Markus Kuhn <Markus.Kuhn@cl.cam.ac.uk>,
	Paul Eggert <eggert@twinsun.com>

In the beginning there were only solar days: sunset was considered to
be the end of the day and the beginning of the next day.  The Jewish
and Moslem calendars, which nowadays are used only for religious
purposes, still start a new date at sunset instead of midnight.

Later, the solar days were divided into hours: 12 hours for the day and
12 hours for the night.  The different lengths of day/night were ignored,
therefore the daylight hours were longer in summer than in winter.

APPARENT (or TRUE) SOLAR TIME: Still later, the hours were made
equally long: the day+night was 24 hours.  The "day" now started at
midnight, not at sunset, which was marked as 00:00 (or 12:00 midnight
in English time format).  Noon was at 12:00 (or 12:00 noon in English
time format).  This is what we now refer to as "true solar time"---it
is the time shown by a properly setup sundial.  This time is local, it
is different for different longitudes.  (In strict English
construction, 12:00 cannot be given either an A.M. = ante meridiem or
P.M. = post meridiem designation, but it has become common to use 
12 A.M. to mean midnight and 12 P.M. to mean noon.  In traditional
English, 12 M. = meridies means _noon_; nowadays one is just as likely
to see 12 M. = midnight and 12 N. = noon.)

(In general, the old English A.M./P.M. notation is extremely
problematic.  A shorter and more obvious time notation is the modern
24h notation in which the hours in the day range from 00:00 to 23:59.
This notation even allows one to distinguish midnight at the start of
the day [00:00] from midnight at the end of the day [24:00], while the
old English notation requires kludges like starting a contract at
12:01 A.M. in order to make clear which of the two midnights
associated with a date had been intended.  The 24h notation is the
official international standard time notation (ISO 8601) and displayed
by almost all digital clocks outside the U.S.A.  The 24h notation is
also recommended by the U.S. Naval Observatory in Washington, which
defines official time in the U.S.)

MEAN SOLAR TIME: True Solar Time isn't a uniform time.  The time
difference between one noon and the next noon varies through the year,
due to two causes: 1. The earth's orbit is elliptical, not perfectly
circular, and the Earth's speed in its orbit is greater when closer to
the sun.  This makes the solar days shorter in July and longer in
January. 2. The Earth's axis of rotation does not point in the same
direction as the axis of the Earth's orbit round the Sun.  (The angle
between these two is called the "obliquity of the ecliptic" and is
about 23.45 degrees.)  This makes the solar days shorter in March and
September and longer in June and December.  To account for these
effects, a fictitious sun, "The Mean Sun," was invented: it moves with
uniform velocity in the plane of the Earth's equator, with the same
average speed as the true Sun.  This Mean Sun defines Mean Solar Time:
When the Mean Sun is due south (for northern hemisphere observers), it
is noon Mean Solar Time.  Now the time difference between two
consecutive local noons is always the same (ignoring small
irregularities in the Earth's rotation---more about that later).

SIDEREAL TIME: Closely connected with the Mean Solar Time is the
Sidereal Time, which is defined as the RA (Right Ascension) of the
Local Meridian: when the Vernal Point passes the meridian it is 00:00
Sidereal Time.  When Orion is at its maximum altitude, it is between
5h and 6h Sidereal Time; when the Big Dipper can be seen close to the
zenith it is about 12h Sidereal Time; and when Sagittarius, with all
its glories close to the center of our Galaxy, reaches maximum
altitude it is around 18h Sidereal Time.  The Sidereal Time at a
particular place and location is the same as the local Mean Solar
Time, plus 12 hours, plus the Right Ascension of the Mean Sun (which
is the same as the Mean Longitude of the true sun).  It can be
computed from this formula:

  LST(hours) = 6.6974 + 2400.051336 * T + 24 * FRAC(JD+0.5) + long/15

where:

  LST  = Local Sidereal Time in hours
  JD   = the Julian Day Number for the moment, including fractions of a day
         Note that a new Julian Day starts at Greenwich Noon
  T    = ( JD - 2451545.0 ) / 36525.0
  long = your local longitude: east positive, west negative
  FRAC = a function discarding the integral part and returning only the
         fractional part of a real number.

STANDARD TIME ZONES: Some 100+ years ago the railway made fast
transportation possible for the first time.  Quite soon it became
awkward for the travellers to continually have to adjust their clocks
when travelling between different places, and the railway companies
had the problem to select which city's time to use for their own
schedules.  An interim solution was to use a specific "railway time,"
but soon standard time zones were created.  At first the time to be
used within a country was the local time of the capital of the
country.  A few very large countries employed several time zones.  It
took a few decades to arrive at a worldwide agreement here, and in
particular there was a "battle" between England and France whether the
world's prime meridian was to be the meridian of the Greenwich or the
Paris observatory.  England won this battle, and "Greenwich Mean Time"
(GMT) was universally agreed upon as the world's standard time zones.
Almost all other parts of the world were assigned time zones, which
usually differ from GMT by an integral number of hours.  Some
countries (e.g., India) use differences that are not an integral
number of hours.

