This question is inspired by:
I was reading the answers, or actually the source quotations, and realized that the answer to the questions about circumnavigation during Omer, Shabbat on the North Pole etc. should really be based on a more fundamental issue:
Take any Mitzvah of the form: "Do X at time Y every Z time units."
Is it more important that all Jews do this simultaneously, or in a consistently-synchronized manner? Or is it generally the case that you should make some Drash into the timing? Or maybe it's more of a symbolic/spiritual aspect of the exact timing?
For example, "Rest for the entire day every 7 days." (Yes I know that's not a very exact definition.) If the second option is true, maybe a Jewish community on another planet might make it every 6 days because the day is longer, and the intention is more that people rest and that the community allot Qodesh time appropriately. If the first option is true, then why even have a dateline, and not just have Shabbat start whenever it starts around Jerusalem? And if the third options is true, maybe you do need sophisticated ritual arrangements for flying over the north pole...
PS - I'm actually an Atheist of Jewish descent so please excuse my lack of religious perspective.