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

A sinusoidally time-varying pattern of the values of Newton's constant of gravitation G measured in Earth-based laboratories over the last few decades has been recently reported in the literature. We put to the test the hypothesis that the aforementioned harmonic variation may pertain to 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, 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 alpha, declination delta and range rho would be affected by up to 10(4)-10(5) milliarcseconds and 10(5) km, respectively; the present-day 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 omega 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 to the 10(-4) arcseconds per century level. The rejection level provided by the Mercury's perihelion rate is of the same order of magnitude.