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

Abstract

In this paper, we explicitly work out the secular perturbations induced on all the Keplerian orbital elements of a test body to order 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 ω and the mean anomaly are affected by secular rates which depend on the orbital eccentricity via 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 λ which would undergo a 1.2 × 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 × 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 × 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 ∼7%. The systematic error due to the present-day uncertainties in the solar quadrupole mass moment J2, the Keplerian mean motions, the general relativistic Schwarzschild field and the asteroid ring would amount to some tens of per cent.