8 Time scales

The observations from the Earth are generally referred to UTC, a time scale that is based on the International Atomic Time (TAI), but has the great disadvantage of not being continuous because from time to time steps of one second are introduced. Therefore, IAU (1992) recommends use of Terrestrial Time (TT), which is defined by its origin in 1977 with respect to TAI and the Système International (SI) second. Realizations of TT are designated as TT(x). For instance,

$${\rm TT(TAI) = TAI} + 32.184~{\rm s}.$$

Other realizations may be achieved by analyses of the indications of very accurate time standards and their determinations of the SI second. The value of TT was exact at its origin but, at other times, uncertainties due to the realizations add up. In 2001 the uncertainty is about 20-30 microsec. TT is the time reference for apparent geocentric ephemerides.

But, when dealing with bodies outside the Earth, one must use the coordinate times that correspond to the space-time coordinate system. The IAU (1992) stated that the units of measurement of the coordinate times of all coordinate systems centered at the barycenters of ensembles of masses must be chosen so that they are consistent with the proper time, the SI second. The coordinate times are to be consistent with the relativistic transformations between the coordinate systems and such that the definitions of units of mass, length and time are consistent. As a consequence, two coordinate times were defined.

8.1 Geocentric Coordinate Time (TCG)

Around the Earth, the space-time coordinate is centered at the center of mass of the Earth. The corresponding time coordinate is the Geocentric Coordinate Time (TCG) whose scale unit is such that the relation between TCG and TT is linear and is:

$${\rm TCG - TT} = L_{\rm G} \times ({\rm JD} - 2~443~144.5) \times 86~400~{\rm s}$$ (19)

with $L_{\rm G} = 6.969~290~134 \times 10^{-10}$ and being a defining constant, not subject to change. JD is the Julian date. The bracket vanishes on January 1, 1977, 0h.TT. Note that TT replaces, since 1992 (IAU 1992), the Terrestrial Dynamical Time (TDT) previously in use.

8.2 Barycentric Coordinate Time (TCB)

For the space-time coordinates in the Solar system, the origin is the barycenter of the Solar system. The corresponding time coordinate is the Barycentric Coordinate Time (TCB). It is related to TCG by:

$${\rm (TCB - TCG)_{secular}} = L_{\rm C} \times ({\rm JD} - 2~443~144.5)~ 86~400~{\rm s}$$ (20)

with $L_{\rm C} = 1.480~826~8457 \times 10^{-8}$. The uncertainty of $L_{\rm C}$ is of the order of 10^-17. In addition, the expression (20) has a non-linear variation described by a number of periodic terms depending on the various periods present in the motion of planets. They are discussed in Fukushima (1995) who finds that there are 515 terms that are greater in amplitude than 0.1 ns. The most important periodic terms in TCB - TCG are, in seconds,

$$0.001~658 \sin g + 0.000~014 \sin 2g,$$

where $g = 357\hbox{$.\!\!^\circ$ }53 + 0\hbox{$.\!\!^\circ$ }985~003~({\rm JD} - 2451~545.0)$ represents essentially the mean anomaly of the Earth's orbit.

The change from the earlier coordinate time in the Solar system (Barycentric Dynamical Time, TDB) is that, while TDB-TDT were defined in such a way that they differed only by periodic terms, TCB-TCG have also a secular trend resulting from the full four-dimensional transformation between geocentric and the barycentric space-time coordinates. This makes the time scales consistent with relativistic transformations. The IAU (2001) gives the relations between the coordinate times very accurately in 2000.