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Leap seconds

Civil time is occasionally adjusted by one-second increments to ensure that the difference between a uniform time scale defined by atomic clocks (TAI) does not differ from the Earth’s rotational time by more than 0.9 seconds.

Coordinated Universal Time (UTC), an atomic time, is this adjusted time scale and it forms the basis for our civil time.

In 1956, following several years of work, two astronomers at the U. S. Naval Observatory (USNO) and two astronomers at the National Physical Laboratory (Teddington, England) determined the relationship between the frequency of the Cesium atom (the standard of time) and the rotation of the Earth at a particular epoch.

As a result, they defined the second of atomic time as the length of time required for 9 192 631 770 cycles of the Cesium atom at zero magnetic field.

The second thus defined was equivalent to the second defined by the fraction 1 / 31 556 925.9747 of the year 1900.

The atomic second was set equal, then, to an average second of Earth rotation time near the end of the 19th century.

The Rapid Service/Prediction Center of the International Earth Rotation Service (IERS), located at the U.S. Naval Observatory, monitors the Earth’s rotation. Part of its mission involves the determination of a time scale based on the current rate of the rotation of the Earth. UT1 is the non-uniform time based on the Earth’s rotation.

The Earth is constantly undergoing a deceleration caused by the braking action of the ocean tides. Through the use of ancient observations of eclipses, it is possible to determine the deceleration of the Earth to be roughly 2 milliseconds per day per century. This is an effect which causes the Earth’s rotational time to slow with respect to the atomic clock time.

Since it has been about 1 century since the defining epoch (i.e., the duration since 1900), the difference has accumulated to roughly 2 milliseconds per day. Other factors also affect the Earth’s dynamics, some in unpredictable ways, so that it is necessary to monitor the Earth’s rotation continuously.

In order to keep the cumulative difference in UT1-UTC less than 0.9 seconds, a leap second is inserted periodically in the atomic UTC time scale to decrease the difference between the two.

This leap second can be either positive or negative depending on the Earth’s rotation.

Since the first leap second in 1972, all leap seconds have been positive ..This reflects the general slowing trend of the Earth due to tidal braking.

Confusion sometimes arises over the misconception that the occasional insertion of leap seconds every few years indicates that the Earth should stop rotating within a few millennia.

The confusion arises because some mistake leap seconds as a measure of the rate at which the Earth is slowing.

The one-second increments are, however, indications of the accumulated difference in time between the two systems.

As an example, the situation is similar to what would happen if a person owned a watch that lost two seconds per day. If it were set to a perfect clock today, the watch would be found to be slow by two seconds tomorrow. At the end of a month, the watch will be roughly a minute in error (thirty days of the two 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.

This scenario is analogous to that encountered with the leap second. The difference is that instead of resetting the clock that is running slow, we choose to adjust the clock that is keeping a uniform, precise time.

The reason for this is that we can change the time of 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 one second. Instead of allowing this to happen a leap second is inserted to bring the two times closer together.

The decision of when to introduce a leap second in UTC is the responsibility of the International Earth Rotation Service (IERS). According to international agreements, first preference is given to the opportunities at the end of December and June, and second preference to those at the end of March and September. Since the system was introduced in 1972, only dates in June and December have been used.



Unbeknownst to much of the lay public, the standard time used across the world is adjusted by the tick of one second every few years—including this one—to ensure that clocks remain aligned to the solar time, based on the sun’s position in the sky, to which we’re all accustomed. Some critics, including the U.S. government, think adding a “leap second” is too disruptive on modern technology and should stop.

A quick history lesson: For decades, the global timekeeping standard most of the world followed was Greenwich Mean Time, which was derived from measuring the sun’s position in the sky at the Royal Observatory in Greenwich, London. British mariners, along with visiting ships, and railroads synchronized their clocks to the measure, and it spread around the globe. International time zones reflected the number of hours they were ahead of or behind GMT.

However, scientists recognized that Earth’s orbit is wobbly and irregular, and measures of time based on the planet’s rotation and sun’s position weren’t precise enough for their needs. So in 1972, the new gold standard for earthly timekeeping became Coordinated Universal Time, or UTC for short.

UTC isn’t based on any single timepiece, but on something called International Atomic Time, a weighted average of the times of more than 400 atomic clocks—devices that measure the passage of time with extreme accuracy through the vibrations of atoms.

