A major impetus for the flowering of astronomy in islam came from religious observances, which presented an assortment of problems in mathematical astronomy, specifically in spherical geometry. At the time of Muhammad both Chistians and Jews observed holy days, such as easter and passover, whose timing was determined by the phases of the moon. Both communities had confronted the fact that the approximately 29.5 day lunar months are not commensurable with the 365 day solar year. 12 lunar months add up to only 354 days. To solve the problem Cristians and Jews had adopted a scheme based on a discovery made in about 430 B.C. by the Athenian astronomer Meton. In the 19 year Metonic cycle there were 12 years of lunar months and seven years of 13 lunar months.
The periodic insertion of a 13th mont kept calendar dates in step with the seasons. Apparently, however, not every jurisdiction followed the standard pattern. Unscrupulous ruler occasionally added the 13th month when it suited their own interests. To Muhammad this was the work of the devil. In the Koran (chapter 9, verse 36) he decreed that “ the number of months in the sight of God is 12 [in a year] so ordained by Him the day He created the heavens and the earth, of them four are sacred: that is the straight usage.” Caliph ‘Umar 1 (634 – 44) interpreted this decree as requiring a strictly lunar
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The observer must know the altitude of the sun and that of the pole; the former can be observed, and the latter is equal to the observer’s latitude. The time is then given by the angle at the intersection of the meridian (the arc through the zenith and the pole) and the sun’s hour circle (the arc through the sun and the