In this paper we explicitly work out the secular perturbations induced on all the Keplerian orbital elements of a test body to order \mathcal { 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 .
Both the Gauss and the Lagrange perturbative schemes are used .
It turns out that the argument of pericentre \omega and the mean anomaly \mathcal { M } are affected by secular rates which depend on the orbital eccentricity via \mathcal { O } ( e ^ { 2 } ) terms , but are independent of the semimajor axis of the orbit of the test particle .
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 J _ { 2 } , the Keplerian mean motions , the general relativistic Schwarzschild field and the asteroid ring would amount to some tens of percent .