God called the light Day, and the darkness He called Night. And there was evening and there was morning, a first day.
www.nasa.gov
The International Space Station travels in orbit around Earth at a speed of roughly17,150 miles per hour (that's about 5 miles per second!). This means that the Space Station orbits Earth (and sees a sunrise) once every 92 minutes.
How should you count days when there is no sunrise?
It is rare for one who has sold his animal in exchange for money to change his mind and request then animal back from the purchaser. And it is only with regard to a common matter that the Sages issued a decree, whereas with regard to an uncommon matter, the Sages did not issue a decree.
J. David Bleich, "Mitzvoth in the polar regions and in earth orbit"
A response from 1886, Rabbi Simcha Ha'Levi Bamberger, "...Why should a person, even during weekdays, place himself in a state of doubt with regard to reading of the Shema and prayer? At the minimum, do not remain in that country on Shabbat [where] there is doubt with regard to what to do..." (Letter to his son who was considering a business trip to Norway)
R. Jacob Emden (Germany, End of 17th-18th Century) Mor u-Kezi'ah 334
It is necessary to reflect upon the manner in which those who dwell or travel in the lands near the poles should conduct themselves. For...there exists a place where the day is prolonged to half a year and similarly the night is half a year ...if so, how should they establish Shabbat there? It seems to me that there it is necessary to count seven equal days of twenty-four of our equal hours, and calculating from the day that one arrived there
R. Israel Lipschutz, Tiferet Yisra'el
The traveler should adopt the clock of "the place from which he departed" (makom she-yaza mesham) in determining the beginning and end of each day and the various divisions thereof. [Tiferet Yisra'el himself notes one resultant incongruity: A traveler arriving at the North Pole from England and a traveler arriving from America would both observe Shabbat on the same "day" but at different hours.]
How should you count days when you have no idea what day it is?
(א) דין ההולך במדבר בשבת ובו ב' סעיפים: ההולך במדבר ואינו יודע מתי הוא שבת מונה שבעה ימים מיום שנתן אל לבו שכחתו ומקדש השביעי בקידוש והבדלה...
One who is walking in the wilderness, and does not know when is Shabbat should count seven days from the day he lost track of time, and sanctify the seventh with Kiddush and Havdalah...
The Hid”a (Rav Haim Yosef David Azulai, 1724-1806) ruled that he should recite the weekday prayer service every day, including the seventh day. A person who recites the weekday prayer service on Shabbat fulfills his obligation of prayer, despite the fact that he did not recite the special Shabbat prayer text.