Many years ago, I heard that an astronaut would keep Shabbos based on counting 24 hour days from the last [Jewish?] community he was in, but I can't find anyone who discusses this. Do you have a reference?
Rabbi Pesach Feldman, Yerushalayim
Dear Rav Feldman,
I have been told (by Rav Dovid Solomon of Har Nof) that Rav Levi Yitzchak Halperin has written specifically about the issue of Jews in space. A similar, and more practical, issue is Jews living above the Artic circle (e.g. Mashgichim on fishing boats that operate in the far north). The Sefer haZemanim baHalachah (Rav Beinish, Chapter 8) discusses this issue and delineates three Shitos in the Achronim (the Rishonim mention the possibility but don't address the Halachah). The Shitos are as follows:
1) The rotation of the earth (as measured by the sun or the stars making a complete circut overhead) is used to measure the days. How one determines the beginning of the day - Shekiah - is unclear (Chatzos Yom and Chatzos Lilah would be determined by the sun's southernmost and northernmost points in the sky,etc.).
2) From one Shekiah to the next is considered one day even if that takes several months.
3) There is no system for measuring time and therefore one is Patur from all time bound Mitzvos including Shabbos.
The first Shitah seems to be the normative Halachah but it wouldn't apply to a Jew in outer space - only the third does. I seem to remember that when I discussed this issue with Rav Moshe Sternbuch he held of the third Shitah - or at least held that we had to consider it a valid possibility - and therefore one either shouldn't or is forbidden to go to the North pole (or at least to live there; flights from the U.S. to Japan routinely fly over the Artic circle to save travelling time. It would be difficult to forbid Jewish businessman from using these flights) because one is removing themselves from an obligation to keep Mitzvos.
It seems very arbitrary to fix an astronaut's "Jewish time zone" based on either the last community he was in or on the place from which he took off. Why should a frum astronaut who spent his last Shabbos in Boca Raton keep Shabbos in space like the Jews of Boca or according to Cape Kennedy time? In truth, though, I seem to remember that in the Encyclopedia Talmudit's article about the Artic circle they brought this opinion, i.e. that a person who travels so far north that there is no sunrise and sunset, should measure time based on the last place that he was in that did have sunrise and sunset.
b'Chavod,
Yonasan Sigler
This is not a Psak Halachah