  There is a growing population of relativistically relevant minor bodies in
the Solar System and a growing population of massive extrasolar planets with
orbits very close to the central star where relativistic effects should have
some signature. Our purpose is to review how general relativity affects the
orbital dynamics of the planetary systems and to define a suitable relativistic
correction for Solar System orbital studies when only point masses are
considered. Using relativistic formulae for the N body problem suited for a
planetary system given in the literature we present a series of numerical
orbital integrations designed to test the relevance of the effects due to the
general theory of relativity in the case of our Solar System. Comparison
between different algorithms for accounting for the relativistic corrections
are performed. Relativistic effects generated by the Sun or by the central star
are the most relevant ones and produce evident modifications in the secular
dynamics of the inner Solar System. The Kozai mechanism, for example, is
modified due to the relativistic effects on the argument of the perihelion.
Relativistic effects generated by planets instead are of very low relevance but
detectable in numerical simulations.
