in New Zealand (41°S), Blackburn in the UK (54°N) … The results for Subh Sadiq (as well as for the two phases of Isha, as we will see later) were plotted in a curve that gives the number of minutes to be **subtracted** from sunrise in order to obtain the time for Subh Sadiq. The results are of course a function of the latitude and the day number of the year. This “curve fit technique” was used to develop an algorithm that we have used with the permission of Syed Khalid Shaukat. This algorithm is valid for latitudes up to 55° north or south.

However, if the sun does reach the position of 18° below the horizon, it is necessary to compare two values: the one given by the position of the sun and the value obtained from the algorithm of Syed Khalid Shaukat. *We retain for Fajr the later of the two values. *The later value is retained in order to avoid a situation of *hardship* for the faithful with too early a Fajr as we approach more and more the latitude of 55°. Calculation shows that, for latitudes up to 33°, the method of 18° gives a later value for Fajr and describes best the phenomenon of Subh Sadiq. Beyond 33°, the algorithm of Syed Khalid Shaukat is used, as it gives a later value for Fajr.

The Muslims must clearly distinguish themselves from the sun worshippers. Thus, it is forbidden to pray Zuhr when the sun is at its zenith. We must wait until the rim of the solar disk has clearly quit the position of zenith in the sky. As a matter of precaution, we wait for five minutes after the zenith position of the sun for praying Zuhr.

The time of praying Asr varies according to the major schools of jurisprudence in Islam. One always calculates the length of the shadow of an object towards the middle of the afternoon. The object can be, for instance, a stick planted in the ground. For the Maliki, Shafi and the Hanbali schools, Asr is prayed when the shadow of the object is equal to the length of the object itself. For the Hanafi school, the shadow should reach twice the length of the object. Finally, for the Shia Ja’friya school, the shadow should attain 4/7th the size of the object.

One should not forget, however, that for most latitudes, the sun is never at the vertical with respect to the horizon when it reaches the zenith position. Thus, even at solar noon, an object will cast a shadow. We must always add the length of this shadow at solar noon (the residual shadow) to the lengths of the shadows in the above calculations.

The different traditions are all legitimate. We leave to the user the choice of the method for praying Asr.

We retain as the time for praying Maghrib 3 minutes after theoretical sunset. This is due to the following reasons:

1. The effects of refraction due to atmospheric humidity, temperature and pressure can lead to slightly different values for actual sunset.

2. The effect of a sloping ground: if the ground is not perfectly horizontal, the sun will appear to set at different moments according to the position of the observer.

3. For metropolitan cities, the sun will set at slightly different times within a radius of about thirty kilometres.

These considerations apply to the four major schools of Sunni jurisprudence. For the Ja’friya Shia school, Maghrib should be prayed 17 minutes after sunset, when the golden and bronze hues of sunset disappear from the horizon.*We have not retained this method in our calculation of Maghrib.*

The considerations for Isha very much follow those for Fajr. Thus we request the reader to have in mind the paragraph **III.1** above.

Just as for the two times of dawn for Fajr, Islamic jurisprudence recognises two times of dusk (Shafaq) for the prayer of Isha.

After the sun sets, the horizon is ablaze with red. This is Shafaq al Ahmar. The red colour then disappears. There follows a phase of paleness which inclines more and more towards a white hue. This is Shafaq al Abyad. Finally, the whiteness too disappears, leaving the place to the blackness of the night.

The Maliki, Shafi and Hanbali schools, as well as the Shias advocate the praying of Isha at the disappearance of Shafaq al Ahmar. The Hanafi school prefers the disappearance of Shafaq al Abyad. For the higher latitudes, it might become necessary to use an “in between” time which we call Shafaq General. We leave the user the choice between these different options.

*How we have proceeded to calculate the times for Isha*

Just as for Fajr, from the 19th century onwards, the Muslims started to attribute the disappearance of Shafaq al Abyad to a depression of the sun at 18° below the horizon. This value corresponds to astronomical twilight and remains a reference.

But what do we do if at higher latitudes the sun never reaches a position of 18° below the horizon in summer? Just as for Fajr, it is possible to choose lower values for the depression of the sun, such as 15° or 12° or even 9° in order to fix the time for Isha. But these choices are arbitrary. The observational campaign conducted by Syed Khalid Shaukat, which we described in paragraph **III.1** above, as well as the algorithm obtained from these observations, are valid not only for Fajr, but also for Isha. This algorithm applies to latitudes up to 55°.

However, if the sun does reach a position of 18° below the horizon, it is necessary to compare two values: that given by the position of the sun and that given by the algorithm. The time we retain for Isha is the *earlier* of the two values. This choice avoids a very late hour for Isha, and thus avoids a situation of hardship for the faithful.

In practice, for latitudes up to 33°, it is the method of 18° which gives the earlier value for Isha, beyond, it is Syed Khalid Shaukat’s algorithm that applies. For these altitudes, the algorithm takes into account the disappearance of Shafaq al Ahmar in summer (Shafaq al Abyad never disappears in summer at certain latitudes) and the disappearance of Shafaq al Abayad in winter. For the intermediary seasons, a combination of the two is applied.