A model-independent test of the spatial variations of the Newtonian gravitational constant in some extrasolar planetary systems

In this paper, we directly constrain possible spatial variations of the Newtonian gravitational constant G over the range  ≈ 0.01–5 au  in various extrasolar multiplanet systems. Using the third Kepler law, we determine the quantity  Γ_XY= G _X/ G _Y  for each couple of planets X and Y located at different distances from their parent star; deviations of the measured values of Γ from unity would signal variations of G . The obtained results for  η= 1 −Γ  are found to be very compatible with zero within the experimental errors  (η/δη≈ 0.2–0.3)  . We make a comparison with an analogous test previously performed in our Solar system.