Does the Newton’s gravitational constant vary sinusoidally with time? An independent test with planetary orbital motions

Abstract

A sinusoidally time-varying pattern of the values of theNewton’s constant of grav- itation G measured in Earth-based laboratories over the latest decades has been re- cently reported in the literature. Its amplitude and period amount to AG = 1.619 × 10−14 kg−1 m3 s−2, PG = 5.899 yr, respectively. Given the fundamental role played by G in the currently accepted theory of gravitation and the attempts to merge it with quantum mechanics, it is important to put to the test the hypothesis that the aforemen- tioned harmonic variation may pertain G itself in a direct and independent way. The bounds on ˙ G/G existing in the literature may not be extended straightforwardly to the present case since they were inferred fromplanetary and lunarmotions by considering just secular variations. Thus, we numerically integrated the ad-hocmodified 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 astrometricmeasurements. In the case of Saturn, its geocentric right as- cension α, declination δ and range ρ would be affected up to 104−105 milliarcseconds and 105 km, respectively; the present-day residuals of such observables are as little as about 4 milliarcseconds and 10−1 km, respectively.