Global Positioning System Reference
In-Depth Information
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GMST from (2.33) and substitute it in (2.31). Finally, assuming that the observations
were taken at known UTC epochs, Expression (2.31) can be solved for the correction
∆
UT1
=
UT1
−
UTC
(2.39)
UTC is related to TAI as established by atomic clocks. Briefly, at the 13th General
Conference of Weights and Measures (CGPM) in Paris in 1967, the definition of
the atomic second, also called the international system (SI) second, was defined as
the duration of 9,192,631,770 periods of the radiation corresponding to the state-
energy transition between two hyperfine levels of the ground state of the cesium-133
atom. This definition made the atomic second agree with the length of the ephemeris
time (ET) second, to the extent that measurement allowed. ET was the most stable
time available around 1960 but is no longer in use. ET was derived from orbital
positions of the earth around the sun. Its second was defined as a fraction of the
year 1900. Because of the complicated gravitational interactions between the earth
and the moon, potential loss of energy due to tidal frictions, etc., the realization
of ET was difficult. Its stability eventually did not meet the demands of emerging
measurement capabilities. It served as an interim time system. Prior to ET, time was
defined in terms of the earth rotation, the so-called earth rotational time scales such
as GMST. The rotational time scales were even less constant because of the earth's
rotational variations. It takes a good cesium clock 20 to 30 million years to gain or
lose one second. Under the same environmental conditions, atomic transitions are
identical from atom to atom and do not change their properties. Clocks based on
such transitions should generate the same time. Bergquist et al. (2001) offer up-to-
date insight on modern atomic clocks.
TAI is based on the SI second; its epoch is such that ET
[26
Lin
—
0.0
——
Nor
PgE
[26
32
s
.
184 on
January 1, 1977. TAI is related to state transitions of atoms and not to the rotation
of the earth. Even though atoms are suitable to define an extremely constant time
scale, it could in principle happen that in the distant future we would have noon, i.e.,
lunchtime at midnight TAI. The hybrid time scale UTC avoids a possible divergence
by using the SI second but changing the epoch labeling such that
−
TA I
=
<
0
s
.
9
|∆
UT1
|
(2.40)
UTC is the time that is broadcast on TV, on radio, and by other time services.
To visualize the mean universal time (UT1), consider a mean (mathematical) earth
traveling in the ecliptic in a circular orbit at constant angular rate. Let this mean
earth begin its motion at the time when the true earth is in the direction of the vernal
equinox. At each consecutive annual rotation, the mean earth and the true earth should
arrive at the vernal equinox at the same time. One often adopts the view as seen
from the center of the earth. In that case, one speaks about a mean sun moving around
the earth at a constant rate. Twenty-four hours of UT1, i.e., a mean solar day, equals
the time it takes for two consecutive transits of the sun over a meridian of the mean
earth, or equivalently, two consecutive transits of the mean sun when viewed from the
earth-fixed reference frame. If we consider the actual earth or sun, as opposed to their
