Qibla

Qibla , kibla , kiblat or kiblet in Arabic qibla (RTL rear قبلة: direction; south) indicates the direction of the prayer for the Moslems.

According to the tradition (Sunna) the prophet Mahomet in the beginning would have recommended to direct the prayer towards Jerusalem. In that it conformed to the use of the Jews ( 1 Kings (VIII; 29,30,44); 2 Chronicles (VI; 21); Daniel (VI; 10)).

However, since the hégire with Médine in 622 (beginning of the Hégire), Mecque became at the same time the object of its resentment and the objective of its military campaigns. It also became, quite naturally, the direction of the prayer, i.e. the qibla . The Moslems turn during their prayers to the Ka' Ba. A sourate confirmed this obligation: “Thus your face in the direction of the crowned Mosque Turns. Where that you are, turn your face in its direction” Coran (II; 144).

Many worships direct their places of prayer. Most of the time, it is the race of the sun which determines this orientation and the determination of the axis of the building rests on the simple observation. On the other hand, the calculation of the qibla is complex and stimulated the Moslem geographers in the search of mathematical tools and instruments as precise as possible.

In practice however, the precision is quite relative: at a distance of only 1000 kilometers, the angular measurement of the Ka' Ba is of less than one thousandths of degree. Consequently, only the intention of the Moslem would determine the validity of the prayer.

Formulate calculation of Qibla

Data

• A = (39,8261° - longitude of the place)
  (Difference in longitudes between Mecque and the place of the prayer);
• B = Latitude of the place of the prayer;
• C = 21,4225° Latitude of Kaaba.

*La latitude must be counted positive in North and negative in the South.

*La longitude must be counted positive in the East and negative in the West

Calculation

• With a computer:

$Q\; =\; \backslash \; arctan\; \backslash \; left\; \{\backslash \; sin\; (A)\; \backslash \; over\; \{\backslash \; cos\; (B).\; \backslash \; tan\; (C)\}\; -\; \backslash \; sin\; (B).\; \backslash \; cos\; (A)\}\; \backslash \; right$

*Si the denominator is negative:

*Ajouter 180° with Q if the numerator is positive

*Retranchez 180° with Q if the numerator is negative

• With a computer programming language having a function atan2

$Q\; =\; \backslash \; operatorname\; \{atan2\}\; (\backslash \; cos\; (B).\; \backslash \; tan\; (C)\; -\; \backslash \; sin\; (B).\; \backslash \; cos\; (A),\; \backslash \; sin\; (A))$

One obtains the good performance directly

Result

Q = Direction of the qibla

• Q > 0 angle on the basis of the direction of the North and counted in the retrograde direction (direction of the needles of a watch).
• Q < 0 angle on the basis of the direction of the North and counted in the direct direction (opposite direction of the needles of a watch, trigonometrical direction).

Controversies on the formula employed

The Moslems of North America, of African or average-Eastern origin, had first of all directed their mosques towards south-east. But when later one made the calculations based on the calculation of the large circle, giving a direction directed towards the North-East, a polemic was followed from there, the result running up against the common direction because of the representation of the world by planisphere. To leave itself there, some proposed to replace the large circle by a Loxodromie (a line which cuts each meridian line according to a fixed angle, which gives same calculation as if one had traced a straight line on a planisphere).

References

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