Orbital effects of spatial variations of fundamental coupling constants

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 $ζ(\bds r)/\barζ$ 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).

Latex2e, 20 pages, 1 figure, 7 tables. Version accepted by Monthly Notices of the Royal Astronomical Society (MNRAS). Error in the caption of Table 5 corrected. References updated

References in corpus (8)

• Varying constants, Gravitation and Cosmology
• Equivalence Principle Violations and Couplings of a Light Dilaton
• Phenomenology of the Equivalence Principle with Light Scalars
• Space-based tests of gravity with laser ranging
• On the anomalous secular increase of the eccentricity of the orbit of the Moon
• Is there further evidence for spatial variation of fundamental constants?
• Laser Ranging for Gravitational, Lunar, and Planetary Science
• Spatial variation of fundamental couplings and Lunar Laser Ranging

Cited by in corpus (4)

• New Constraints on Spatial Variations of the Fine Structure Constant from Clusters of Galaxies
• A uniform treatment of the orbital effects due to a violation of the Strong Equivalence Principle in the gravitational Stark-like limit
• Spatial variation of fundamental constants: testing models with thermonuclear supernovae
• Constraining A String Gauge Field by Galaxy Rotation Curves and Perihelion Precession of Planets