# Leap Seconds

The last leap second was introduced in UTC on 30 June 2015.

(See IERS Bulletin C 43)COORDINATED UNIVERSAL TIME (UTC) WILL SEQUENCE AS FOLLOWS: 30 JUN 2015 23 HOURS 59 MINUTES 59 SECONDS 30 JUN 2015 23 HOURS 59 MINUTES 60 SECONDS 01 JUL 2015 00 HOURS 00 MINUTES 00 SECONDS

Civil time is occasionally adjusted by one second increments to ensure
that the difference between a uniform time scale defined by atomic clocks
does not differ from the Earth's rotational time by more than 0.9 seconds.
**Coordinated
Universal Time (UTC)**, an atomic time, is the basis for civil time.

Historically, the second was defined in terms of the rotation of the
Earth as 1/86,400 of a mean solar day. In 1956, the International
Committee for Weights and Measures, under the authority given it by the
Tenth General Conference on Weights and Measures in 1954, defined the second
in terms of the period of revolution of the Earth around the Sun for a
particular epoch, because by then it had become recognized that the Earth's
rotation was not sufficiently uniform as a standard of time. The
Earth's motion was described in Newcomb's *Tables of the Sun*, which
provides a formula for the motion of the Sun at the epoch 1900 based on
astronomical observations made during the eighteenth and nineteenth centuries.
The *ephemeris second* thus defined is

*the fraction 1/31,556,925.9747
of the tropical year for 1900 January 0 at12 hours ephemeris time.*

This definition was ratified by the Eleventh General Conference on Weights and Measures in 1960. Reference to the year 1900 does not mean that this is the epoch of a mean solar day of 86,400 seconds. Rather, it is the epoch of the tropical year of 31,556,925.9747 seconds of ephemeris time. Ephemeris Time (ET) was defined as the measure of time that brings the observed positions of the celestial bodies into accord with the Newtonian dynamical theory of motion.

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 ephemeris second. They determined the
orbital motion of the Moon about the Earth, from which the apparent motion
of the Sun could be inferred, in terms of time as measured by an
atomic clock. As a result, in 1967 the Thirteenth General Conference
on Weights and Measures defined the **second** of atomic time in the
International System of Units (SI) as

The ground state is defined at zero magnetic field. The second thus defined is equivalent to the ephemeris second.the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

The **Sub-bureau for Rapid Service
and Predictions of Earth Orientation Parameters** of the **International
Earth Rotation Service (IERS)**, located at the USNO, 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 tides. Through the use of ancient observations of eclipses, it is possible to determine the average deceleration of the Earth to be roughly 1.4 milliseconds per day per century. This deceleration causes the Earth's rotational time to slow with respect to the atomic clock time. Thus, the definition of the ephemeris second embodied in Newcomb's motion of the Sun was implicitly equal to the average mean solar second over the eighteenth and nineteenth centuries. Modern studies have indicated that the epoch at which the mean solar day was exactly 86,400 SI seconds was approximately 1820. This is also the approximate mean epoch of the observations analyzed by Newcomb, ranging in date from 1750 to 1892, that resulted in the definition of the mean solar day on the scale of Ephemeris Time. Before then, the mean solar day was shorter than 86,400 seconds and since then it has been longer than 86,400 seconds.

The length of the mean solar day has increased by roughly 2 milliseconds since it was exactly 86,400 seconds of atomic time about 1.88 centuries ago (i.e. the 188 year difference between 2008 and 1820). That is, the length of the mean solar day is at present about 86,400.002 seconds instead of exactly 86,400 seconds. Over the course of one year, the difference accumulates to almost one second, which is compensated by the insertion of a leap second into the scale of UTC with a current regularity of a little less than once per year. Other factors also affect the Earth, 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 added to the atomic time 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, and there have been 26 leap seconds in the 43 years to January, 2015.

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 some mistake leap
seconds for a measure of the *rate *at which the Earth is slowing.
The 1 second increments are, however, indications of the *accumulated
difference* in time between the two systems. (Also, it is important
to note that the current difference in the length of day from 86,400 seconds
is the accumulation over nearly two centuries, not just the previous year.)
As an example, the situation is similar to what would happen if a person
owned a watch that lost 2 seconds per day. If it were set to a perfect
clock today, the watch would be found to be slow by 2 seconds tomorrow.
At the end of a month, the watch will be roughly a 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.

