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It's not just time zones and leap seconds. SI seconds on Earth are slower because of relativity, so there are time standards for space stuff (TCB, TGC) that use faster SI seconds than UTC/Unix time. T2 - T1 = [God doesn't know and the Devil isn't telling.]
All dates and times shall be stored and manipulated in Unix time. Only convert to a readable format at the top of the UI, and forget trying to parse user inputs :P that's just impossible
I picture this being read by the fred armisen "believe it or not, straight to jail" character