Context. The development of precise numerical integrations of the motion of the planets, taking into account the most recent observations, lead us to improve the two families of analytical planetary theories built in the Institut de mécanique céleste et de calcul des éphémérides (IMCCE), the Variations Séculaires des Orbites Planétaires (VSOP) and the Theory of the Outer Planets (TOP) theories.
Aims: We have built the solutions VSOP2010 and TOP2010 fitted to the Jet Propulsion Laboratory (JPL) numerical integration DE405 and the solutions VSOP2013 and TOP2013 fitted to the European recent numerical integration INPOP10a. This paper specifically considers VSOP2013 and TOP2013.
Methods: We have improved the construction of VSOP by analytically computing the pertubations due to the asteroids and to Pluto. We have increased the precision of the VSOP solutions of Jupiter and Saturn by using TOP solutions. We have also improved the construction of TOP by computing the perturbations due to the telluric planets from VSOP solutions. Moreover, TOP contains a solution of the motion of the Pluto-Charon barycenter.
Results: From 1890 to 2000, the precision of VSOP2013 goes from a few 0.01 mas (planets except Mars and Uranus) up to 0.7 mas (Mars and Uranus). Compared to the previous solution (VSOP2000), this represents an improvement of a factor of 2 to 24, depending on the planet. From -4000 to 8000, the precision is of a few 0.1″ for the telluric planets (1.6″ for Mars), i.e. an improvement of about a factor of 5 compared to VSOP2000. The TOP2013 solution is the best for the motion of the major planets from -4000 to 8000. Its precision is of a few 0.1″ for the four planets, i.e. a gain between 1.5 and 15, depending on the planet compared to VSOP2013. The precision of the theory of Pluto remains valid up to the time span from 0 to 4000. The VSOP2013 and TOP2013 data are available on the WEB server of the IMCCE.