We study scalar-tensor theories of gravity which satisfies the strong equivalence principle: the independence of the motion of a self-gravitating body from its internal structure. By solving $eta=4beta-gamma-3=0$ for the coupling function $omega(Phi)$, such a theory is obtained which is different from general relativity and is known as constant-$G$ theory. The theory has peculiar features: the coupling function asymptotes to a conformal coupling ($omegarightarrow -3/2$) for large $Phi$ and the theory is cosmologically attracted toward the conformal coupling.
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