Relativistic clock correction: the difference between proper time at a point on the surface of the Earth and coordinate time in the Solar System barycentric space-time frame of reference. The proper time is Terrestrial Time TT; the coordinate time is an implementation of the Barycentric Dynamical Time TDB.
TDB double coordinate time (MJD: JD-2400000.5) UT1 double universal time (fraction of one day) WL double clock longitude (radians west) U double clock distance from Earth spin axis (km) V double clock distance north of Earth equatorial plane (km)
The clock correction, TDB-TT, in seconds. TDB may be considered to be the coordinate time in the Solar System barycentre frame of reference, and TT is the proper time given by clocks at mean sea level on the Earth. The result has a main (annual) sinusoidal term of amplitude approximately 0.00166 seconds, plus planetary terms up to about 20 microseconds, and lunar and diurnal terms up to 2 microseconds. The variation arises from the transverse Doppler effect and the gravitational red-shift as the observer varies in speed and moves through different gravitational potentials. The argument TDB is, strictly, the barycentric coordinate time; however, the terrestrial proper time (TT) can in practice be used. The geocentric model is that of Fairhead & Bretagnon (1990), in its full form. It was supplied by Fairhead (private communication) as a FORTRAN subroutine. The original Fairhead routine used explicit formulae, in such large numbers that problems were experienced with certain compilers (Microsoft Fortran on PC aborted with stack overflow, Convex compiled successfully but extremely slowly). The present implementation is a complete recoding in C, with the original Fairhead coefficients held in a table. To optimize arithmetic precision, the terms are accumulated in reverse order, smallest first. A number of other coding changes were made, in order to match the calling sequence of previous versions of the present routine, and to comply with Starlink programming standards. Under VAX/VMS, the numerical results compared with those from the Fairhead form are essentially unaffected by the changes, the differences being at the 10-20 sec level. The topocentric part of the model is from Moyer (1981) and Murray (1983). During the interval 1950-2050, the absolute accuracy is better than +/- 3 nanoseconds relative to direct numerical integrations using the JPL DE200/LE200 solar system ephemeris. The IAU definition of TDB is that it must differ from TT only by periodic terms. Though practical, this is an imprecise definition which ignores the existence of very long-period and secular effects in the dynamics of the solar system. As a consequence, different implementations of TDB will, in general, differ in zero-point and will drift linearly relative to one other.
Bretagnon P, 1982 Astron. Astrophys., 114, 278-288. Fairhead L & Bretagnon P, 1990, Astron. Astrophys., 229, 240-247. Meeus J, 1984, l'Astronomie, 348-354. Moyer T D, 1981, Cel. Mech., 23, 33. Murray C A, 1983, Vectorial Astrometry, Adam Hilger. Defined in slamac.h: D2PI P.T.Wallace Starlink 30 October 1993