Does Newton’s gravitational constant vary sinusoidally with time? Orbital motions say no

Abstract

A sinusoidally time-varying pattern of the values of the Newton's constant of gravitation G measured in Earth-based laboratories over the latest decades has been recently reported in the literature. We put to the test the hypothesis that the aforementioned harmonic variation may pertain G itself in a direct and independent way. We numerically integrated the ad-hoc modified equations of motion of the major bodies of the Solar System by finding that the orbits of the planets would be altered by an unacceptably larger amount in view of the present-day high accuracy astrometric measurements. In the case of Saturn, its geocentric right ascension α, declination δ and range ρ would be affected up to 10 4 − 10 5 milliarcseconds and 10 5 km, respectively; the presentday residuals of such observables are as little as about 4 milliarcseconds and 10 −1 km, respectively. We analytically calculated the long-term orbital effects induced by the putative harmonic variation of G at hand finding non-zero rates of change for the semimajor axis a, the eccentricity e and the argument of pericenter ω of a test particle. For the LAGEOS satellite, an orbital increase as large as 3.9 m yr −1 is predicted, in contrast with the observed decay of −0.203 ± 0.035 m yr −1 . An anomalous perihelion precession as large as 14 arcseconds per century is implied for Saturn, while latest observations constrain it down to the 10 −4 arcseconds per century level. The rejection level provided by Mercury is of the same order of magnitude.

General Relativity and Cosmology: Unsolved Questions and Future Directions

“…A non-constant G would have serious implications both for Newtonian physics and for General Relativity. This motivates ongoing efforts to devise new methods to measure this quantity, and to push the limits of experimental accuracy in order to test the constancy of G [358][359][360][361][362].…”

Oscillating scalar fields in extended quintessence

“…Note that tighter constraints on oscillations in G can be derived from the orbits of the planets in the Solar System when ν ∼ yr −1 [30].…”

Temporal Variation of Earth-Based Gravitational Constant Measurements

“…Besides, after enlarging the Glab data base and a few corrections to the time interval the measurements were carried out, Schlamminger et al concluded that this significantly weakens the correlation to the LOD [8]. Besides, based on the aforementioned hypothesis, L. Iorio could predict for the LAGEOS satellite an orbital increase as large as 3.9 m yr −1 in contrast with the observed decay of − 0.203 ± 0.035 m yr −1 and an anomalous perihelion precession as large as 14 arcseconds per century for Saturn [9]. Moreover, these claims have been disputed by other authors [10,11,12].…”