The Arctic Circle and the Sabbath

Something that’s been nagging me for a long time now:

It is my understanding that Jews observe the Sabbath from sundown on Friday until sundown on Saturday. For those observant Jews who are currently residing (for whatever reason) above the Arctic Circle or below the Antarctic Circle, how is the timing of “sundown” determined during those periods of the year when the sun fails to set or to rise during the course of a specified 24 hour period?

I imagine that if and when such a situation arises, a Rabbi will go ahead and make a ruling. At the moment, though, that’s purely a hypothetical.

Not being a Rabbi, I can’t be sure what the ruling might be when it happens.

This is addressed in Do They Keep Kosher On Mars?

Jews in the Arctic circle, space shuttles, or space stations can either observe the time of the place they started from, or follow a hypothetical day with sunset and sunrise 12 hours apart.

I seem to remember a discussion about this when the Israeli astronaut who died aboard the Columbia went up.

According to the Jerusalem Post, he observed the Sabbath based on Houston time.

http://www.jpost.com/servlet/Satellite?pagename=JPost/JPArticle/ShowFull&cid=1042863313253