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times, there was the concept of two-part clocks for timekeeping. The rotation of Earth provided the first component
of the clock in terms of the periodic events of sunrise and sunset; a calendar provided the second component of the
clock to count days, months, and years.
Based on Earth's rotation on its axis, several time scales, known as Universal Time (UT), have been used. Earth
motion, around its axis and the sun, is irregular. Because of the irregularities in Earth motion, the length of the
day from day to day and the number of the fractional days in a year from year to year vary. A solar day (also called
an apparent or true solar day) is the length of time measured by observing two consecutive passings of the sun at
local noon. If you use a perfect clock to observe the sun at a local meridian at noon every day, you would find that,
throughout the year, position of the sun in the sky varies about four degrees (about 16 minutes in time) East-West of
the local meridian. This implies that, on a particular day during a year, there could be up to 16 minutes difference
between the time when it is noon shown by the clock and when the sun passes the local meridian. The difference
between the clock time and the sun time, which arises because of the tilt of the earth rotation axis relative to its orbital
plane and its elliptical orbit around the sun, is known as the equation of time. The time that is measured using the
solar day is called apparent solar time.
The time obtained by applying corrections to the solar time to account for the equation of time is known as
Universal Time Zero (UT0) or mean solar time. The midnight at prime meridian (zero degree longitude), which passes
through Greenwich, England, is defined as 00 hours for UT0. The second is defined as 1/86400 of a mean solar day.
The wobbling of Earth relative to its axis of rotation is known as polar motion. UT0 corrected for polar motion
yields another time scale, which is called UT1. Earth's rotational speed is not uniform. UT1 corrected for the seasonal
variation in the rotational speed of Earth yields another time scale, which is called UT2.
The irregular spin rate of Earth led to another time scale known as Ephemeris Time (ET). ET was based on the
period of one revolution of Earth around the sun and motion of other celestial bodies. On ET scale, the ephemeris
second was defined as the fraction 1/31556925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.
ET was replaced by Terrestrial Dynamical Time (TDT) and Barycentric Dynamical Time (TDB) in early 1980s.
The International Atomic Time (also known as TAI, for the French name Temps Atomique International) scale
is an atomic time scale. The atomic second, the unit of time in the TAI scale, is defined as the duration of 9192631770
periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the
cesium-133 atom. In 1967, the definition of the atomic second became the definition of the International System of
Units (SI) second. The International Bureau of Weights and Measures (BIPM) is the official timekeeper of atomic time.
There are 65 laboratories with over 230 atomic clocks contributing to the TAI scale. Each clock contributing to TAI is
assigned a weighting factor based on its performance. The weighted average of all the contributing atomic clocks
gives TAI.
Why do we use many atomic clocks to measure TAI? One clock may fail and stop measuring time. Even atomic
clocks are affected by environmental changes. To avoid such failures and inaccuracies, several atomic clocks are used
to track TAI.
On January 1, 1972, Coordinated Universal Time (UTC) was adopted as the official time scale for the world for all
civil purposes. UTC and atomic clocks run at the same rate. As BIPM counts the seconds on TAI scale, astronomers
continue to measure time using the rotation of earth on its axis. Astronomical time is compared to UTC, and if they
differ by more than 0.9 seconds, a leap second is added or subtracted to UTC to keep the time scales UT0 and UTC as
close as possible. International Earth Rotation Service (IERS) makes the decision to introduce a leap second to UTC.
At any time, UTC differs from TAI by an integral number of seconds. The relation between UTC and TAI may be
given as follows:
UTC = TAI - (algebraic sum of leap seconds)
As of July 1, 2012, 35 leap seconds have been added to UTC. So far, no leap second has been subtracted from
UTC. Therefore, on July 1, 2012 and until another leap second is introduced, UTC and TAI are related as follows:
UTC = TAI - 35
 
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