GMT (Greenwich Mean Time): This term is a historic term which is in a
strict sense obsolete, though often used (although not in astronomy,
e.g., BBC still uses this abbreviation for patriotic reasons ;-) as a
synonym for UTC.  In 1972, an international atomic time scale has been
introduced and since then, the time on the zero meridian, which goes
through the old observatory in Greenwich, London, UK, has been called
Universal Time (UT).  Prior to 1925, it was reckoned for astronomical
purposes from Greenwich mean noon (12h UT).  Sometimes GMT is referred
to as Z ("Zulu").  (This arises from the military custom of writing
times as hours and minutes run together and suffixed with a single
letter designating the time zone: 2100Z = 21:00 UTC.  The word "zulu"
is the phonetic word associated with the letter "z.")

UT (Universal time): Defined by the Earth's rotation and determined by
astronomical observations.  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. Usually one means UT2
when saying UT.  UT2 is UT corrected for pole wandering and seasonal
variations in the Earth's rotational speed.

If you are interested in time more precisely than 1 s, then you'll
have to differentiate between the following versions of Universal
Time:

 UT0 is the precise solar local time on the zero meridian. It is today
    measured by radio telescopes which observe quasars.

 UT1 is UT0 corrected by a periodic effect known as Chandler wobble or
    "polar wandering", i.e., small changes in the longitude/latitude
    of all places on the Earth due to the fact that the geographical
    poles of the Earth "wander" in semi-regular patterns: the poles
    follow (very approximately) small circles, about 10--20 meters in
    diameter, with a period of approximately 400--500 days.  The
    changes in the longitude/latitude of all places of Earth due to
    this amounts to fractions of an arc second 
    (1 arc second = 1/3600 degree).
 
 UT2 is an even better corrected version of UT0 which accounts for
    seasonal variations in the Earth's rotation rate and is sometimes
    used in astronomy.

 UTC is a time defined not by the movement of the earth, but by a
    large collection of atomic clocks located all over the world, the
    atomic time scale TAI. When UTC and UT1 are about to drift apart
    more than 0.9 s, a leap second will be inserted (or deleted, but
    this never has happened) into UTC to correct this. When necessary,
    leap seconds are inserted as the 61th second of the last UTC
    minute of June or December. During a leap second, a UTC clock
    (e.g., a radio clock such as MSF, HBG, or DCF77) shows: 

        1995-12-31 23:59:59
        1995-12-31 23:59:60
        1996-01-01 00:00:00

    Today, practically all national civil times are defined relative
    to UTC and differ from UTC by an integral number of hours
    (sometimes also half- or quarter-hours). UTC is defined in ITU-R
    Recommendation TF.460-4 and was introduced in 1972.

    If you are interested in UTC more precisely than a microsecond,
    then you also have to consider the following differences:

    The abbreviation UTC can be followed by an abbreviation of the
    organization who publishes this time reference signal.
    For example, UTC(USNO) is the US reference time published by the
    US Naval Observatory, UTC(PTB) is the official German reference
    time signal published (via a 77.5 kHz long-wave broadcast) by the
    Physikalisch Technische Bundesanstalt in Braunschweig and
    UTC(BIPM) is the most official time published by the Bureau
    International des Poids et Mesures in Paris, however UTC(BIPM) is
    only a filtered paper clock published each year that is used by
    the other time maintainers to resynchronize their clocks against
    each other. All these UTC versions do not differ by more than a
    few nanoseconds.

    The acronym UTC stands for Coordinated Universal Time.  In 1970
    when this system was being developed by the International
    Telecommunication Union, it felt it was best to designate a single
    abbreviation for use in all languages in order to minimize
    confusion.  Unanimous agreement could not be achieved on using
    either the English word order, CUT, or the French word order, TUC,
    so a compromise using neither, UTC, was adopted.

 DUT1 is the difference between UTC and UT1 as published by the US
    Naval Observatory rounded to 0.1 s each week. This results in the
    UT1 which is used e.g., for space navigation.

ET (Ephemeris Time): Somewhere around 1930--1940, astronomers noticed
that errors in celestial positions of planets could be explained by
assuming that they were due to slow variations on the Earth's
rotation.  Starting in 1960, the time scale Ephemeris Time (ET) was
introduced for astronomical purposes.  ET closely matches UT in the
19th century, but in the 20th century ET and UT have been diverging
more and more.  Currently ET is running almost precisely one minute
ahead of UT.  In 1984, ET was replaced by Dynamical Time and TT.  For
most purposes, ET up to 1983-12-31 and TDT from 1984-01-01 can be
regarded as a continuous time-scale.

