Abstract
We use the corrections to the Newton-Einstein secular precessions
of the longitudes of the perihelia of the inner planets,
phenomenologically estimated E.V. Pitjeva by fitting almost one
century of data with the EPM2004 ephemerides, to constrain some
long-range models of modified gravity recently put forth to
address the dark energy and dark matter problems. They are the
four-dimensional ones obtained with the addition of inverse powers
and logarithm of some curvature invariants, and the DGP
multidimensional braneworld model. 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 extra-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. The curvature
invariants-based models are ruled out, even by rescaling by a
factor 10 the errors in the estimated planetary orbital
parameters. 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 EPM force
models, passes such a test.