Qibla observation by shadows

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.

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.

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.

[7][8] 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.

[8][16][a] During any of these events, observations made within a five-minute interval, and at the same time one or two days before or after the prescribed date, are accurate with negligible deviation.

The phenomenon cannot be viewed in New York City and Ottawa, while in Boston and Montreal, the Sun appears so low that the place of observation must be completely unobstructed by buildings or terrain.

[18][8][b] The method of observing the qibla by shadows was attested by the Central Asian astronomer Jaghmini, who wrote c. 1221 it can be done twice a year when the Sun's position in the ecliptic is at 7°21′, in the constellation Gemini, and 22°39′, in Cancer.

Let an observation be made on that day at that time – before noon if Mecca is to the east or after if [Mecca] is to the west; the direction of the shadow [of the sun] at that time is [opposite to that of] the qibla bearing.Al-Tusi stated the two rasd al-qibla days by specifying the Sun's position on the ecliptic (8° Gemini and 23° Cancer), rather than giving specific dates.

The qibla determines the direction, from any point in the world to the Kaaba , in the Great Mosque of Mecca .
As a result of the Earth's orbit around the Sun, the Sun's latitude position appears to move seasonally between the Tropic of Cancer and the Tropic of Capricorn .
On this azimuthal equidistant projection centred on Mecca and shaded to show where rasd al-qibla can be used, when the subsolar point is on the Kaaba, shadows of vertical poles on the sunlit hemisphere point away from it
At the time of rasd al-qibla , the shadow of a vertical object indicates the direction of qibla.
Nasir al-Din al-Tusi (1201—1276), an early astronomer who wrote about qibla observation by shadows.