I understand that Jewish astronauts have been advised to observe Shabbat by Cape Canaveral time, by analogy with traveling to a place that doesn't have daily sunrise/sunset where some rule you use the last place you were that did. But this seems to describe a temporary journey, such as a shuttle flight. What is the rule if one is living in space for an extended time? Edit: Would each individual determine his own time (if it's based on home/departure city), or would the community living there determine a time together to reduce the chaos of varied Shabbat times in the same place?
You might first ask, Rabbi Ben-Zion Firrer asked, whether the mitzvahs are required at all in space. After all, the Torah says that you should do the commandments "all of the days which you are alive on this earth" (Deut. 12:1), maybe we aren't obligated to perform the commandments in space or on the moon. Rabbi Shlomo Goren, in an interview published in HaZofeh (and republished in J.David Bleich, Contemporary Halakik Problems, Vol. I, at 211) reasoned that since one cannot survive in the environment of space without bringing earthly oxygen and water with him, he is still "on this earth" for purposes of this, now, very real discussion.
The simple answer is that when outside of the earth's atmosphere, normal measures of time, such as sunrise and sunsets, and lunar rotations that help us count the months, are useless. Therefore, one would designate the time and calendar events that occur in his home port, e.g. Houston or Cape Canaveral. One would do much the same thing if going to the North or South Pole. Much of Rabbi Bleich's article is available on Google Books. Also see the Keren B'Yavneh website which has some papers on the subject, although I don't think any are in English.
Based on this article: I would say that people in the ISS would keep Shabbat based on the location of the place they will be landing when they come back, or based on the location of the earth crew that is working with them. This is how the people aboard the ISS mantain their daily lives, and it would be peculiar to do it another way.