An alanytical approach to the time transformation TDB-TDT

An analytical formula for the time transformation TDB-TDT (Temps Dynamique Terrestre, Temps Dynamique Barycentrique) valid over a few thousand years around J2000 has been computed with accuracy at 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 (Parametrised Post Newtonian) parameters, γ and β, and of the 3 most commonly-used coordinate systems (standard, isotropic, Painleve), at least at the 1 ns level. The analytical theories ELP2000 (lunar) and VSOP82 (planetary) developed at the Bureau des Longitudes were used for motions of the solar system bodies. Furthermore, the numerical procedures described by Hellings and Davis to calculate this transformation yield results differing from our own procedure. These differences are due to the long-period terms of the planetary theories which are averaged out in numerical procedures. These terms are generated by resonances in the Solar System. (author). 13 refs