INTEGRATION OF THE RELATIVISTIC BARYCENTRIC EQUATIONS OF MOTION OF THE SOLAR SYSTEM BODIES.

Moisson X.

Bureau des Longitudes, URA 707 CNRS, 77 av. Denfert Rochereau 75014 Paris
E-mail: moisson@bdl.fr

Up to this time, the VSOP theories of the motion of the planets were constructed on the base of the integration of the Lagrange's differential equations. The development of the pertubative function included the mutual perturbations of the bodies and was performed up to the third order of the perturbative masses using the Newtonian perturbative function given by :

The relativistic complements were limited to the Schwarzschild problem. The accuracy reached by such solutions are few milliarcseconds for the inner planets and less for the outer ones.

The solutions are expressed in terms of rectangular and elliptic variables and are much more compact when using the rectangular ones (Bretagnon, Francou, 1988).

The present astrometric accuracies reach the milliarcseconds so that the mutual relativistic perturbations of the planets are to be included in the ephemeris constructions. Moreover, the necessity of harmonisation of the time scales used in astronomy or in geodesy and the recent IAU recommendations (1991) of using the TCB and TCG time scales imply to integrate the barycentric equations of motion found in (Brumberg, 1991).

So, the aim of this paper is to present the integration of the equations of motion of the solar system bodies in rectangular coordinates, the solution being expressed in Fourier and Poisson's series of the mean anomaly of the planets related to the ecliptic and equinox J2000.

We also present the new expression of the difference between the two time scales TCB and TCG at the geocenter developed to the fourth order in 1/c, c being the velocity of light in the vacum. The accuracy of this expression is at the nanosecond level which is the requirement in many different applications. A new determination of the constant of proportionality L_c is given. This will also be useful inconverting the numerical values of some astronomical constants determined in the old IAU time scale TDB.