Misconception regarding the Duhr prayer time


Misconception: When the sun reaches its zenith, there is no shadow. Or, when the Duhr time is about to start, there is no shadow.

Correct conception: In anywhere in the world, for most of the time, there always be shadow (even though very small) when the Duhr prayer time is about to start.


Analysis:

It has been a common knowledge among the Muslims that Duhr time starts few minutes after the sun's reaches its zenith. The term 'zenith' is used to refer to the highest point reached by the sun during its apparent orbit around a given point of observation, see Fig.1 below. This knowledge is of course correct. However, there is also a common understanding that when the sun reaches its zenith, there is no shadow. Unfortunately, this understanding for most of the time is not correct!

No shadow when the sun reaches its zenith is only occur when the sun is directly overhead at noon. In fact, this phenomenon is very rare to happen. As indicated in Sect.\ref{ss_imaginary}, for the tropics area, i.e. area between 23.5° north and south (including equator), it happens only two days in a year. For the area along the Tropic of Cancer and Capricorn, it happens only one day in a year. While for the rest of globe, it never happens! Therefore, for the whole Norway as an example, there always be shadow when the sun reaches its zenith in any day during the year. If someone in Norway looking for the sun to be directly overhead and the inexistent of shadow during the noon, then he will never find it, see Fig.1 and Table 1.

Figure 1 shows the length of shadow (S) at noon relative to object's length (H), i.e the ratio S/H. If S/H=0, it means no shadow at noon. If S/H=1, it means the shadow at noon and its object have the same length. If S/H=2, it means the shadow at noon is twice the object's length. Some of the lines in the figure reach S/H = ∞, which means the sun at noon is very close to the horizon or even below the horizon (i.e. 24-hour of night period). Some numbers of S/H at selected dates are extracted and presented in Table 1.

As indicated in Fig.1 and Table 1, even in Makkah, the sun to be directly overhead and the inexistent of shadow during the noon only happen during the peak of summer, i.e. in the vicinity of 21st of June. During the peak of winter, i.e. in the vicinity of 21st of December, the shadow at noon in Makkah is even equal to the object's length. The phenomena of the existing of shadow during noon is also very important for the determination of Asr times and therefore is described in the succeeding section.

The Shadow at noon.
Fig.1. The shadow at noon.

Table 1. The length of shadow at noon relative to object’s length for selected dates.
Cities Latitude 21 Mar 21 Jun 21 Sep 21 Dec
Makkah 21°25′N 0.4 0.0 0.4 1.0
Kristiansand 58°10′N 1.6 0.7 1.6 6.8
Oslo 59°57′N 1.7 0.7 1.7 8.6
Trondheim 63°26′N 2.0 0.8 1.9 18.2
Mo i Rana 66°18′N 2.2 0.9 2.2 219.
Tromsø 69°41′N 2.7 1.0 2.6
Longyearbyen 78°13′N 4.7 1.4 4.5