LEAP SECONDS
The last leap second was introduced in UTC on 31 December 2008, and the next one will be on 30 June 2012.
(See the IERS Bulletin C)
Civil time is occasionally adjusted by one second increments to ensurethat the difference between a uniform time scale defined by atomic clocksdoes not differ from the Earth's rotational time by more than 0.9 seconds.CoordinatedUniversal Time (UTC), an atomic time, is the basis for civil time.
Historically, the second was defined in terms of the rotation of theEarth as 1/86,400 of a mean solar day. In 1956, the InternationalCommittee for Weights and Measures, under the authority given it by theTenth General Conference on Weights and Measures in 1954, defined the secondin terms of the period of revolution of the Earth around the Sun for aparticular epoch, because by then it had become recognized that the Earth'srotation was not sufficiently uniform as a standard of time. TheEarth's motion was described in Newcomb'sTables of the Sun, whichprovides a formula for the motion of the Sun at the epoch 1900 based onastronomical observations made during the eighteenth and nineteenth centuries. Theephemeris second thus defined is
the fraction 1/31,556,925.9747of the tropical year for 1900 January 0 at12 hours ephemeris time.
This definition was ratified by the Eleventh General Conference on Weightsand 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 secondsof ephemeris time. Ephemeris Time (ET) was defined as the measureof time that brings the observed positions of the celestial bodies intoaccord 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 cesiumatom (the standard of time) and the ephemeris second. They determined theorbital motion of the Moon about the Earth, from which the apparent motionof the Sun could be inferred, in terms of time as measured by anatomic clock. As a result, in 1967 the Thirteenth General Conferenceon Weights and Measures defined thesecond of atomic time in theInternational System of Units (SI) as
the duration of 9,192,631,770 periods of the radiationcorresponding to the transition between the two hyperfine levels of theground state of the cesium 133 atom.The ground state is defined at zero magnetic field. The second thusdefined is equivalent to the ephemeris second.
TheSub-bureau for Rapid Serviceand Predictions of Earth Orientation Parameters of theInternationalEarth Rotation Service (IERS), located at the USNO, monitors theEarth's rotation. Part of its mission involves the determination of a timescale based on the current rate of the rotation of the Earth. UT1 is thenon-uniform time based on the Earth's rotation.
The Earth is constantly undergoing a deceleration caused by the brakingaction of the tides. Through the use of ancient observations of eclipses,it is possible to determine the average deceleration of the Earth to beroughly 1.4 milliseconds per day per century. This deceleration causesthe Earth's rotational time to slow with respect to the atomic clock time.Thus, the definition of the ephemeris second embodied in Newcomb's motionof the Sun was implicitly equal to the average mean solar second over theeighteenth and nineteenth centuries. Modern studies have indicatedthat the epoch at which the mean solar day was exactly 86,400 SI secondswas approximately 1820. This is also the approximate mean epoch ofthe 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 EphemerisTime. Before then, the mean solar day was shorter than 86,400 secondsand since then it has been longer than 86,400 seconds.
The length of the mean solar day has increased by roughly 2 millisecondssince it was exactly 86,400 seconds of atomic time about 1.88 centuriesago (i.e. the 188 year difference between 2008 and 1820). Thatis, the length of the mean solar day is at present about 86,400.002 secondsinstead of exactly 86,400 seconds. Over the course of one year, thedifference accumulates to almost one second, which is compensated by theinsertion of a leap second into the scale of UTC with a current regularityof a little less than once per year. Other factors also affect theEarth, some in unpredictable ways, so that it is necessary to monitor theEarth's rotation continuously.
In order to keep the cumulative difference in UT1-UTC less than 0.9seconds, a leap second is added to the atomic time to decrease the differencebetween the two. This leap second can be either positive or negative dependingon the Earth's rotation. Since the first leap second in 1972, all leapseconds have been positive and there were 23 leap seconds in the 34 yearsto January, 2006. This pattern reflects the general slowingtrend of the Earth due to tidal braking.
Confusion sometimes arises over the misconception that the regular insertionof leap seconds every few years indicates that the Earth should stop rotatingwithin a few millennia. The confusion arises because some mistake leapseconds for a measure of therateat which the Earth is slowing.The 1 second increments are, however, indications of theaccumulateddifference in time between the two systems. (Also, it is importantto note that the current difference in the length of day from 86,400 secondsis the accumulation over nearly two centuries, not just the previous year.) As an example, the situation is similar to what would happen if a personowned a watch that lost 2 seconds per day. If it were set to a perfectclock 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 (30days of 2 second error accumulated each day). The person would then findit convenient to reset the watch by one minute to have the correct timeagain.