But—and this is where time gets tricky—the atomic clocks are almost too accurate for ordinary earthlings to handle.

If left unadjusted over a few centuries, the disparity between atomic clocks and time based on the rotation of the Earth would gradually increase. The time of sunrise and sunset would be roughly a half-hour different than it is today. And in a few more centuries, it would expand to a full hour.

So, as a compromise of sorts to stay close to astronomical time, and avoid freaking people out, leap seconds are added to UTC when the atomic clock average edges toward 0.9 second different than time based on the rotation of the planet. That compromise allows elapsed time to be measured with atomic precision, while still linking time of day to the rotation of the Earth.

The next numerical adjustment is set to take place this summer, when the world’s official timekeepers will extend June 30 by one “leap second,” causing the final minute of the day to last an aberrant 61 seconds and momentarily delay the start of July. The International Earth Rotation and Reference Systems Service, which monitors the position and movement of the planet, recommends leap seconds as needed.

Tinkering with time, even for a second, has consequences, however, and these adjustments can create real-world problems. And because leap seconds are introduced sporadically—there was a seven-year gap from 1998 to 2005 with none—adjustments to modern technologies can’t be systematized. On the fly, mistakes get made, and some systems fail.

“The last time we had a leap second, a whole bunch of websites went down,” said John P. Lowe of the National Institute of Standards and Technology, which distributes standard time and frequency signals in the U.S. “It was like a mini Y2K.”

That year, 2012, the electronic reservation system for Qantas airline failed, delaying hundreds of flights and forcing the airline to check in passengers manually. Websites such as LinkedIn, Reddit and Yelp crashed. And Japan, concerned about potential errors, suspended the time-stamp system it uses to authenticate electronic documents for several hours while it adjusted its clocks.

The past disruptions have led the U.S. to lobby to eliminate the leap second. The International Telecommunication Union, which, among other things, develops standards that ensure networks seamlessly connect, is scheduled to vote on it at the World Radiocommunication Conference in November.


What causes variations in Earth’s orientation?

There are various factors which cause the orientation of the Earth to change with time. Polar motion is caused, in part, by large scale movements of water and changes in the atmospheric angular momentum. For example, the yearly melting of snow and ice in northern Spring contributes to the annual term of polar motion. It is also thought that large earthquakes and the embayment of water by dams and reservoirs might affect polar motion, but this has yet to be quantitatively demonstrated.

The secular variation of the rotational speed seen by the apparently linear increase in the length of the day is due chiefly to tidal friction. The Moon raises tides in the ocean diminishing the speed of rotation. This effect causes a slowing of the Earth’s rotational speed resulting in a lengthening of the day by about 0.0015 to 0.0020 seconds per day per century.

The irregular changes in speed appear to be the result of random accelerations, but may be correlated with physical processes occurring on or within the Earth. These cause the length of the day to vary by as much as 0.001 to 0.002 seconds. Irregular changes consist of “decade fluctuations” with characteristic periods of five to fifteen years as well as variations which occur at shorter time scales. The decade fluctuations are related apparently to processes occurring deep within the Earth. The higher frequency variations with periods less than two years are now known to be related largely to the changes in the total angular momentum of the atmosphere.

Periodic variations are associated with periodically repeatable physical processes affecting the Earth. Tides raised in the solid Earth by the Moon and the Sun produce variations in the length of the day with a total amplitude on the order of 0.001 seconds and with individual periods of 18.6 years, 1 year, 1/2 year, 27.55 days, 13.66 days and others. A standard model including 62 periodic components, can be employed to correct the observations for tidal effects.

The rotational speed of the Earth remains essentially unpredictable in nature due to incompletely understood variations. Because of this, astronomical observations continue to be made regularly with increasing accuracy, and the resulting data are the subject of continuing research in the field.



Since this system of correction was implemented in 1972, 25 such leap seconds have been inserted. The most recent one happened on June 30, 2012 at 23:59:60 UTC.

A leap second, the 26th, will again be inserted at the end of June 30, 2015 at 23:59:60 UTC.

Leap seconds are irregularly spaced because the Earth’s rotation speed changes irregularly. Indeed, the Earth’s rotation is quite unpredictable in the long term, which explains why leap seconds are announced only six months in advance.

External links:



Pendulum Time: TryEngineering

Ultimate Clocks: Scientific American

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