TT and Dynamical Time: Introduced in 1984 as a replacement for ET, it
defines a uniform astronomical time scale more accurately, taking
relativistic effects into account.  There are two kinds of Dynamical
Time: TDT (Terrestrial Dynamical Time), which is a time scale tied to the
Earth, and TDB (Barycentric Dynamical Time), used as a time reference
for the barycenter of the solar system.  The difference between TDT and
TDB is always smaller than a few milliseconds.  When the difference
TDT-TDB is not important, TDT is referred to as TT.  For most purposes,
TDT can be considered equal to TAI + 32.184 seconds.

TAI (Temps Atomique International = International Atomic Time):
Defined by the same worldwide network of atomic clocks that defines
UTC. In contrast to UTC, TAI has no leap seconds. TAI and UTC were
identical in the late 1950s. The difference between TAI and UTC is
always an integral number of seconds. TAI is the most uniform time
scale we currently have available.


                RELATION BETWEEN THE TIME SCALES
                --------------------------------

    TDT = TAI+32.184s  ==>  UT-UTC = TAI-UTC - (TDT-UT) + 32.184s

    Starting at    TAI-UTC  ET/TDT-UT  UT-UTC
    
    1972-01-01     +10.00    +42.23    -0.05
    1972-07-01     +11.00    +42.80    +0.38
    1973-01-01     +12.00    +43.37    +0.81
    1973-07-01       -"-     +43.93    +0.25
    1974-01-01     +13.00    +44.49    +0.69
    1974-07-01       -"-     +44.99    +0.19
    1975-01-01     +14.00    +45.48    +0.70
    1975-07-01       -"-     +45.97    +0.21
    1976-01-01     +15.00    +46.46    +0.72
    1976-07-01       -"-     +46.99    +0.19
    1977-01-01     +16.00    +47.52    +0.66
    1977-07-01       -"-     +48.03    +0.15
    1978-01-01     +17.00    +48.53    +0.65
    1978-07-01       -"-     +49.06    +0.12
    1979-01-01     +18.00    +49.59    +0.59
    1979-07-01       -"-     +50.07    +0.11
    1980-01-01     +19.00    +50.54    +0.64
    1980-07-01       -"-     +50.96    +0.22
    1981-01-01       -"-     +51.38    -0.20
    1981-07-01     +20.00    +51.78    +0.40
    1982-01-01       -"-     +52.17    +0.01
    1982-07-01     +21.00    +52.57    +0.61
    1983-01-01       -"-     +52.96    +0.22
    1983-07-01     +22.00    +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     +23.00    +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     +24.00    +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     +25.00    +56.86    +0.32
    1990-07-01       -"-     +57.22    -0.04
    1991-01-01     +26.00    +57.57    +0.61
    1991-07-01       -"-     +57.94    +0.24
    1992-01-01       -"-     +58.31    -0.13
    1992-07-01     +27.00    +58.72    +0.46
    1993-01-01       -"-     +59.12    +0.06
    1993-07-01     +28.00    +59.5     +0.7
    1994-01-01       -"-     +59.9     +0.3
    1994-07-01     +29.00    +60.3     +0.9
    1995-01-01       -"-     +60.7     +0.5
    1995-07-01       -"-     +61.1     +0.1
    1996-01-01     +30.00    +61.63    +0.55
    1996-07-01       -"-     +62.0     +0.2
    1997-01-01       -"-     +62.4     -0.2
    1997-07-01     +31.00    +62.8     +0.4
    1998-01-01       -"-     +63.3     -0.1
    1998-07-01       -"-     +63.7     -0.5
    1999-01-01     +32.00    +64.1     +0.1

Additional information about the world time standard UTC (e.g., when
will the next leap second be inserted in time) is available from the
US Naval Observatory and the International Earth Rotation Service
(IERS):

<URL:http://tycho.usno.navy.mil/time.html>
<URL:http://tycho.usno.navy.mil/gps_datafiles.html>
<URL:http://maia.usno.navy.mil/>
<URL:ftp://maia.usno.navy.mil/ser7/tai-utc.dat>
<URL:ftp://tycho.usno.navy.mil/pub/series/ser14.txt>
<URL:ftp://maia.usno.navy.mil/ser7/deltat.preds>
     
<URL:ftp://mesiom.obspm.fr/iers/>. 
<URL:ftp://hpiers.obspm.fr/iers/bul/bulc/BULLETINC.GUIDE>
     
Also <URL:http://www.eecis.udel.edu/~ntp/> is a good start if you want
to learn more about time standards.