By "day" I mean the rotation period of the planet.

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This constant rotation will mean that troops from many countries will have to meet the stringent standards set for the new force.

BBC: NEWS | Europe | Nato's force for change

Over a few decades this would amount to a minute's difference, but over several hundred years this would mean the atomic clock time-scale and the time-scale based on the Earth's rotation would be out by an hour.

BBC: Changes to the world's time scale debated