Lower bounds of characteristic scale of topological modification of the Newtonian gravitation

TL;DR

This paper analytically investigates the long-term orbital effects of a topological modification to Newtonian gravity, providing bounds on the compactification radius based on planetary data, and suggests further modeling for confirmation.

Contribution

It derives general analytical expressions for orbital perturbations caused by a specific topological modification of gravity without restricting orbital configurations.

Findings

Preliminary lower bound on the radius R of the topological modification: 4-6 kau.

Long-term orbital variations affect all Keplerian elements except the semimajor axis.

Results are based on analysis of Saturn's orbital data from Cassini.

Abstract

We analytically work out the long-term orbital perturbations induced by the first term of the expansion of the perturbing potential arising from the local modification of the Newton's inverse square law due to a topology R^2 x S^1 with a compactified dimension of radius R recently proposed by Floratos and Leontaris. We neither restrict to any specific spatial direction for the asymmetry axis nor to particular orbital configurations of the test particle. Thus, our results are quite general. Non-vanishing long-term variations occur for all the usual osculating Keplerian orbital elements, apart from the semimajor axis which is left unaffected. By using recent improvements in the determination of the orbital motion of Saturn from Cassini data, we preliminarily inferred R >= 4-6 kau. As a complementary approach, the putative topological effects should be explicitly modeled and solved-for with a modified version of the ephemerides dynamical models with which the same data sets should be reprocessed.