T I M E S C A L E S

By Paul Schlyter, Stockholm, Sweden
email: pausch@stjarnhimlen.se WWW: http://stjarnhimlen.se/

1993? First version as an ASCII document.
1995 and on: Posted on Usenet several times and became part of the sci.astro FAQ part 3
2004-09-?? First HTML version, for an article in the Swedish ham radio magazine QTC
2005-04-19 Replaced obsolete links with working ones
2005-06-22 Major overhaul: corrected several small errors, updated tables, added new links.
Thanks to John Stockton (http://www.merlyn.demon.co.uk/) for a number of suggestions to this page.
2005-07-10 Added a link to Steve Allen's detailed history of the time scales.


The different time scales

TAI = International Atomic Time (Temps Atomique International = TAI) is
      defined as the weighted average of the time kept by about 200
      atomic clocks in over 50 national laboratories worldwide.
      TAI-UT1 was approximately 0 on 1958 Jan 1.


UTC = Coordinated Universal Time. Differs from TAI by an integral
      number of seconds. When needed, leap seconds are introduced in UTC
      to keep the difference between UTC and UT less than 0.9 s.
      UTC was introduced in 1972.


UT  = Universal time. Defined by the Earth's rotation, formerly determined
      by astronomical observations but today GPS satellites are used
      instead.  This time scale is slightly irregular.  There are several
      different definitions of UT, but the difference between them is always
      less than about 0.03 s.

UT0 = "raw", uncorrected UT as derived from meridian circle observations
      or from more modern methods involving GPS satellites.

UT1 = UT0 corrected for polar wandering - usually one means UT1 when
      saying UT.

UT2 = UT1 corrected for seasonal variations in the Earth's rotational
      speed, by adding
             + 0.022 * sin(2*pi*t) - 0.017 * cos(2*pi*t)
             - 0.007 * sin(4*pi*t) + 0.006 * cos(4*pi*t)
      seconds to UT1, where t is the fraction of the year (zero at 1 Jan).
      UT2 is nowadays considered obsolete.
      

ET  = Ephemeris Time. Was used 1960-1983, and was replaced by TDT and TDB
      in 1984.  For most purposes, ET up to 1983 Dec 31 and TDT from 1984
      Jan 1 can be regarded as a continuous time-scale.

TDT = Terrestial Dynamical Time.  Was used 1984-2000 as a time-scale of
      ephemerides from the Earth's surface.  TDT = TAI + 32.184.  Replaced
      ET (Ephemeris Time) in 1984, was replaced by TT (Terrestial Time)
      in 2001.

TDB = Barycentric Dynamical Time. Used as a time-scale of ephemerides
      referred to the barycentre of the solar system. Differs from TDT
      by at most a few milliseconds.
          TDB  =  TT  +  0.001 658s * sin(g)  +  0.000 014s * sin(2*g)
            g  =  357.53_d + 0.985 600 28_d * ( JD - 245 1545.0 )
          (higher order terms neglected; g = Earth's mean anomaly)

TT  = Terrestial Time. Originally used instead of TDT or TDB when the
      difference between them didn't matter.  Was defined in 1991 to be
      consistent with the SI second and the General Theory of Relativity.
      Replaced TDT in the ephemerides from 2001 and on.

TCG = Geocentric Coordinate Time. Defined in 1991 along with TT

TCB = Barycentric Coordinate Time. Defined in 1991 along with TT


delta-T =
      ET - UT   prior to 1984
      TDT - UT  1984 - 2000
      TT - UT   from 2001 and on

delta-UT =  UT - UTC

DUT = predicted value of delta-UT, rounded to 0.1s, given in some radio
      time signals.


GPS time = TAI - 19 seconds.  GPS time matched UTC from 1980-01-01
      to 1981-07-01.  No leap seconds are inserted into GPS time, thus
      GPS time is 13 seconds ahead of UTC on 2000-01-01.  The GPS epoch
      is 00:00 (midnight) UTC on 1980-01-06.
      The differences between GPS Time and International Atomic Time (TAI)
      and Terrestrial Time (TT), also know as Terrestrial Dynamical Time
      (TDT), are constant at the level of some tens of nanoseconds while
      the difference between GPS Time and UTC changes in increments of
      seconds each time a leap second is added to UTC time scale.

GPS week = a numbering of weeks starting at the GPS epoch 1980-01-06 00:00
      GPS time (which back then was equal to UTC).  Weeks are numbered from
      0 and up until 1023, then it "rolls back" to 0 and are again numbered
      from 0 and up, etc.  One GPS week rollover cycle is therefore 1024
      weeks = 7168 days = ca 19.62 years.  So far there's been one such GPS
      week number roll-over, on 1999-08-22 00:00 GPS time - a few older GPS
      receivers then ceased to show the correct date.


