### SLA_RCC

Barycentric Coordinate Time

CALL:
D = sla_RCC (TDB, UT1, WL, U, V)
ACTION:
The relativistic clock correction: the difference between proper time at a point on 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 Barycentric Dynamical Time, TDB.
##### GIVEN:
 TDB D TDB (MJD: JD$-$2400000.5) UT1 D universal time (fraction of one day) WL D clock longitude (radians west) U D clock distance from Earth spin axis (km) V D clock distance north of Earth equatorial plane (km)

##### RETURNED:
 sla_RCC D TDB$-$TT (sec; Note 1)

NOTES:
(1)
TDB is coordinate time in the solar system barycentre frame of reference, in units chosen to eliminate the scale difference with respect to terrestrial time. TT is the proper time for clocks at mean sea level on the Earth.
(2)
The number returned by sla_RCC comprises a main (annual) sinusoidal term of amplitude approximately 1.66ms, plus lunar and planetary terms up to about 20$\mu$s, and diurnal terms up to 2$\mu$s. 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.
(3)
The argument TDB is, strictly, the barycentric coordinate time; however, the terrestrial time (TT) can in practice be used without significant loss of accuracy.
(4)
The geocentric model is that of Fairhead & Bretagnon (1990), in its full form. It was supplied by Fairhead (private communication) as a Fortran subroutine. A number of coding changes were made to this subroutine in order match the calling sequence of previous versions of the present routine, to comply with Starlink programming standards and to avoid compilation problems on certain machines. The numerical results are essentially unaffected by the changes.
(5)
The topocentric model is from Moyer (1981) and Murray (1983). It is an approximation to the expression
$\frac{{}_{}}{}$ve (x xe) c2

where ${}_{}$ve is the barycentric velocity of the Earth, x and ${}_{}$xe are the barycentric positions of the observer and the Earth respectively, and c is the speed of light. It can be disabled, if necessary, by setting the arguments U and V to zero.

(6)
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.
(7)
The IAU 1976 definition of TDB was 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. In 1991 the IAU introduced new time scales designed to overcome these objections: geocentric coordinate time, TCG, and barycentric coordinate time, TCB. In principle, therefore, TDB is obsolete. However, sla_RCC can be used to implement the periodic part of TCB$-$TCG.
REFERENCES:
(1)
Fairhead, L., & Bretagnon, P., Astron. Astrophys., 229, 240-247 (1990).
(2)
Moyer, T.D., Cel. Mech., 23, 33 (1981).
(3)
Murray, C.A., Vectorial Astrometry, Adam Hilger (1983).
(4)
Seidelmann, P.K. et al, Explanatory Supplement to the Astronomical Almanac, Chapter 2, University Science Books (1992).
(5)
Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G. & Laskar, J., Astron.Astrophys., 282, 663-683 (1994).