According to halakha, where is the international date line?
More specifically, I have heard that some people say you should observe Shabbat on Sunday in Japan & New Zealand and/or on Friday in Hawaii. Should I worry about this if I go to these places?
Also, what if I am on an eastward nonstop flight from Beijing to New York, that departs on Saturday night and also arrives on Saturday night. However, as I am flying over California it is Shabbat there. Is this a problem?
Also, what if I circumnavigate the Earth during the Omer, thereby inserting or deleting a day between Pesach and Shavuot? How would I conduct my Omer count? Also what if I just cross the International Date Line temporarily and return back the same way, all during the Omer?
Are there any other international date line issues I should be concerned about?