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Leap seconds to date
Year June 30 December 31
1972 +1 +1
1973 0 +1
1974 0 +1
1975 0 +1
1976 0 +1
1977 0 +1
1978 0 +1
1979 0 +1
1980 0 0
1981 +1 0
1982 +1 0
1983 +1 0
1984 0 0
1985 +1 0
1986 0 0
1987 0 +1
1988 0 0
1989 0 +1
1990 0 +1
1991 0 0
1992 +1 0
1993 +1 0
1994 +1 0
1995 0 +1
1996 0 0
1997 +1 0
1998 0 +1
1999 0 0
2000 0 0
2001 0 0
2002 0 0
2003 0 0
2004 0 0
2005 0 +1
2006 0 0
2007 0 0
2008 0 +1
2009 0 0
Year June 30 December 31
Total 9 15

A leap second is a positive or negative one-second adjustment to the Coordinated Universal Time (UTC) time scale that keeps it close to mean solar time. UTC, which is used as the basis for official time-of-day radio broadcasts for civil time, is maintained using extremely precise atomic clocks. To keep the UTC time scale close to mean solar time, UTC is occasionally corrected by an intercalary adjustment, or "leap", of one second. Over long time periods, leap seconds must be added at an ever increasing rate (see ΔT). The timing of leap seconds is now determined by the International Earth Rotation and Reference Systems Service (IERS). Leap seconds were determined by the Bureau International de l'Heure (BIH) prior to January 1, 1988, when the IERS assumed that responsibility.

When a positive leap second is added at 23:59:60 UTC, it delays the start of the following UTC day (at 00:00:00 UTC) by one second, effectively slowing the UTC clock.

Reason for leap seconds

Leap seconds are necessary partly because the length of the mean solar day is very slowly increasing, and partly because the SI second, when adopted, was already a little shorter than the current value of the second of mean solar time. Time is now measured using stable atomic clocks (TAI or International Atomic Time), whereas the rotation of Earth is much more variable. Originally, the second was defined as 1/86400 of a mean solar day (see solar time) as determined by the rotation of the Earth around its axis and around the Sun. By the middle of the 20th century, it was apparent that the rotation of the Earth did not provide a sufficiently uniform time standard and in 1956 the second was redefined in terms of the annual orbital revolution of the Earth around the Sun. In 1967 the second was redefined, once again, in terms of a physical property: the oscillations of an atom of caesium-133, which were measurable by anatomic clock. But the solar day becomes 1.7 ms longer every century due mainly to tidal friction (2.3 ms/cy, reduced by 0.6 ms/cy due to glacial rebound).

The SI second counted by atomic time standards has been defined on the basis of a history going back to the former standard time scale of ephemeris time (ET). It can now be seen to be close to the average second of 1/86400 of a mean solar day between 1750 and 1892. The current SI second was defined in 1967, as 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. This number first arose from calibration of the caesium standard by the second of ET: in 1958, the second of ET was determined as the duration of cycles of the chosen caesium transition, (while at about the same time, and with the same caesium standard, the then-current mean length of the second of mean solar time (UT2) had been measured at 9,192,631,830 cycles). Later verification showed that the SI second referred to atomic time was in agreement, within 1 part in 1010, with the second of ephemeris time as determined from lunar observations. Time as measured by Earth's rotation has accumulated a delay with respect to atomic time standards. From 1961 to 1971, the rate of (some) atomic clocks was (for purposes of UTC) constantly slowed to stay in sync with Earth's rotation. (Before 1961, broadcast time was synchronized to astronomically determined Greenwich Mean Time.) Since 1972, broadcast seconds have been exactly equal to the standard SI second chosen in 1967.

UTC is counted by atomic clocks, but is kept approximately in sync with UT1 (mean solar time) by introducing a leap second when necessary. This happens when the difference (UT1 − UTC) approaches 0.9 seconds, and is typically scheduled either at the end of June 30 or December 31 (though leap seconds can be applied at the end of any month). On January 1, 1972, the initial offset of UTC from TAI was chosen to be 10 seconds, which approximated the total difference which had accumulated since 1958, when TAI was defined equal to UT2, a smoothed version of UT1 (GMT) no longer used. The table shows the number of leap seconds added since then. The total difference between TAI and UTC is 10 seconds more than the total number of leap seconds.

