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The issue with using the lunar cycle for timekeeping at night is that the moon is not always visible in the sky at night. It is also not at the same spot in the sky every night, so the math on describing the time based on moon position is actually pretty complex, and unreliable for a consistent overnight clock. You might think that tides could be used as well, but it that is even more complex. In fact, some of the first analog computers were created to do the calculus required to solve the question of timing and tides.
The issue with using the lunar cycle for timekeeping at night is that the moon is not always visible in the sky at night. It is also not at the same spot in the sky every night, so the math on describing the time based on moon position is actually pretty complex, and unreliable for a consistent overnight clock. You might think that tides could be used as well, but it that is even more complex. In fact, some of the first analog computers were created to do the calculus required to solve the question of timing and tides.