An analytical formula for the time transformation TDB-TDT valid over a few thousand years around J2000 has been computed with an accuracy at the 1 ns level. This computation was carried out by integrating the differential equation derived from a general metric.
The transformation TDB-TDT is independent of the PPN parameters, γ and β, and of the 3 most commonly-used coordinate systems (standard, isotropic, Painlevé), at least at the 1 ns level.
The analytical theories ELP2000 and VSOP82 developped at the Bureau des Longitudes were used for the motions pf the solar systém bodies, Furthermore, the numerical procedures described by Hellings and Davis to calculate this transformation yield different results to our own procedure. These differences are due to the long-period terms of the planetary theories which are averaged out
in the numerical procedures. These terms are generated by resonances in the Solar System.