Graph showing the difference between UT1 and UTC.
Vertical segments correspond to leap seconds.
The leap second adjustment (which is approximately 0.6 seconds per year) is necessary because of the difference between the length of the SI day (based on the mean solar day between 1750 and 1892) and the length of the current mean solar day (which is about 0.002 seconds longer). The difference between these two will increase with time, but only by 0.0017 seconds per century. In other words, the adjustment is required because we have decoupled the definition of the second from the current rotational period of the Earth. The actual rotational period varies due to unpredictable factors such as the motion of mass within Earth, and has to be observed rather than computed.

For example, suppose an atomic clock is used to count seconds from the Unix epoch of 00:00:00 on January 1, 1970. UTC and mean solar time (UT1) were almost identical at that time. After Earth makes one full rotation with respect to the mean Sun, the counter will register 86400.002 seconds (once again, the precise value will vary). Based on the counter, and assuming that a day is 24×60×60=86400 seconds long, the date will be calculated as 00:00:00.002 January 2, 1970. After 500 rotations, it will be 00:00:00 May 16, 1971 in solar time (UT1), but the counter will register 43,200,001 atomic seconds. Since 86400 × 500 is 43,200,000 seconds, the date will be calculated as 00:00:01 on May 16, 1971, as measured by atomic time. If a leap second had been added on December 31, 1970, then the date would be computed as 00:00:00 on May 16, 1971. The system involving leap seconds was set up to allow TAI and UT1 to have an offset of 10 seconds on January 1, 1972.

Tidal braking slows down Earth's rotation, causing the number of SI seconds in a mean solar day to increase from approximately 86400.002 to 86400.004 over 100 years. For unknown reasons, Earth sped up after year 2000, so the mean solar day has become 1 ms shorter and fewer leap seconds have been needed after year 2000.

Announcement of leap seconds

International Earth Rotation and Reference Systems Service (IERS) announces the insertion of a leap second whenever the difference between UTC and UT1 approaches 0.6 s, to keep the difference between UTC and UT1 from exceeding 0.9 s. The announcement appears in IERS "Bulletin C", typically published every six months.

The most recent leap second was added at the end of 2008.

After UTC 23:59:59, a positive leap second at 23:59:60 would be counted, before the clock indicates 00:00:00 of the next day. Negative leap seconds are also possible, should the Earth's rotation become slightly faster - in that case, 23:59:58 would be followed by 00:00:00 - but have not yet been used. Leap seconds occur only at the end of a UTC month, and have only ever been inserted at the end of June 30 or December 31. Unlike leap days, they occur simultaneously worldwide; for example, the leap second on December 31, 2005 occurred at 23:59:60 UTC. This was 6:59:60 p.m. U.S. Eastern Standard Time and 12:59:60 a.m. on January 1, 2006 Central European Time.

Historically, leap seconds have been inserted about every 18 months. However, because the Earth's rotation rate is unpredictable in the long term, it is not possible to predict the need for them more than six months in advance. From June 1972 through December 2005, the BIH/IERS gave instructions to insert a leap second on 23 occasions, after an initial 10 second offset from TAI on January 1, 1972. The interval between January 1, 1999 and December 31, 2005 was the longest period without a leap second since the system was introduced.

Some time signal broadcasts give voice announcements of the impending leap-second.

Proposal to abolish leap seconds

On July 5, 2005, the Head of the Earth Orientation Center of the IERS sent a notice to IERS Bulletins C and D subscribers, soliciting comments on a U.S. proposal before the ITU-R Study Group 7's WP7-A to eliminate leap seconds from the UTC broadcast standard before 2008. (The ITU-R is responsible for the definition of UTC). The Wall Street Journal noted that the proposal was considered by a U.S. official to be a "private matter internal to the ITU", . It was expected to be considered in November 2005, but the discussion has since been postponed. Under the proposal, leap seconds would be technically replaced by leap hours as an attempt to satisfy the legal requirements of several ITU-R member nations that civil time be astronomically tied to the Sun.

