On the possibility of testing the Dvali-Gabadadze-Porrati brane-world scenario with orbital motions in the Solar System

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 a 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 similar to -/+ 4 x 10(-3) milliarcseconds per year. In this paper we show that, according to the recently released EIGEN-CG01C Earth gravity model which combines data from the dedicated CHAMP and GRACE missions, the quite large systematic errors due to the Newtonian part of the terrestrial gravitational potential would rule out any attempts to detect such a small effect. Improvements in our knowledge of the Earth's gravitational field of, for example, up to four orders of magnitude in the low degree even zonal harmonics would be required. Also the obtainable observational accuracy in reconstructing the LARES orbit rules out the possibility of measuring the Lue - Starkman (LS) effect with the perigee of LARES. The situation is much more favourable 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 x 10(-2) milliarcseconds over a 92-year time span; the LS precession is similar to -/+ 4 x 10(-1) milliarcseconds per century. A suitable combination of the perihelia and the nodes of Mars and Mercury, which disentangles the LS effect from the competing larger Newtonian and general relativistic precessions, might allow one to reach a 1-sigma 41% level of accuracy.