                                                 ET 1960-1983
                                                TDT 1984-2000
 UTC 1972-  GPS 1980-    TAI 1958-               TT 2001-
----+---------+-------------+-------------------------+-----
    |         |             |                         |
    |<------ TAI-UTC ------>|<-----   TT-TAI    ----->|
    |         |             |      32.184s fixed      |
    |<GPS-UTC>|<- TAI-GPS ->|                         |
    |         |  19s fixed  |                         |
    |                                                 |
    <> delta-UT = UT1-UTC                             |
     | (max 0.9 sec)                                  |
-----+------------------------------------------------+-----
     |<-------------- delta-T = TT-UT1 -------------->|
    UT1 (UT)                                       TT/TDT/ET




Older time scales:

GMT = Greenwich Mean Time.  It's ambiguous, and is now used (although
      not in astronomy) in the sense of UTC in addition to the earlier
      sense of UT (in astronomical navigation, GMT still means UT).
      Prior to 1925, GMT was reckoned for astronomical purposes from
      Greenwich mean noon (12h UT) to avoid a date change in the middle
      of the night in Europe - a new GMT date then started 12 hours after
      the start of the corresponding civil date.  (Prior to 1805 the
      Royal Navy Day started 12 hour before local mean solar time, thus
      the Royal Navy Day was then approx. 24 hours ahead of GMT).

GCT = Greenwich Civil Time.  Used in the US from 1925 to mean the "new"
      GMT starting at Greenwich mean midnight, to distinguish it from
      the "old" GMT.  When UT was adopted, GCT fell out of use.

LMT = Local Mean Time.  The mean solar time at the local meridian.

LCT = Local Civil Time, the same as LMT.  Used in the US together with GCT.



Delta-T

delta-T varies continuously, depending on the Earth's rotation.

UT1 is variable with respect to UTC. Leap seconds were introduced in UTC to keep delta-UT within +-0.9s.

TAI-UTC is always an integral number of seconds, and is varied when leap seconds are added (or removed, but that hasn't happened yet) at the end of every year, or every half-year, or every third month, in that order of priority.


Table of time scales 1972-present, and some predictions

TT = TAI+32.184s ==> UT-UTC = TAI-UTC - (TT-UT) + 32.184s
Starting at    TAI-UTC   GPS-UTC   TT-UT1    UT1-UTC

