# IAU(1991) RECOMMENDATION III

## Standardisation of the units and origins of coordinate times used in astronomy: Geocentric Coordinate Time (TCG) and Barycentric Coordinate Time (TCB)

The XXIst General Assembly of the International Astronomical Union,

considering,

the desirability of the standardisation of the units and origins of coordinate times used in astronomy,

recommends that,

1. the units of measurement of the coordinate times of all coordinate systems centred at the barycentres of ensembles of masses be chosen so that they are consistent with the proper unit of time, the SI second,

2. the reading of these coordinate times be 1977 January 1, 0h 0m 32.184s exactly, on 1977 January 1, 0h 0m 0s TAI exactly (JD = 2443144.5, TAI), at the geocentre,

3. coordinate times in coordinate systems having their spatial origins respectively at the centre of mass of the Earth and at the solar system barycentre, and established in conformity with the above sections (1) and (2), be designated as Geocentric Coordinate Time (TCG) and Barycentric Coordinate Time (TCB).

Notes for Recommendation III

1. In the domain common to any two coordinate systems, the tensor transformation law applied to the metric tensor is valid without re scaling the unit of time. Therefore, the various coordinate times under consideration exhibit secular differences. Recommendation 5 (1976) of IAU Commissions 4, 8 and 31, completed by Recommendation 5 (1979) of IAU Commissions 4, 19 and 31, stated that Terrestrial Dynamical Time (TDT) and Barycentric Dynamical Time (TDB) should differ only by periodic variations. Therefore, TDB and TCB differ in rate. The relationship between these time scales in seconds is given by (with Fortran expressions for squares):

TCB - TDB = L_B x (JD - 2443144.5) x 86400.

The present estimate of the value of L_B is 1.550505 x 10**-8 (+/- 1 x 10**-14) (Fukushima et al., Celestial Mechanics, 38, 215, 1986). 2. The relation TCB - TCG involves a full 4 dimensional transformation

TCB - TCG =(1/c**2) . [ I (t_o -> t) ( 0.5 v_e**2 + U_ext ( x_e) ) dt + v_e . (x - x_e)],

x_e and v_e denoting the barycentric position and velocity of the Earth's centre of mass and x the barycentric position of the observer. The external potential U_ext is the Newtonian potential of all solar system bodies apart from the Earth. The external potential must be evaluated at the geocentre. In the integral I(t_o -> t), t = TCB and t_o is chosen to agree with the epoch of Note 3. As an approximation to TCB - TCG in seconds one might use:

TCB - TCG = L_C x (JD - 2443144.5) x 86400 + c**-2 v_e .(x - x_e) + P.

The present estimate of the value of L_C is 1.480813 x 10**-8 (+/- 1 x 10**-14) (Fukushima et al., Celestial Mechanics, 38, 215, 1986). It may be written as [3G M/2c**2 a] + Epsilon, where G is the gravitational constant, M is the mass of the Sun, a is the mean heliocentric distance of the Earth, and Epsilon is a very small term (of order 2 x 10**-12) arising from the average potential of the planets at the Earth.

The quantity P represents the periodic terms which can be evaluated using the analytical formula by Hirayama et al., ("Analytical Expression of TDB TDT_o", in Proceedings of the IAG Symposia, IUGG XIX General Assembly, Vancouver, August 10-22, 1987). For observers on the surface of the Earth, the terms depending upon their terrestrial coordinates are diurnal, with a maximum amplitude of 2.1 microseconds.

3. The origins of coordinate times have been arbitrarily set so that these times all coincide with the Terrestrial Time (TT) of Recommendation IV at the geocentre on 1977 January 1, 0h 0m 0s TAI. (See Note 3 of Recommendation IV.)

4. When realizations of TCB and TCG are needed, it is suggested that these realizations be designated by expressions such as TCB(xxx), where xxx indicates the source of the realized time scale (e.g., TAI) and the theory used for the transformation into TCB or TCG.