Astronomical Time Systems
Time can be defined using several different phenomena:
1. The solar and sidereal times are based on the rotation of the Earth.
2. The standard unit of time in the current SI system, the second, is based on quantum mechanical atomary phenomena.
3. Equations of physics like the ones describing the motions of celestial bodies involve a time variable
WORLD MAP OF TIME ZONES
s% International Date Line \
s% International Date Line \
Fig. 2.31. The time zones. The map gives the difference of the local zonal time from the Greenwich mean time (UT). During daylight saving time, one hour must be added to the given figures. When travelling across the date line westward, the date must be incremented by one day, and decremented if going eastward. For example, a traveller taking a flight from Honolulu to Tokyo on Monday morning will arrive on Tuesday, even though (s)he does not see a single night en route. (Drawing U.S. Nval Observatory)
corresponding to an ideal time running at a constant pace. The ephemeris time and dynamical time discussed a little later are such times.
Observations give directly the apparent sidereal time as the hour angle of the true vernal equinox. From the apparent sidereal time the mean sidereal time can be calculated.
The universal time UT is defined by the equation GMST(0UT) = 24,110.54841 s
+ T x 8,640,184.812866 s + T2 x 0.093104 s  T3 x 0.0000062 s ,
where GMST is the Greenwich mean sidereal time and T the Julian century. The latter is obtained from the Julian date J, which is a running number of the day (Sect. 2.15 and *Julian date, p. 41):
This gives the time elapsed since January 1, 2000, in Julian centuries.
Sidereal time and hence also UT are related to the rotation of the Earth, and thus contain perturbations due to the irregular variations, mainly slowing down, of the rotation.
In (2.47) the constant 8,640,184.812866 s tells how much sidereal time runs fast compared to the UT in a Julian century. As the rotation of the Earth is slowing down the solar day becomes longer. Since the Julian century T contains a fixed number of days, it will also become longer. This gives rise to the small correction terms in (2.47).
Strictly speaking this universal time is the time denoted by UT1. Observations give UT0, which contains a small perturbation due to the wandering of the geographical pole, or polar variation. The direction of the axis with respect to the solid surface varies by about 0.1" (a few metres on the surface) with a period of about 430 days (Chandler period). In addition to this, the polar motion contains a slow nonperiodic part.
The z axis of the astronomical coordinates is aligned with the angular momentum vector of the Earth, but the terrestrial coordinates refer to the axis at the epoch 1903.5. In the most accurate calculations this has to be taken into account.
Nowadays the SI unit of time, the second, is defined in a way that has nothing to do with celestial phenomena. Periods of quantum mechanical phenomena remain more stable than the motions of celestial bodies involving complicated perturbations.
In 1967, one second was defined as 9,192,631,770 times the period of the light emitted by cesium 133 isotope in its ground state, transiting from hyperfine level F = 4 to F = 3. Later, this definition was revised to include small relativistic effects produced by gravitational fields. The relative accuracy of this atomic time is about 1012.
The international atomic time, TAI, was adopted as the basis of time signals in 1972. The time is maintained by the Bureau International des Poids et Mesures in Paris, and it is the average of several accurate atomic clocks.
Even before atomic clocks there was a need for an ideal time proceeding at a perfectly constant rate, corresponding to the time variable in the equations of Newtonian mechanics. The ephemeris time was such a time. It was used e. g. for tabulating ephemerides. The unit of ephemeris time was the ephemeris second, which is the length of the tropical year 1900 divided by 31,556,925.9747. Ephemeris time was not known in advance. Only afterwards was it possible to determine the difference of ET and UT from observational data.
In 1984 ephemeris time was replaced by dynamical time. It comes in two varieties.
The terrestrial dynamical time (TDT) corresponds to the proper time of an observer moving with the Earth. The time scale is affected by the relativistic time dilation due to the orbital speed of the Earth. The rotation velocity depends on the latitude, and thus in TDT it is assumed that the observer is not rotating with the Earth. The zero point of TDT was chosen so that the old ET changed without a jump to TDT.
In 1991 anew standard time, the terrestrial time (TT), was adopted. Practically it is equivalent to TDT.
TT (or TDT) is the time currently used for tabulating ephemerides of planets and other celestial bodies. For example, the Astronomical Almanac gives the coordinates of the planets for each day at 0 TT.