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. Thereason for this is that we can change the time on an atomic clock, whileit is not possible to alter the Earth's rotational speed to match the atomicclocks! Currently the Earth runs slow at roughly 2 milliseconds per day.After 500 days, the difference between the Earth rotation time and theatomic time would be 1 second. Instead of allowing this to happen, a leapsecond is inserted to bring the two times closer together.
International Atomic Time (TAI) is a statistical atomictime scale based on a large number of clocks operating at standards laboratoriesaround the world that is maintained by theBureauInternational des Poids et Mesures; its unit interval is exactlyone SI second at sea level. The origin of TAI is such that UT1-TAI is approximately0 (zero) on January 1, 1958. TAI is not adjusted for leap seconds. It is recommended by the BIPM that systems which cannot handle leapsecondsuse TAI instead.
Coordinated Universal Time (UTC) is defined by theCCIR Recommendation460-4 (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 oftheInternational Earth RotationService (IERS). According to the CCIR Recommendation, first preferenceis given to the opportunities at the end of December and June, and secondpreference to those at the end of March and September. Since the systemwas introduced in 1972, only dates in June and December have been used. TAI is expressed in terms of UTC by the relation TAI = UTC +dAT,where dAT is the total algebraic sum of leap seconds.
The first leap second was introduced on June 30, 1972. The historical listof leap seconds can be foundhere.
TheGlobal Positioning System (GPS) epoch is January 6, 1980and is synchronized to UTC. GPS Time is NOT adjusted for leap seconds.
BEFORE THE 2012 LEAP SECOND: GPS-UTC IS 15 (GPS IS AHEAD OF UTC BY 15 SECONDS)AFTER THE 2012 LEAP SECOND: GPS-UTC WILL BE 16 (GPS WILL BE AHEAD OF UTC BY 16 SECONDS)
As of 1 January 2008, and until the leap second of June 30 2012 TAI is ahead of UTC by 34 seconds. TAI is ahead of GPS by 19 seconds. GPS is ahead of UTC by 15 seconds.
After June 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.Until 1960, Universal Time (UT) was taken as the independent variable ofastronomical ephemerides. UT was then replaced by Ephemeris Time(ET), based on the motion of the sun. However, ET didnot include relativistic effects, such as corrections for the gravitationalpotential and velocity, as required by advances in the accuracy of timecomparisons. Thus ET was superseded in 1981 by Terrestrial DynamicalTime (TDT) and Barycentric Dynamical Time (TDB), which distinguish coordinatesystems with origins at the center of the Earth and the center of the solarsystem, respectively, and are consistent with the general theory of relativity. In the language of general relativity, TDT is a proper time while TDB isa coordinate time. In 1991, TDT was renamed simply Terrestrial Time(TT) and two additional relativistic time scales, Geocentric CoordinateTime (TCG) and Barycentric Coordinate Time (TCB) were adopted. Definitionsof these time scales are given inSystemsof Time.
Terrestrial Time (TT) is a uniform atomic time scale, whose unit isthe SI second, that replaces Ephemeris Time and maintains continuity withit. TT may be regarded as the time that would be kept by an idealatomic clock on the geoid. To convert a TT value to a predictionof UT1, it is necessary to know the differencedT = TT -UT1. Values ofdT are tabulated in the AstronomicalAlmanac. For example, mathematical predictions of lunar and solareclipses in the distant past and future depend sensitively on estimatesofdT. The computed path of a solar eclipse that occurred2000 years ago would be in error by about 3 hours, or some 45 degrees inlongitude to the west, on the assumption that the rate of rotation of theearth were uniform. Conversely, records of well documented ancienteclipses, together with modern telescopic observations of occultations,Very Long Baseline Interferometry, satellite laser ranging, lunarlaser ranging, and other measurements correlated to atomic time scalessince 1955, have provided the data on which long term trends and shortterm fluctuations have been derived. SincedT was approximately32.184 seconds at the origin of TAI in 1958, a practical realization ofTT is TT = TAI + 32.184 seconds. Although this expression gives TT in termsof TAI, in practice TT is obtained from the relation TT = UTC +dAT+ 32.184 seconds for a known value of UTC and a given number of leap seconds.
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Time Service Dept., U.S. Naval Observatory, Washington, DC