[skissane]

> How do you handle the date changing in the middle of the day?

In the Jewish and Islamic calendars, the day begins/ends at sunset, and hence the date changes at that point.

Traditionally, (Western) astronomers used the astronomical day, going back to Ptolemy, in which a new day starts at noon. Part of the reason for this was that in pre-modern times it was a lot easier to precisely determine the moment of noon than the moment of midnight. Contemporary astronomy has mostly abandoned that tradition, but it still survives in the definition of Julian dates (but not Modified Julian dates which moved the day boundary to midnight)