Ramadan lasts from sunset to sunrise (or vice-versa).
Obviously this can’t work in the North Pole, or any Arctic area - they would all starve to death.
When does an arctic Muslim fast?
There aren’t many Arctic Muslims, are there? Now we know why.
Conversely, do Muslims at the South Pole not have to fast at all?
With the ISS orbiting about every 90 minutes, does that Muslims on board have 45 minutes to eat and 45 minutes to fast? 16 times in one day? That would seem pretty easy.
While we’re asking fanciful questions, in what direction do Muslims in the vicinity of Betelguese pray?
Most Muslims at extreme latitudes just use the times for Mecca or some point in a more moderate latitude close to them.
I had a friend here in DC who nonetheless used the Mecca times.
According to this group, there most acceptable way is either to use Saudi time or the time of the closest nonpolar region. Either way just ignoring Ramadan rules isn’t an option.
I had a muslim co-worker once; I asked her this exact question and she said she used the times from home.
I believe that the most common answer is to use the times corresponding to the nearest mosque. And a Muslim on the Space Station probably prays on a schedule corresponding to the time they keep on the station.
Islam really isn’t all that legalistic a religion. It’s more important that you do the best you can by God than it is that you follow all of the rules exactly to the letter. Allah is all-knowing and all-wise, and understands that the rules must necessarily work a little differently at extreme latitudes, or on a space station, or whatever.
It isn’t? Compared to what?
The first Muslim astronaut (as far as I know, or at least the first who cared) went on the ISS in 2007. At the time, a set of guidelines was produced. Here’s an article on the astronaut including a link to the document. It’s important to point out that these are merely guidelines, and while produced by consensus from a group, there’s no particular authority to them that a Muslim would be required to follow.
Judaism. There’s a reason we all become lawyers 
I find that deeply offensive… some of us become doctors and accountants. But seriously, as far as I can tell Judaism and Islam are remarkably similar in their degree of, er, legalisticness. If anything, the Wired article makes Islam seem more centralized and formal compared to Judaism. A (practicing) Jewish astronaut would ask his rabbi what to do about various religious observances in orbit. The rabbi would answer based on his own knowledge, or refer to a previously published p’sak, which exist because individual halachic authorities have discussed the issue in the past. In this case, the Islamic fatwa was made jointly by a large group of scholars. Even the existence of something called the “National Fatwa Council” in Malaysia sounds more organized than anything found in Judaism.
Eh, it was an interesting case, so a lot of folks weighed in on it.
Really? What about the RCA?
[I am not sure how Muslim law treats this, but Jewish laws has many similar issues. For example, what if you’re observing [Shabbat while crossing the International Date Line](View All The Kashrus Kurrents Articles). And, how do you celebrate Shabbat at the poles?
I guess you can assume that Muslims would take a similar position.
People don’t ask halachic questions to the RCA.
This has become a bit of a cliché in Norway, Land of the Midnight Sun and all that. According to the people I’ve asked, if they’re in the north during Ramadan, they either receive dispensation from fasting or get set times to do it. There’s a stubborn rumour that two muslims who went to the north country starved to death in the 60’s, having been caught unawares by the Sun’s refusal to go under the horizon. As there’s nothing to back it up, the story remains apocryphal.
Related question answered by our resident know-it-all:
They’re an Orthodox rabbinical group. Their decisions wouldn’t be considered authoritative by Conservative or Reform Jews. There are probably some Orthodox Jews for whom they’re not Orthodox enough. I’m not sure how much weight their opinions would carry outside the US, either.
Of all the things we Jews fight about, at least the calendar isn’t one of them (other than the quibble about whether holidays should be one day or two).
Islam is like most other religions–there are lots of different flavors, and there is lots to disagree about. Even Muslims in the same location can’t agree about when Ramadan starts. An article in today’s Washington Postgives some insight. Like many such conflicts the motivation is usually more political than theological.
Islam prescribes many behaviors, though a lot of this is interpretation of the life of Mohammed rather than anything spelled out in the Qu’ran. These is readily seen if you look at how Muslim women dress in Saudi Arabia, Taliban-controlled Afghanistan, Egypt, and the U.S. Another such “legislated” behavior is the five prayers each day, their timing, and the ritualistic washing to occur each time.