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Worst is UTC vs GMT
(i.ibb.co)
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We could keep the 0 hour as the "middle" of the night and 12 being the "middle" of the day (though I'm not sure if that's really the sun's high spot for the day for any places).
But with fully controlled mirrors, we could make it exactly 12 hours, so we could just then switch to the 0 hour being when the sun comes up.