## Info

a Astronomical Almanac for 2002, US Naval Obs. and Royal Greenwich Obs.

(US Govt. Printing Office). All offsets from 1988-2002 are listed. b ET - UT

a history of the changing offsets of TT and TAI from UTC. For example, during the 1989-1993 mission of the Hipparcos satellite, the TT offsets were 56-59 s and at the end of the century it was, and is at this writing, 64.184 s (Table 1). The irregular variation of the earth spin is evident from the irregular intervals between inserted leap seconds in Table 1. Table 1 shows that TAI was set to agree with UTC in 1958 and TT (actually ET) was set to agree with UTC in 1902. This is the origin of the 32.184 s offset in (16).

Keep in mind that an added leap second in UTC amounts to holding back the clock for one second before it becomes the next day. Thus TT times are increasingly greater than are UTC times, insofar as the leap seconds continue to be positive. One could imagine that someone, someplace, has a 24-h clock that reads TT time; i.e.,it is never held back by the insertion of a leap second. It would be running ahead (fast) of a UTC clock by about 1 minute. If I were waiting to celebrate my birthday on 1990 Dec. 7, the TT clock would allow me to start whooping it up 57.184 s before the UTC clock strikes midnight.

If I wanted to know how many SI seconds (atomic time) I had lived, I would find the number of days since my date of birth, taking into account leap years (possibly by using Julian days; see discussion below). I would adjust this for partial days at each end of the interval and then multiply by 86400 s/d. Finally I would add the difference in the two TT - UTC offsets at the ends of the interval, (TT - UTC)now - (TT - UTC)birth. The latter step takes into account the leap seconds that were inserted between the two dates.

TT is a terrestrial time scale. It is used for timing events occurring at the earth or distant events observed at earth and timed with clocks located on the earth's surface (mean sea level). For example, it is used for expressing the locations of earth orbiting satellites as a function of time.

### Barycentric times

According to the GR model of time, a clock deep in a potential well will run more slowly than one less deep. Also, a clock moving at high speed relative to some stationary clocks runs more slowly than the "at rest" clocks it passes. The latter is the time dilation effect also encountered in special relativity. A clock on the earth, with its elliptical orbit, experiences both effects relative to a stationary clock far from the solar system. Each effect has a fixed and a cyclic component. The cyclic terms arise from the eccentricity of the earth's orbit; on an annual basis, both the speed and the depth in the solar potential change.

Barycentric Dynamical Time (TDB) is a coordinate time in general relativity; it marks the progress of "time" in the GR model, but is not necessarily the time kept by any particular real clock. It is defined in a coordinate system with spatial origin at the solar-system barycenter. It may be used as the independent variable in the equations of motion that represent the positions and velocities of solar-system bodies in general relativity. One may think of it as the time kept by a clock that is on the surface of a hypothetical earth that orbits the barycenter in a strictly circular orbit at constant velocity, at an orbital radius and velocity typical of the actual earth. It runs at the same rate as TT except that it is free of the cyclical effects of the earth's elliptical orbit, to which TT is subject. The annual periodic term in the difference TT - TDB is of amplitude only 1.7 ms, while other periodic terms due to the planets and moon contribute up to 20 | s.

In 1991 the International Astronomical Union defined Barycentric Coordinate Time (TCB), a coordinate time for another system with spatial origin at the barycen-ter of the solar system. This too can be the independent variable in the equations of motion. TCB is the time kept by a series of synchronized clocks that are at rest relative to the barycenter and far removed from it. They are in flat space where gravitational redshift and velocity effects are null. TCB can be called "far away time". At present, the TCB clock runs faster than TDB by a constant 49 s per century. This time is appropriate for keeping track of events taking place throughout the solar system.

TCB differs from TDB by the constant rate offsets of the two relativistic effects mentioned above, namely time dilation and solar gravitational potential. TCB time runs faster than the TDB clock for each effect. Recall that our hypothetical TDB clock is in an earth-like but circular orbit. It therefore runs slower than the "far away" TCB clocks by (i) 33 s per century because it is in the gravitational potential

(or space distortion) of the sun's gravity, and (ii) 16 s per century because its orbital velocity is 29.8 km s-1, or 10-4 times the speed of light, relative to the solar system barycenter. The latter effect is the relativistic time dilation, or equivalently, the transverse Doppler effect. The two effects together yield the above mentioned total rate difference of 49 s per century.

## Telescopes Mastery

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