The Sun and the Newton Constant
  Several properties of the solar interior are determined with a very high accuracy, which in some cases is comparable to that achieved in the determination of the Newton constant $G_N$. We find that the present uncertainty $\Delta G_N/G_N=\pm 1.5\cdot 10^{-3}$ has significant effects on the profile of density and pressure, however it has negligible influence on the solar properties which can be measured by means of helioseismology and $^8{\rm B}$ neutrinos. Our result do not support recent claims that observational solar data can be used to determine the value of $G_N$ with an accuracy of few part in $10^{-4}$. Present data cannot constrain $G_N$ to much better than $10^{-2}$. 
B. Ricci and F.L. Villante