  We present new splitting methods designed for the numerical integration of
near-integrable Hamiltonian systems, and in particular for planetary N-body
problems, when one is interested in very accurate results over a large time
span. We derive in a systematic way an independent set of necessary and
sufficient conditions to be satisfied by the coefficients of splitting methods
to achieve a prescribed order of accuracy. Splitting methods satisfying such
(generalized) order conditions are appropriate in particular for the numerical
simulation of the Solar System described in Jacobi coordinates. We show that,
when using Poincar\'e Heliocentric coordinates, the same order of accuracy may
be obtained by imposing an additional polynomial equation on the coefficients
of the splitting method. We construct several splitting methods appropriate for
each of the two sets of coordinates by solving the corresponding systems of
polynomial equations and finding the optimal solutions. The experiments
reported here indicate that the efficiency of our new schemes is clearly
superior to previous integrators when high accuracy is required.
