An analytical formula for the time transformation TB-TT.

An analytical formula for the time transformation TB-TT valid over a few thousand years around J2000 has been computed with an accuracy at the 1 ns level. The 127 coefficients presented in this paper provide a formula accurate at the 100 ns level. The numerical and analytical procedures to compute this transformation are discussed and compared. It is noted that these procedures cannot fully comply with recommendations 5 of the 1976 IAU meeting. Furthermore, these procedures yield different units for the corresponding TB time scales. It is verified that this transformation is independent of the two parameterized post Newtonian parameters gamma and beta and of the three most commonly used coordinate systems (isotropic, standard-Schwarzschild, Painleve) at least the 1 ns level.