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

TL;DR

This paper evaluates the feasibility of detecting Brane-World gravity modifications through orbital precessions in the Solar System, concluding that planetary measurements could potentially identify such effects with sufficient precision.

Contribution

It demonstrates that Solar System orbital data, especially from Mars and Mercury, could be used to test Brane-World gravity scenarios, overcoming limitations faced in satellite-based experiments.

Findings

Satellite-based detection is hindered by Earth's gravitational uncertainties.

Mars and Mercury perihelion measurements can potentially detect Brane-World effects.

A combined orbital analysis could achieve nearly 50% accuracy in testing the theory.

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.