Several arguments for the abolition have been presented. Some of these have only become relevant with the recent proliferation of computers using UTC as their internal time representation. For example, currently it is not possible to correctly compute the elapsed interval between two instants of UTC without consulting manually updated and maintained tables of when leap seconds have occurred. Moreover, it is not possible even in theory to compute such time intervals for instants more than about six months in the future. This is not a matter of computer programmers being "lazy"; rather, the uncertainty of leap seconds introduces to those applications needing accurate notions of elapsed time intervals either fundamentally new (and often untenable) operational burdens for computer systems (the need to do online lookups) or insurmountable theoretical concerns (the inability in a UTC-based computer to accurately schedule any event more than six months in the future to within a fewseconds).

A number of objections to the proposal have been raised. Dr. P. Kenneth Seidelmann, editor of the Explanatory Supplement to the Astronomical Almanac, wrote a letter lamenting the lack of consistent public information about the proposal and adequate justification. Steve Allen of the University of California, Santa Cruzmarker cited the large impact on astronomers in a Science News article. He has an extensive online site devoted to the issues and the history of leap seconds, including a set of references about the proposal and arguments against it.

Arguments against the proposal include the unknown expense of such a major change and the fact that universal time will no longer correspond to sundial time. It is also answered that two timescales that do not follow leap seconds are already available, International Atomic Time (TAI) and Global Positioning System (GPS) time. Computers, for example, could use these and convert to UTC or local civil time as necessary for output. Inexpensive GPS timing receivers are readily available and the satellite broadcasts include the necessary information to convert GPS time to UTC. It is also easy to convert GPS time to TAI as TAI is always exactly 19 seconds ahead of GPS time. Examples of systems based on GPS time include the CDMA digital cellular systems IS-95 and CDMA2000.

At the 47th meeting of Civil Global Positioning System Service Interface Committee in Fort Worthmarker, Texasmarker, it was announced that a mailed vote would go out on stopping leap seconds. The plan for the vote is:

  • April 2008: ITU Working Party 7A will submit to ITU Study Group 7 project recommendation on stopping leap seconds
  • During 2008, Study Group 7 will conduct a vote through mail among member states
  • 2011: If 70% of member states agree, the World Radio Conference will approve the recommendation
  • 2013: application of leap seconds will stop and UTC will become a continuous time scale if 70% of member states have voted to abolish the leap second

See also


  1. :(1) In "The Physical Basis of the Leap Second", by D D McCarthy, C Hackman and R A Nelson, in Astronomical Journal, vol.136 (2008), pages 1906-1908, it is stated (page 1908), that "the SI second is equivalent to an older measure of the second of UT1, which was too small to start with and further, as the duration of the UT1 second increases, the discrepancy widens." :(2) In the late 1950s, the caesium standard was used to measure both the current mean length of the second of mean solar time (UT2) (result: 9192631830 cycles) and also the second of ephemeris time (ET) (result:9192631770 +/-20 cycles), see "Time Scales", by L. Essen, in Metrologia, vol.4 (1968), pp.161-165, on p.162. As is well known, the 9192631770 figure was chosen for the SI second. L Essen in the same 1968 article (p.162) stated that this "seemed reasonable in view of the variations in UT2".
  2. F.R. Stephenson, L.V. Morrison. " Long-term fluctuations in the Earth's rotation: 700 BC to AD 1990". Philosophical Transactions of the Royal Society of London, Series A 351 (1995) 165-202.
  3. W Markowitz, R G Hall, L Essen, J V L Parry (1958), 'Frequency of caesium in terms of ephemeris time', Phys Rev Letters v1 (1958), 105-107.
  4. L Essen, "Time Scales", Metrologia, vol.4 (1968), pp.161-165, at p.162.
  5. Wm Markowitz (1988) 'Comparisons of ET(Solar), ET(Lunar), UT and TDT', in (eds.) A K Babcock & G A Wilkins, 'The Earth's Rotation and Reference Frames for Geodesy and Geophysics', IAU Symposia #128 (1988), at pp 413-418.
  6. "And then, in 1999 for reasons still unknown, the rotation of the Earth speeded up a bit, so we haven't had to add a second since then," O'Brian told LiveScience in a telephone interview.
  7. Why the U.S. Wants To End the Link Between Time and Sun by The Wall Street Journal
  8. Leap second talks are postponed by BBC News
  9. UTC redefinition or change by Kenneth Seidelmann
  10. Cowen 2006
  11. UTC might be redefined without Leap Seconds by Steve Allen
  12. Proposed US Contribution to ITU-R WP 7A


External links

UTC redefinition

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