## The Slowing of the Earths Rotation

The gradual slowing of the Earth is known from the geological record and from differences between the computed time of an event in the historical past and records from that time. The effect is cumulative. Suppose the length of the day were to be shorter by 1 second after 100,000 y. Then after only 4000 years, the decrease in the time for a complete Earth rotation would be 4000/100,000 = 0.04. From this, it follows that the time of day at which an event would occur 4000 years later would be different by several hours. The average decrease in daylength over the 4000 years would be (0.04 - 0.00)/2 = 0.02, so that after 4000y, the cumulated "loss" over this interval would be 0.02 x 4000 x 365.25 = 29,400s = 8^12. We can calculate the accumulation also as follows. If the Earth were slowing by 1s per 100,000 years, every day it would slow at the average rate:

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