The earth's rotation is slowing down due to the friction against the tidal bulge produced by the moon's and sun's gravitation. The variation is irregular but in general after 100 years the earth has rotated about .25° less than it would have if the rate were the same as at the beginning of the 100 years. That corresponds to one minute's worth of rotation.
1. How much longer (in seconds) is one day today than 100 years ago?
2. How long a period of time need go by for one complete rotation (day) to be missed using the original rotation rate as a standard?
Assume a constant negative acceleration.
(In reply to Answer
by K Sengupta)
The loss accrued due to the negative acceleration in rotation in a
period of 100 years = 60 seconds (given)
-> Average loss due to negative acceleration per year in the said period = 60/100 = 3/5, which is half of the current defect of rotational rate.
Since there are approximately 365.25 days in a year on an average, it follows that:
Length by which the period of one day today is longer when compared withthe same period 100 years before = 1/365.25 = 4/1461 =0.00438... seconds.
Consequently, one day today is approximately 0.00438 seconds longer than 100 years ago.