1972-01-01       +10       -       +42.23    -0.05
1972-07-01       +11       -       +42.80    +0.38
1973-01-01       +12       -       +43.37    +0.81
1973-07-01        "        -       +43.93    +0.25
1974-01-01       +13       -       +44.49    +0.69
1974-07-01        "        -       +44.99    +0.19
1975-01-01       +14       -       +45.48    +0.70
1975-07-01        "        -       +45.97    +0.21
1976-01-01       +15       -       +46.46    +0.72
1976-07-01        "        -       +46.99    +0.19
1977-01-01       +16       -       +47.52    +0.66
1977-07-01        "        -       +48.03    +0.15
1978-01-01       +17       -       +48.53    +0.65
1978-07-01        "        -       +49.06    +0.12
1979-01-01       +18       -       +49.59    +0.59
1979-07-01        "        -       +50.07    +0.11
1980-01-01       +19       0       +50.54    +0.64
1980-07-01        "        "       +50.96    +0.22
1981-01-01        "        "       +51.38    -0.20
1981-07-01       +20       1       +51.78    +0.40
1982-01-01        "        "       +52.17    +0.01
1982-07-01       +21       2       +52.57    +0.61
1983-01-01        "        "       +52.96    +0.22
1983-07-01       +22       3       +53.38    +0.80
1984-01-01        "        "       +53.79    +0.39
1984-07-01        "        "       +54.07    +0.11
1985-01-01        "        "       +54.34    -0.16
1985-07-01       +23       4       +54.61    +0.57
1986-01-01        "        "       +54.87    +0.31
1986-07-01        "        "       +55.10    +0.08
1987-01-01        "        "       +55.32    -0.14
1987-07-01        "        "       +55.57    -0.39
1988-01-01       +24       5       +55.82    +0.36
1988-07-01        "        "       +56.06    +0.12
1989-01-01        "        "       +56.30    -0.12
1989-07-01        "        "       +56.58    -0.40
1990-01-01       +25       6       +56.86    +0.32
1990-07-01        "        "       +57.22    -0.04
1991-01-01       +26       7       +57.57    +0.61
1991-07-01        "        "       +57.94    +0.24
1992-01-01        "        "       +58.31    -0.13
1992-07-01       +27       8       +58.72    +0.46
1993-01-01        "        "       +59.12    +0.06
1993-07-01       +28       9       +59.55    +0.63
1994-01-01        "        "       +59.98    +0.20
1994-07-01       +29      10       +60.38    +0.80
1995-01-01        "        "       +60.78    +0.40
1995-07-01        "        "       +61.20    -0.02
1996-01-01       +30      11       +61.63    +0.55
1996-07-01        "        "       +61.96    +0.22
1997-01-01        "        "       +62.29    -0.11
1997-07-01       +31      12       +62.63    +0.55
1998-01-01        "        "       +62.97    +0.21
1998-07-01        "        "       +63.22    -0.04
1999-01-01       +32      13       +63.47    +0.71
1999-07-01        "        "       +63.66    +0.52
2000-01-01        "        "       +63.82    +0.36
2000-07-01        "        "       +63.98    +0.20
2001-01-01        "        "       +64.09    +0.09
2001-07-01        "        "       +64.20    -0.02
2002-01-01        "        "       +64.30    -0.12
2002-07-01        "        "       +64.41    -0.23
2003-01-01        "        "       +64.47    -0.29
2003-07-01        "        "       +64.55    -0.37
2004-01-01        "        "       +64.57    -0.39
2004-07-01        "        "       +64.65    -0.47
2005-01-01        "        "       +64.68    -0.50
2005-07-01        "        "       +64.80    -0.62
2006-01-01       +33      14       +64.85    +0.33
2006-07-01        "        "       +64.99    +0.19
2007-01-01        "        "       +65.15    +0.03
2007-07-01        "        "       +65.34    -0.16
2008-01-01        "        "       +65.45    -0.27
2008-07-01        "        "       +65.63    -0.45
2009-01-01       +34      15       +65.78    +0.40
2009-07-01        "        "       +65.95    +0.23
2010-01-01        "        "       +66.07    +0.11
2010-07-01        "        "       +66.24    -0.06
2011-01-01        "        "       +66.32    -0.14
2011-07-01        "        "       +66.47    -0.29
2012-01-01        "        "       +66.60    -0.42
2012-07-01       +35      16       +66.77    +0.41
2013-01-01        "        "       +66.91    +0.27
2013-07-01        "        "       +67.13    +0.05
2014-01-01        "        "       +67.3     -0.1   (pred)
2015-01-01        "        "       +67.7     -0.5   (pred)
2016-01-01        ?        ?       +68              (pred)
2017-01-01        ?        ?       +69              (pred)
2018-01-01        ?        ?       +69              (pred)
2019-01-01        ?        ?       +70              (pred)
2020-01-01        ?        ?       +70              (pred)
2021-01-01        ?        ?       +71              (pred)
2022-01-01        ?        ?       +71              (pred)
2023-01-01        ?        ?       +72              (pred)

(last updated 2013-07-10)

