  Recently it has been suggested to use the perigee of the proposed
LARES/WEBER-SAT satellite in order to measure the secular precession which
would be induced on such Keplerian orbital element by a weak-field modification
of gravity occurring in some Brane-World scenarios put forth by Dvali,
Gabadadze and Porrati. This precession, derived for the first time by Lue and
Starkman, amounts to 4\times 10-3 milliarcseconds per year for an Earth
orbiting satellite. In this paper we show that, according to the recently
released EIGEN-CG01C Earth gravity model the quite larger systematic errors due
to the Newtonian part of the terrestrial gravitational potential would vanish
any attempts to detect a so small effect. The situation is much more favorable
in the Solar System scenario. Indeed, the non-Newtonian perihelion advance of
Mars, which is the currently best tracked planet, has recently been measured
with an accuracy of 1\times 10^-4 arcseconds per century; the Dvali precession
is 4\times 10^-4 arcseconds per century. A suitable combination of the
perihelia and the nodes of Mars and Mercury, which disentangles the Dvali
effect from the competing larger Newtonian and general relativistic
precessions, might allow to reach a 1-sigma 47% level of accuracy.
