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So, I read something on this a little while ago. It has to do with the moon's weaker gravity making time progress at a different rate, so the lunar time zone gives a precise reference for sub-second (nanosecond I guess?) precision manoeuvres and such like.
The time dilation on the surface of the moon would cause a clock to be 20 milliseconds ahead of a clock on earth after one year
it might be easier just to synchronize the space station clock with earth once a month, but I guess NASA would go for nanosecond precision if they could
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