Observational constraints on spatial anisotropy of G from orbital motions

TL;DR

This paper investigates how potential spatial anisotropies in the gravitational constant G could influence orbital dynamics, deriving theoretical effects and constraining G variations using solar system and galactic center observations.

Contribution

It provides a detailed analytical framework for the long-term orbital effects of anisotropic G variations and sets observational bounds on G/G in different astrophysical contexts.

Findings

G/G  10^{-17} over 1 au from solar system data

G/G  10^{-2} over 1 kiloparsec near the Galactic Center

Orbital elements like semi-major axis and eccentricity are affected by G anisotropy

Abstract

A phenomenological anisotropic variation \Delta G/G of the Newtonian gravitational coupling parameter G, if real, would affect the orbital dynamics of a two-body gravitationally bound system in a specific way. We analytically work out the long-term effects that such a putative modification of the usual Newtonian inverse-square law would induce on the trajectory of a test particle orbiting a central mass. Without making any a-priori simplifying assumptions concerning the orbital configuration of the test particle, it turns out that its osculating semi-major axis a, eccentricity e, pericenter \varpi and mean anomaly M undergo long-term temporal variations, while the inclination I and the node \Omega are left unaffected. Moreover, the radial and the transverse components of the position and the velocity vectors r and v of the test particle experience non-vanishing changes per orbit, contrary to the out-of-plane ones. Then, we compute our theoretical predictions for some of the major bodies of the solar system by orienting the gradient of G(r) towards the Galactic Center and keeping it fixed over the characteristic timescales involved. By comparing our calculation to the latest observational determinations for the same bodies, we infer \Delta G/G <= 10^-17 over about 1 au. Finally, we consider also the Supermassive Black Hole hosted by the Galactic Center in Sgr A^* and the main sequence star S2 orbiting it in about 16 yr, obtaining just \Delta G/G <= 10^-2 over 1 kau.