The Astronomical Almanac also gives the difference
Fig. 2.32. The difference between the universal time UT1, based on the rotation of the Earth, and the coordinated universal time UTC during 19722002. Because the rotation of the Earth is slowing down, the UT1 will run slow of the UTC by about 0.8 seconds a year. Leap seconds are added to the UTC when necessary to keep the times approximately equal. In the graph these leap seconds are seen as one second jumps upward
A leap second is added either at the beginning of a year or the night between June and July. The difference
Fig. 2.32. The difference between the universal time UT1, based on the rotation of the Earth, and the coordinated universal time UTC during 19722002. Because the rotation of the Earth is slowing down, the UT1 will run slow of the UTC by about 0.8 seconds a year. Leap seconds are added to the UTC when necessary to keep the times approximately equal. In the graph these leap seconds are seen as one second jumps upward for earlier years. For the present year and some future years a prediction extrapolated from the earlier years is given. Its accuracy is about 0.1 s. At the beginning of 1990 the difference was 56.7 s; it increases every year by an amount that is usually a little less than one second.
The terrestrial time differs from the atomic time by a constant offset is also tabulated in the Astronomical Almanac. According to the definition of UTC the difference in seconds is always an integer. The difference cannot be predicted very far to the future.
which gives the terrestrial time TT corresponding to a given UTC. Table 2.2 gives this correction. The table is easy to extend to the future. When it is told in the news that a leap second will be added the difference will increase by one second. In case the number of leap seconds is not known, it can be approximated that a leap second will be added every 1.25 years.
The unit of the coordinated universal time UTC, atomic time TAI and terrestrial time TT is the same
Table 2.2. Differences of the atomic time and UTC (A AT) and the terrestrial time TT and UTC. The terrestrial time TT used in ephemerides is obtained by adding A AT + 32.184 s to the ordinary time UTC
TT is well suited for ephemerides of phenomena as seen from the Earth. The equations of motion of the solar system, however, are solved in a frame the origin of which is the centre of mass or barycentre of the solar system. The coordinate time of this frame is called the barycentric dynamical time, TDB. The unit of TDB is defined so that, on the average, it runs at the same rate as TT, the difference containing only periodic terms depending on the orbital motion of the Earth. The difference can usually be neglected, since it is at most about 0.002 seconds.
Which of these many times should we use in our alarmclocks? None of them. Yet another time is needed for that purpose. This official wallclock time is called the coordinated universal time, UTC. The zonal time follows UTC but differs from it usually by an integral number of hours.
UTC is defined so that it proceeds at the same rate as TAI, but differs from it by an integral number of seconds. These leap seconds are used to adjust UTC so that the difference from UT1 never exceeds 0.9 seconds.
Table 2.2. Differences of the atomic time and UTC (A AT) and the terrestrial time TT and UTC. The terrestrial time TT used in ephemerides is obtained by adding A AT + 32.184 s to the ordinary time UTC
AAT 
TT  UTC  
1.1.1972 30.6.1972 
10 s 
42.184 s 
1.7.197231.12.1972 
11 s 
43.184 s 
1.1.197331.12.1973 
12s 
44.184 s 
1.1.197431.12.1974 
13 s 
45.184 s 
1.1.197531.12.1975 
14 s 
46.184 s 
1.1.197631.12.1976 
15 s 
47.184 s 
1.1.197731.12.1977 
16 s 
48.184 s 
1.1.197831.12.1978 
17 s 
49.184 s 
1.1.197931.12.1979 
18s 
50.184 s 
1.1.1980 30.6.1981 
19 s 
51.184s 
1.7.1981 30.6.1982 
20 s 
52.184 s 
1.7.1982 30.6.1983 
21 s 
53.184 s 
1.7.1983 30.6.1985 
22 s 
54.184 s 
1.7.198531.12.1987 
23 s 
55.184 s 
1.1.198831.12.1989 
24 s 
56.184 s 
1.1.199031.12.1990 
25 s 
57.184 s 
1.1.1991 30.6.1992 
26 s 
58.184 s 
1.7.1992 30.6.1993 
27 s 
59.184 s 
1.7.1993 30.6.1994 
28 s 
60.184 s 
1.7.199431.12.1995 
29 s 
61.184s 
1.1.1996 31.6.1997 
30 s 
62.184 s 
1.7.199731.12.1998 
31 s 
63.184 s 
1.1.199931.12.2005 
32 s 
64.184 s 
1.1.2006 
33 s 
65.184 s 
second of the SI system. Hence all these times proceed at the same rate, the only difference being in their zero points. The difference of the TAI and TT is always the same, but due to the leap seconds the UTC will fall behind in a slightly irregular way.
Culminations and rising and setting times of celestial bodies are related to the rotation of the Earth. Thus the sidereal time and hence the UT of such an event can be calculated precisely. The corresponding UTC cannot differ from the UT by more than 0.9 seconds, but the exact value is not known in advance. The future coordinates of the Sun, Moon and planets can be calculated as functions of the TT, but the corresponding UTC can only be estimated.
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