My earlier note with the spreadsheet was too large for the mailing list size filter. The spreadsheet is available at http://www3.telus.net/public/rtbailey/WalkingShadow/EWQiblah.xls The earlier note follows.
Hello Mashallah, Today was one of the two days in the year when the sun at noon was directly over Mecca. Solar Declination = Latitude = 21.422º. As you pointed out in your book the shadow of a vertical gnomon gives you the correct direction to Mecca at that time. I could not use this technique as I am too far west at Longitude W 123.4º. You need to know your longitude to determine the correct local time difference from noon at Mecca to use this solar technique. In times past, determining longitude was a difficult problem. The qibla direction for Istanbul is 151.7º, as shown in my slides in the Timelines presentation. The Mosques pictured, including Hagia Sophia, are not oriented in this direction. The mihrab inside Hagia Sophia, built when it was converted from a Christian church to a mosque, is oriented at an angle with the walls but it is still not oriented by the true solar, great circle direction, to Mecca. A good web tool for finding the Qibla is at http://www.qiblalocator.com/ I enjoyed working through the puzzle you presented in your book. "Where on earth is the point where Mecca and Jerusalem are due east?" I agree with you that this in on the Greenland icecap. N 69.19º, W 41.15º I used one of the standard methods of solving spherical triangles for great circle courses, the Four Part equation: Cos A cos b = sin b cot c - Sin A Cot C, where the capital letters are for angles and the small letters for sides. In the case of due east, C = 90º and Cot C = 0. The equation then rearranges to cot b = cot c/ Cos A. In our case b is the co-latitude of the location, c is the co-latitude of Mecca and A is the difference in longitude. The final equation is then: Tan Lat = Tan Mecca / Cos (Long - Long Mecca). Put in values of longitude and solve for latitude and plot the results. Do the same for Jerusalem instead of Mecca, an find the common location where the curves cross. I get N 69.19º, W 41.15º. The north pole is the other solution if you can define east at the pole. A spreadsheet with the solution is attached. At 37.5 kb, I hope it gets through the mail list size filter. Regards, Roger Bailey www.walkingshadow.info ----- Original Message ----- From: Mashallah Ali-Ahyaie To: Roger Bailey Sent: Monday, July 16, 2007 4:25 AM Subject: Re: walking shadow Dear Roger, This is with thanks to inform that I downloaded timlines. It is fantastic indeed. Is the direction of the Qiblah at Hagia Sophia mosque wrong? There are unfortunately, many mosques like that. Two times a year one can correct the direction toward the Qiblah, universally, in certain part of the earth when the sun is at the zenith in Mecca, which this concept is fully described in my book (Chapter 4). Also, the concept applies when the sun is at the nadir of Mecca, for some other part of the globe. Best regards, Mashallah Ali-Ahyaie
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