Materials
Calculators
Student Worksheet (.doc)


Background
adapted from Ocean Tides and Earth's Rotation

Tides affect the Earth's rotation in two ways, (1) by tidal friction, producing an extremely slow change in the Earth's rotation over a long period of time; and (2) by the continual movements of the tides, producing very small but very rapid changes in rotation. These rapid changes occur at exactly the same periods as the tides themselves -- half-daily, daily, etc.  For purpose of this lesson, only the first reason will be applied.

Long-term Tidal Braking of Earth Rotation
The long-term change in the Earth's rotation, or braking, is caused primarily by friction in the oceans, where "friction" may refer to any number of physical mechanisms.  For example, bottom friction, induced by tidal currents flowing across the seabed, various kinds of wave breaking, and scattering of tidal waves into oceanic internal waves are all thought to play a role.

Timekeeping
The U.S. Naval Observatory is charged with the responsibility for precise time determination.  This time is the Observatory's measure of the atomic time called Coordinated Universal Time (UTC).  Today, cesium clocks measure frequency with an accuracy of 2 nanoseconds per day or one second in 1,400,000 years.  It is the most accurate realization of a unit that mankind has yet achieved.

Due to tidal braking, after 1000 days our earth clock loses about 2.3 seconds, falling further behind the atomic clock. This long-term slowing of the rotation is a primary reason for periodically inserting leap seconds into the timekeeping process.

adapted from the "U.S.N.O.'s Leap Seconds" web page:
Confusion sometimes arises over the misconception that the regular insertion of leap seconds every few years indicates that the Earth should stop rotating within a few millennia. The confusion arises because people sometimes mistake leap seconds for a measure of the rate at which the Earth is slowing.  The 1 second (leap second) increments are indications of the accumulated difference in time between the two systems, atomic clocks and the Earth's rotational time, not the rate at which the Earth is slowing.  As an example, if a person owned a watch that lost 2 seconds per day, at the end of a month, the watch will be roughly one minute in error (30 days of 2 second error accumulated each day).  The person would then find it convenient to reset the watch by one minute to have the correct time again.  The person did not "lose" one minute, the time keeping device was simply adjusted to reflect the actual time.

This scenario is analogous to that encountered with the leap second. The difference is that instead of setting the clock that is running slow, we choose to set the clock that is keeping a uniform, precise time. The reason for this is that we can change the time on an atomic clock, while it is not possible to alter the Earth's rotational speed to match the atomic clocks! Currently the Earth runs slow at roughly 2 milliseconds per day. After 500 days, the difference between the Earth rotation time and the atomic time would be 1 second. Instead of allowing this to happen, a leap second is inserted to bring the two times closer together.


Procedure
Have you ever tried running through water?  Is it easier or more difficult than running on land?  Think about the Earth rotating in space.  With all the movement of the water around it through tidal cycles, do you think it is easier or more difficult for the Earth to rotate?

The long-term change in the Earth's rotation, or braking, is caused primarily by friction in the oceans, where "friction" may refer to any number things including, bottom friction, various kinds of wave breaking, and scattering of tidal waves are all thought to play a role.

Due to tidal braking, after 1000 days our earth clock loses about 2.3 seconds, falling further behind the atomic clock. This long-term slowing of the rotation is a primary reason for periodically inserting leap seconds into the timekeeping process.

1.  1,000 days equals how many years?

2.  500 days equals how many years?

3.  By the year 2020, how many leap seconds will have to be added to correct our Earth clock?

4.  What would happen by the year 5000?



So why doesn't the Earth stop rotating?
Confusion sometimes arises over the misconception that the addition of leap seconds to the timekeeping process every few years indicates that the Earth should stop rotating within a few millennia.

The confusion arises because people sometimes mistake leap seconds for a measure of the rate at which the Earth is slowing.  The 1 second (leap second) increments are actually indications of the accumulated difference in time between the two systems, atomic clocks and the Earth's rotational time, not the rate at which the Earth is slowing. 

As an example, if a person owned a watch that lost 2 seconds per day, at the end of a month, the watch will be roughly one minute in error (30 days of 2 second error accumulated each day).  The person would then find it convenient to reset the watch by one minute to have the correct time again.  The person did not "lose" one minute, the time keeping device was simply adjusted to reflect the actual time.

Since we cannot change the rotation of the Earth, we simply change the atomic clock to reflect the overall difference between the two systems.

Currently the actual long-term change in the rotation rate increases the length of day by some 2.3 milliseconds per century.

Official U.S. Time


Assessement
1.  Using the currently accepted long-term change in the rotation rate change of 2.3 milliseconds per century, how long would it take for a day to increase by 1 hour?