A Muslim Astronaut's Dilemma: How to Face Mecca From Space

Wired teases a bit, so that the ending is actually kind of anti-climactic, but it’s a wonderfully geeky puzzle.

From ISS, orbiting 220 miles above the surface of the Earth, the qibla (an Arabic word meaning the direction a Muslim should pray toward Mecca) changes from second to second. During some parts of the space station’s orbit, the qibla can move nearly 180 degrees during the course of a single prayer. What’s a devout Muslim to do?