Twice every year, the Sun culminates at the zenith of the Kaaba in Mecca, the holiest site in Islam, at local solar noon, allowing the qibla (the direction towards the Kaaba) to be ascertained in other parts of the world by observing the shadows cast by vertical objects. This phenomenon occurs at 12:18 Saudi Arabia Standard Time (SAST; 09:18 UTC) on 27 or 28 May (depending on the year), and at 12:27 SAST (09:27 UTC) on 15 or 16 July (depending on the year). At these times, the sun appears in the direction of Mecca, and shadows cast by vertical objects determine the qibla. At two other moments in the year, the sun passes through the nadir (the antipodal zenith) of the Kaaba, casting shadows that point in the opposite direction, and thus also determine the qibla. These occur on 12, 13, or 14 January at 00:30 SAST (21:30 UTC on the preceding day), and 28 or 29 November at 00:09 SAST (21:09 UTC on the preceding day).
The shadow points towards Mecca because the sun path makes the subsolar point travel through every latitude between the Tropic of Cancer and the Tropic of Capricorn every year, including the latitude of the Kaaba (21°25′N), and because the sun crosses the local meridian once a day. This observation has been known since at least the 13th century, when it was noted by the astronomers Jaghmini and Nasir al-Din al-Tusi, but their timings could not be fixed to a particular date because the Islamic calendar is lunar rather than solar; the solar date on which the sun culminates at the zenith of Mecca is constant, but the lunar date varies from year to year.
Context
Qibla
The qibla is the direction of the Kaaba, a cube-shaped building at the centre of the Great Mosque of Mecca (al-Masjid al-Haram) in the Hejaz region of Saudi Arabia. This direction is special in Islamic rituals and religious law because Muslims must face it during daily prayers (salat) and in other religious contexts. The determination of qibla was an important problem for Muslim communities because Muslims are required to know the qibla to perform their daily prayers and because it is needed to determine the orientation of mosques. When Muhammad lived among the Muslims in Medina, which is also in the Hejaz region, he prayed due south, the known direction of Mecca. Within a few generations of Muhammad's death in 632, Muslims had reached places far distant from Mecca, making the determination of the qibla in these new locations problematic. Initially, Muslims relied on traditional folk knowledge methods, but after the introduction of astronomy into the Islamic world, solutions based on mathematical and astronomical knowledge began to be developed in the early 9th century. The shadow-observation method has been attested since at least the 13th century CE.
Apparent motions of the Sun
Places on earth experience the apparent diurnal motion of the sun from the east to the west, during which it culminates, or reaches its highest point of the day and crosses the local meridian. The sun also appears to move seasonally between the Tropic of Cancer (approximately 23.5°N) and the Tropic of Capricorn (approximately 23.5°S); therefore, the solar culmination usually occurs to the north or south of the zenith. For locations between the tropics, at certain times of the year, the sun crosses the local latitude and then culminates at or near the zenith; this location is known as the subsolar point. The Kaaba is located at a latitude of 21°25′N, inside the zone that experiences this phenomenon. In the terminology of Islamic astronomy ('ilm al-falak), these events are called the "great culmination" (al-istiwa al-a'dham).
Observation
The great culmination, when the Sun appears directly over the Kaaba, occurs on 27 or 28 May at approximately 12:18 SAST (09:18 UTC), and on 15 or 16 July at 12:27 SAST (09:27 UTC), coinciding with the solar noon and the Zuhr adhan (midday call to prayer) in Mecca. As the sun crosses almost directly above the Kaaba, any shadow cast by vertical objects on earth will point directly away from the Kaaba, which casts nearly no shadow. This phenomenon allows the direction of the qibla to be determined without needing to perform calculations or to use sophisticated instruments. This observation is called rasd al-qibla ('observing the qibla').