On the Nature of the Gravitational Constant G

It is shown that free fall, light deflection, perihelion precession, and gravitational redshift are expressed through the local expansion rate \(T = \sqrt{g/R}\), its square \(\tau = T^2\), the radius \(R\), the density ratio \(\rho_{\text{body}}/\rho_{\text{ref}}\), and the speed of light \(c\) without using \(G\). The quantity \(T\) has dimension s\(^{-1}\) and coincides with the local Hubble parameter up to sign, while \(\tau\) has dimension s\(^{-2}\). The quantity \(g\) is interpreted as the projection of the 5D expansion of matter onto non-expanding 4D space: in the comoving frame it is the flow velocity, in the spatial one~--- acceleration. The weight of a body is treated as the force needed to prevent the body from participating in the expansion of matter. The quantity \(G\) arises only in the transition to mass units and depends on the choice of reference density, whereas physical predictions do not depend on this choice. Numerical checks are presented for Solar System bodies, light deflection at the Sun, and perihelion precession of Mercury. In the section on refraction a decisive testable prediction is formulated: the dependence of the refraction angle at the vacuum~--- glass boundary on the radial expansion flow \(v = Tr\), testable on Earth.