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Disclaimer: Although my results are correct but I don't think that this translation is accurate so if you are Trigonometry buff please look at the forumula.
Shaykh (Mufti) Rasheed Ahmed Ludhyanwi (RA) in his book Ahsanul-Fatawa has published 9 separate ways of finding Qiblah direction. His student Shaykh (Mufti) Sultan Alam (HA) [Head of Astronomy, Jamiatur-Rasheed] states that for laymen method 2 is the easiest to understand and follow and this is also found in most modern Astronomy books, so here is the English translation for the example mentioned in the book (Karachi).
In order to calulcate the Qiblah direction you will need to know four things:
You can easily find these using Google these by using the following terms:
Before proceeding further I would like to add a small detail here which is not explained properly in the book as follows:
Please also that all my firgures are in decimal formation! If you get your Longitudes mixed up with Latitudes you will have some serious problems, pay attention to directions!
Step 1:
Obtain the difference in Longitude between your city and Makkah by subtracting the Higher Longitude from the Lower Longitude and we will call this number F.
For Karachi:
F = (67.0100-39.8167) = 27.1933
For Mumbai:
F = (72.8258-39.8167) = 33.0091
For London:
Remember that you actually have a NEGATIVE (-) so watch what happens!
F = (39.8167-(-0.1275)) = 39.8167+0.1275 = 39.9442
For New York:
Remember that you actually have a NEGATIVE (-) so watch what happens!
F = (39.8167-(-74.0059)) = 39.8167+74.0059 = 113.8226
Step 2:
Qiblah = ATAN (Sin F/(Cos B * Tan M)-(Sin B * Cos F))
For Karachi:
Step 3:
There are two significant things to look at in your number:
Test Mumbai:
Mumbai Latitude Longitude (Answer given is 18.9750° N, 72.8258° E)
The number I get is -100.1811428
Shaykh (Mufti) Rasheed Ahmed Ludhyanwi (RA) had created a graph by hand in 1969 for worldwide Qiblah directions and this was one of a kind graph for Qiblah directions. In 1983 Engineer Basheer Ahmed Baghwi tried to create an A4 size version of the graph to make it accessible to laymen.
These days Engineer Mohammad Odeh of ICOP has amalgamated the new computer generated graph into his Accurate Times App
Qibla by the Sun
______________________________________________
Sun over the Kaaba on Saturday 15 July
التعامد الثاني للشمس على الكعبة.. السبت المقبل
At the time of noon at the Sacred Mosque at 12:27pm local Makkah time (9:27am) (GMT)
This cannot be undone and I am sure it will be greatly appreciated.
Please wait...