On the effects of Dvali-Gabadadze-Porrati braneworld gravity on the orbital motion of a test particle

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. Both the Gauss and the Lagrange perturbative schemes are used. It turns out that the argument of pericentre omega and the mean anomaly M are affected by secular rates which depend on the orbital eccentricity via O(e(2)) terms, but are independent of the semimajor axis a of the orbit of the test particle. For almost 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 x 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 x 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 x 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 I-sigma obtainable observational accuracy would be similar to 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 per cent.