Numerical expressions for precession formulae and mean elements for the Moon and the planets.

We present, in this paper, a coherent set of formula giving numerical expressions for precession quantities and mean elements of the Moon and the planets. First, using the notations of Lieske et al. (1977), we construct expressions for the precession quantities based upon the use of the secular variations of the ecliptic pole from the planetary theories built at the Bureau des Longitudes and taking into account recent determinations of the precession constant and of the obliquity in J2000. Also we give the derivatives of these expressions with respect to the masses of the planets, to the precession constant and to the obliquity. So, this set of formulas is applicable whenever the values of the planetary masses and of the constants are improved. Afterwards, we give the mean elements of the Moon and the planets connected to the fixed J2000 ecliptic and connected to the ecliptic of date. At last, we give formula which enable one to compute approximate ephemerides of the Moon and the planets from mean elements.