Orbital effects of spatial variations of fundamental coupling constants

TL;DR

This paper analytically examines how hypothetical spatial variations in fundamental constants could cause long-term orbital changes in a two-body gravitational system, providing general results applicable to any orbital configuration.

Contribution

It derives comprehensive formulas for orbital element variations caused by spatially varying fundamental constants without simplifying assumptions on orbit shape or orientation.

Findings

All six Keplerian elements experience long-term changes.

Radial, transverse, and normal shifts in position and velocity are analytically calculated.

Results are valid for any orbital geometry and gradient direction.

Abstract

We deal with the effects induced on the orbit of a test particle revolving around a central body by putative spatial variations of fundamental coupling constants $\zeta$. In particular, we assume a dipole gradient for $\zeta(\bds r)/\bar{\zeta}$ along a generic direction $\bds{\hat{k}}$ in space. We analytically work out the long-term variations of all the six standard Keplerian orbital elements parameterizing the orbit of a test particle in a gravitationally bound two-body system. It turns out that, apart from the semi-major axis $a$, the eccentricity $e$, the inclination $I$, the longitude of the ascending node $\Omega$, the longitude of pericenter $\pi$ and the mean anomaly $\mathcal{M}$ undergo non-zero long-term changes. By using the usual decomposition along the radial ($R$), transverse ($T$) and normal ($N$) directions, we also analytically work out the long-term changes $\Delta R,\Delta T,\Delta N$ and $\Delta v_R,\Delta v_T,\Delta v_N$ experienced by the position and the velocity vectors $\bds r$ and $\bds v$ of the test particle. It turns out that, apart from $\Delta N$, all the other five shifts do not vanish over one full orbital revolution. In the calculation we do not use \textit{a-priori} simplifying assumptions concerning $e$ and $I$. Thus, our results are valid for a generic orbital geometry; moreover, they hold for any gradient direction (abridged).