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.

**International Atomic Time (TAI) ** is a statistical atomic
time scale based on a large number of clocks operating at standards laboratories
around the world that is maintained by the **Bureau
International des Poids et Mesures**; its unit interval is exactly
one SI second at sea level. The origin of TAI is such that UT1-TAI is approximately
0 (zero) on January 1, 1958. TAI is not adjusted for leap seconds.
It is recommended by the BIPM that systems which cannot handle leapseconds
use TAI instead.

**Coordinated Universal Time (UTC)** is defined by the *CCIR Recommendation
460-4 (1986)*. It differs from TAI by the total number of leap seconds,
so that UT1-UTC stays smaller than 0.9s in absolute value.
The decision to introduce a leap second in UTC is the responsibility of
the **International Earth Rotation
Service (IERS).** According to the CCIR Recommendation, 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.
TAI is expressed in terms of UTC by the relation TAI = UTC + ** d**AT,
where

**AT is the total algebraic sum of leap seconds.**

*d*The first leap second was introduced on June 30, 1972. The historical list
of leap seconds can be found **here**.

The **Global Positioning System (GPS) epoch** is January 6, 1980
and is synchronized to UTC. GPS is NOT adjusted for leap seconds.

BEFORE THE 2015 LEAP SECOND: GPS-UTC IS 16 (GPS IS AHEAD OF UTC BY 16 SECONDS) AFTER THE 2015 LEAP SECOND: GPS-UTC WILL BE 17 (GPS WILL BE AHEAD OF UTC BY 17 SECONDS)

As of 1 July 2012, TAI is ahead of UTC by 35 seconds. TAI is ahead of GPS by 19 seconds. GPS is ahead of UTC by 16 seconds.

After June 2015, TAI is ahead of UTC by 36 seconds. TAI is ahead of GPS by 19 seconds. GPS is ahead of UTC by 17 seconds.

Until 1960, Universal Time (UT) was taken as the independent variable of
astronomical ephemerides. UT was then replaced by Ephemeris Time
(ET), based on the motion of the sun. However, ET did
not include relativistic effects, such as corrections for the gravitational
potential and velocity, as required by advances in the accuracy of time
comparisons. Thus ET was superseded in 1981 by Terrestrial Dynamical
Time (TDT) and Barycentric Dynamical Time (TDB), which distinguish coordinate
systems with origins at the center of the Earth and the center of the solar
system, respectively, and are consistent with the general theory of relativity.
In the language of general relativity, TDT is a proper time while TDB is
a coordinate time. In 1991, TDT was renamed simply Terrestrial Time
(TT) and two additional relativistic time scales, Geocentric Coordinate
Time (TCG) and Barycentric Coordinate Time (TCB) were adopted. Definitions
of these time scales are given in **Systems
of Time.**

Terrestrial Time (TT) is a uniform atomic time scale, whose unit is
the SI second, that replaces Ephemeris Time and maintains continuity with
it. TT may be regarded as the time that would be kept by an ideal
atomic clock on the geoid. To convert a TT value to a prediction
of UT1, it is necessary to know the difference ** d**T = TT -
UT1. Values of

**T are tabulated in the Astronomical Almanac. For example, mathematical predictions of lunar and solar eclipses in the distant past and future depend sensitively on estimates of**

*d***T. The computed path of a solar eclipse that occurred 2000 years ago would be in error by about 3 hours, or some 45 degrees in longitude to the west, on the assumption that the rate of rotation of the earth were uniform. Conversely, records of well documented ancient eclipses, together with modern telescopic observations of occultations, Very Long Baseline Interferometry, satellite laser ranging, lunar laser ranging, and other measurements correlated to atomic time scales since 1955, have provided the data on which long term trends and short term fluctuations have been derived. Since**

*d***T was approximately 32.184 seconds at the origin of TAI in 1958, a practical realization of TT is TT = TAI + 32.184 seconds. Although this expression gives TT in terms of TAI, in practice TT is obtained from the relation TT = UTC +**

*d***AT + 32.184 seconds for a known value of UTC and a given number of leap seconds.**

*d*