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And which way should you face if you're in orbit around the Earth? This made 
news a couple of years ago. Here's a little article about it from wired.com:
http://www.wired.com/science/space/news/2007/09/mecca_in_orbit

Meanwhile, no surprise, there's a wikipedia article about this:
http://en.wikipedia.org/wiki/Qiblah

It's all there... the issue of rhumb line versus great circle and even which 
way one should face when praying at the anti-Mecca (yes, they thought of this 
too... centuries ago). 

There's also a very nice description of a technique for finding the correct 
direction using some simple positional astronomy: 
there are "two moments in each year when the sun is directly overhead the 
Kaaba, the direction of shadows in any sunlit place will point directly away 
from the Qiblah. This happens on May 27 or May 28 at 9:18 GMT and on July 15 
or July 16 at 9:27 GMT.
Likewise there are two moments in each year when the Sun is directly over the 
antipodes of the Kaaba. This happens on January 12 or January 13 at 21:29 GMT 
and on November 28 at 21:09 GMT." 

Nice trick. And apparently it was described by muslim scholars at least as early as the 11th century AD.

It is also well-established in Islamic law that the goal is to make an effort 
to face the right way, not to be exact or obsessive about it. Of course, 
being exact and obsessive are rituals of the NavList religious persuasion, so 
for some calculational fun, how much would the above shadow method for 
finding the direction of Mecca differ from a great circle azimuth or the 
projection to the horizontal of the "true" line-through-the-earth direction?

-FER


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