In this paper we study the effects of f(R) Theories of Gravity on Solar
System gravitational tests. In particular, starting from an exact solution of
the field equation in vacuum, in the Palatini formalism, we work out the
effects that the modifications to the Newtonian potential would induce on the
Keplerian orbital elements of the Solar System planets, and compare them with
the latest results in planetary orbit determination from the EPM2004
ephemerides. It turns out that the longitudes of perihelia and the mean
longitudes are affected by secular precessions. We obtain the resulting best
estimate of the parameter k which, being simply related to the scalar
curvature, measures the non linearity of the gravitational theory. We use our
results to constrain the cosmological constant and show how f(R) functions
can be constrained, in principle. What we obtain suggests that, in agreement
with other recent papers, the Solar System experiments are not effective to set
such constraints, if compared to the cosmologically relevant values.Comment: 6 Pages, RevTeX, minor revision, new references added, to appear in
JCA
