Muslim astronauts

How would a muslim astronaut orient himself towards Mecca?

I'm not being snarky here, I'm genuinely interested. And it's not as if there wasn't a great tradition of muslim travellers... why not extend it into the Space Age?

On a related note, what happens when a muslim finds himself in the exact antipodes of Mecca?

The problem of organizing prayer in strange new environments is not new:

During this march, Timur's army got far enough north to be in a region of very long summer days, causing complaints by his Muslim soldiers about keeping a long schedule of prayers in such northern regions.

(Wikipedia entry for Tamerlane)

Edit: I have searched Google for "muslim astronaut", and apparently the problem of space prayer has already been worked out:

Malaysian scientists and religious scholars are trying to determine how Muslims should behave in space, as the predominantly Islamic country prepares to dispatch its first astronaut next year.

More than 150 delegates attended a seminar to consider how to pray in space given the difficulties of locating Mecca and holding the prayer position in zero gravity; as well as other questions such as halal food and washing.