Delta-T 1620-1972

delta-T = ET - UT for the years 1620 - 1972
         ET-UT, s

Year      +0.0     +1.0    +2.0     +3.0     +4.0
----------------------------------------------------
1620      +124     +119    +115     +110     +106
1625      +102      +98     +95      +91      +88
1630       +85      +82     +79      +77      +74
1635       +72      +70     +67      +65      +63
1640       +62      +60     +58      +57      +55
1645       +54      +53     +51      +50      +49
1650       +48      +47     +46      +45      +44
1655       +43      +42     +41      +40      +38
1660       +37      +36     +35      +34      +33
1665       +32      +31     +30      +28      +27
1670       +26      +25     +24      +23      +22
1675       +21      +20     +19      +18      +17
1680       +16      +15     +14      +14      +13
1685       +12      +12     +11      +11      +10
1690       +10       +9      +9       +9       +9
1695        +9       +9      +9       +9       +9
1700       +10       +9      +9       +9       +9
1705        +9       +9      +9      +10      +10
1710       +10      +10     +10      +10      +10
1715       +10      +10     +11      +11      +11
1720       +11      +11     +11      +11      +11
1725       +11      +11     +11      +11      +11
1730       +11      +11     +11      +11      +12
1735       +12      +12     +12      +12      +12
1740       +12      +12     +12      +12      +13
1745       +13      +13     +13      +13      +13
1750       +13      +14     +14      +14      +14
1755       +14      +14     +14      +15      +15
1760       +15      +15     +15      +15      +15
1765       +16      +16     +16      +16      +16
1770       +16      +16     +16      +16      +16
1775       +17      +17     +17      +17      +17
1780       +17      +17     +17      +17      +17
1785       +17      +17     +17      +17      +17
1790       +17      +17     +16      +16      +16
1795       +16      +15     +15      +14      +14
1800       +13.7    +13.4   +13.1    +12.9    +12.7
1805       +12.6    +12.5   +12.5    +12.5    +12.5
1810       +12.5    +12.5   +12.5    +12.5    +12.5
1815       +12.5    +12.5   +12.4    +12.3    +12.2
1820       +12.0    +11.7   +11.4    +11.1    +10.6
1825       +10.2     +9.6    +9.1     +8.6     +8.0
1830        +7.5     +7.0    +6.6     +6.3     +6.0
1835        +5.8     +5.7    +5.6     +5.6     +5.6
1840        +5.7     +5.8    +5.9     +6.1     +6.2
1845        +6.3     +6.5    +6.6     +6.8     +6.9
1850        +7.1     +7.2    +7.3     +7.4     +7.5
1855        +7.6     +7.7    +7.7     +7.8     +7.8
1860        +7.88    +7.82   +7.54    +6.97    +6.40
1865        +6.02    +5.41   +4.10    +2.92    +1.81
1870        +1.61    +0.10   -1.02    -1.28    -2.69
1875        -3.24    -3.64   -4.54    -4.71    -5.11
1880        -5.40    -5.42   -5.20    -5.46    -5.46
1885        -5.79    -5.63   -5.64    -5.80    -5.66
1890        -5.87    -6.01   -6.19    -6.64    -6.44
1895        -6.47    -6.09   -5.76    -4.66    -3.74
1900        -2.72    -1.54   -0.02    +1.24    +2.64
1905        +3.86    +5.37   +6.14    +7.75    +9.13
1910       +10.46   +11.53   +13.36   +14.65   +16.01
1915       +17.20   +18.24   +19.06   +20.25   +20.95
1920       +21.16   +22.25   +22.41   +23.03   +23.49
1925       +23.62   +23.86   +24.49   +24.34   +24.08
1930       +24.02   +24.00   +23.87   +23.95   +23.86
1935       +23.93   +23.73   +23.92   +23.96   +24.02
1940       +24.33   +24.83   +25.30   +25.70   +26.24
1945       +26.77   +27.28   +27.78   +28.25   +28.71
1950       +29.15   +29.57   +29.97   +30.36   +30.72
1955       +31.07   +31.35   +31.68   +32.18   +32.68
1960       +33.15   +33.59   +34.00   +34.47   +35.03
1965       +35.73   +36.54   +37.43   +38.29   +39.20
1970       +40.18   +41.17   +42.23

Links to more information

More information can be obtained at:

Wikipedia: http://en.wikipedia.org/wiki/International_Atomic_Time

Steve Allen's detailed history of the different time scales: http://www.ucolick.org/~sla/leapsecs/timescales.html

BIPM - Bureau International des Poids et Mesures: http://www.bipm.fr/en/scientific/tai/

USNO Time Service Department: http://tycho.usno.navy.mil/

IERS - International Earth Rotation and Reference Systems Service: http://www.iers.org/

Past leap seconds info:
ftp://maia.usno.navy.mil/ser7/tai-utc.dat

Delta-T data: ftp://maia.usno.navy.mil/ser7/deltat.data TT/ET - UT1 UT1-UTC data: ftp://maia.usno.navy.mil/ser7/
Daily data since 1972, and predictions -- large! ftp://maia.usno.navy.mil/ser7/finals.all
Explanation to the previous file ftp://maia.usno.navy.mil/ser7/readme.finals

Rapid service and prediction of Earth orientation parameters: http://maia.usno.navy.mil/

USNO Earth Orientation Service: http://maia.usno.navy.mil/eo/eo_prod.html

IERS - International Earth Rotation Service: http://hpiers.obspm.fr/
IERS Leap Seconds Bulletins: ftp://hpiers.obspm.fr/iers/bul/bulc/ ftp://hpiers.obspm.fr/iers/bul/bulc/bulletinc.dat
Info on GPS time:
http://tycho.usno.navy.mil/gpstt.html
http://tycho.usno.navy.mil/gps_datafiles.html


Time signals by shortwave radio

Europe:
RWM (Moscow)    CW   4996, 9996, 14996 kHz

North America:
WWV (USA)       AM   2500, 5000, 10000, 15000, 20000  kHz
CHU (Canada)    AM   3330, 7335, 14670  kHz
Worldwide list - Another list - Time signals (Wikipedia)

World standard time zones


In October 1884, an International Time Conference adopted the Greenwich Meridian as the prime meridian or zero degree point and divided the world into 24 equal divisions of 15 degrees each.

Here is a table of the current International Time Zones:
http://en.wikipedia.org/wiki/Time_zone
Map of time zones