  In this paper we use the corrections to the usual Newton-Einstein secular
precessions of the perihelia of the inner planets of the Solar System,
phenomenologically estimated as solve-for parameters by the Russian astronomer
E.V. Pitjeva by fitting almost one century of data with the EPM2004
ephemerides, in order to constrain some long-range models of modified gravity
recently put forth to address the dark energy and dark matter problems. The
models examined here are the four-dimensional ones obtained with the addition
of inverse powers and logarithm of some curvature invariants, and the
multidimensional braneworld model by Dvali, Gabadadze and Porrati (DGP). After
working out the analytical expressions of the secular perihelion precessions
induced by the corrections to the Newtonian potential of such models, we
compare them to the estimated corrections to the rates of perihelia by taking
their ratio for different pairs of planets instead of using one perihelion at a
time for each planet separately, as done so far in literature. As a result, the
curvature invariants-based models are ruled out, even by re-scaling by a factor
10 the errors in the planetary orbital parameters estimated by Pitjeva. Less
neat is the situation for the DGP model. Only the general relativistic
Lense-Thirring effect, not included, as the other exotic models considered
here, by Pitjeva in the dynamical force models used in the estimation process,
passes such a test. It would be important to repeat the present analysis by
using corrections to the precessions of perihelia independently estimated by
other teams of astronomers as well, but, at present, such rates are not yet
available.
