On the possibility of testing the 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 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∼ ∓4×10−3 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 larger systematic errors due to the Newtonian part of the terrestrial gravitational potential would vanish any attempts to detect a so small effect. Improvements in our knowledge of the Earth’s gravitational field of, e.g., 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 LS effect with the perigee of LARES. The situation is much more favorable 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 × 10 arcseconds per century; the LS precession is ∼ ∓4 × 10 arcseconds 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 to reach a 1-sigma 46% level of accuracy.