On the possibility of testing the Brane-World scenario with orbital motions in the Solar System

Abstract

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\times 10-3 milliarcseconds per year for an Earth orbiting satellite. In this paper we show that, according to the recently released EIGEN-CG01C Earth gravity model 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. 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\times 10^-4 arcseconds per century; the Dvali precession is 4\times 10^-4 arcseconds per century. A suitable combination of the perihelia and the nodes of Mars and Mercury, which disentangles the Dvali effect from the competing larger Newtonian and general relativistic precessions, might allow to reach a 1-sigma 47% level of accuracy.