  In this paper we explicitly work out the secular perturbations induced on all
the Keplerian orbital elements of a test body to order O(e^2) in the
eccentricity e by the weak-field long-range modifications of the usual
Newton-Einstein gravity due to the Dvali-Gabadadze-Porrati (DGP) braneworld
model. The Gauss perturbative scheme is used. It turns out that the argument of
pericentre and the mean anomaly are affected by secular rates which are
independent of the semimajor axis of the orbit of the test particle. The first
nonvaishing eccentricity-dependent corrections are of order O(e^2). For
circular orbits the Lue-Starkman (LS) effect on the pericentre is obtained.
Some observational consequences are discussed for the Solar System planetary
mean longitudes lambda which would undergo a 1.2\cdot 10^-3 arcseconds per
century braneworld secular precession. According to recent data analysis over
92 years for the EPM2004 ephemerides, the 1-sigma formal accuracy in
determining the Martian mean longitude amounts to 3\cdot 10^-3 milliarcseconds,
while the braneworld effect over the same time span would be 1.159
milliarcseconds. The major limiting factor is the 2.6\cdot 10^-3 arcseconds per
century systematic error due to the mismodelling in the Keplerian mean motion
of Mars. A suitable linear combination of the mean longitudes of Mars and Venus
may overcome this problem. The formal, 1-sigma obtainable observational
accuracy would be \sim 7%. The systematic error due to the present-day
uncertainties in the solar quadrupole mass moment, the Keplerian mean motions,
the general relativistic Schwarzschild field and the asteroid ring would amount
to some tens of percent.
