There are non-stop flights such as those from Chicago to Hong Kong which take off on Friday lunch time, and land after nightfall on a Saturday. This is due to the 15 hour flight duration and the 14 hour time difference. Is it permissable to take such a flight, and keep shabbos in the sky? Melacha on board the plane would have to be avoided of course - no movies, heated food and possibly not even locking the bathroom door as that turns on more light.
Shalom, Your question is an interesting one. Of course it is only discussed by the modern day Rabbis - but it also involves a question of where the Jewish international date-line is, which has been discussed by many earlier Rabbis also. Assuming that one takes off well before Shabbat starts, and lands after Shabbat has departed, then there are opinions who allow this. I saw in the name of Rav Elyashiv zt"l that in times of absolute need, one could take such a flight. (I saw this on the Star-K website, in their article "A Traveler's Guide To The International Dateline by Rabbi Dovid Heber, Star-K Kashrus Administrator", who writes this in the name of "Sefer Taarich Yisroel 21:15 [who] quotes several poskim, including Rav Elyashiv [zt"l] who holds this is permissible in order to be home with one’s family for Shabbos".) If you are asking because of a real need to take such a trip, I would advise you to be in contact with a Rabbi personally, as there are many issues you need to consider - such as candle lighting, kiddush, Shabbat meals, etc. Blessings.