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.

1. The negative acceleration resulted in a loss of 60 seconds of time over 100 years. If the acceleration is constant, the average rotational difference of .6 seconds per year is half the current defect of rotational rate, so that is 1.6 seconds per year or 1.6/365.25 seconds per day. The answer to part 1 is 0.00438056 seconds or 1/228 of a second.
2. As the positional difference increases as the square of the time when the acceleration is constant and we want a time over which the accumulated difference is 1440 times what it is over 100 years (as there are 1440 minutes in a day), we need x centuries, where x²=1440. That's about 38 centuries or 3800 years.

Comments: (
You must be logged in to post comments.)