  We compare Mercury's precession test in standard General Relativity (GR),
Brans-Dicke theories (BD), and Palatini f(R)-theories. We avoid post Newtonian
(PN) approximation and compute exact precession in these theories. We show that
the well-known mathematical equivalence between Palatini f(R)-theories and a
specific subset of BD theories does not extend to a really physical equivalence
among theories since equivalent models still allow different incompatible
precession for Mercury depending on the solution one chooses. As a result one
cannot use BD equivalence to rule out Palatini f(R)-theories. On the contrary,
we directly discuss that Palatini f(R)-theories can (and specific models do)
easily pass Solar System tests as Mercury's precession.

General Relativity and Quantum Cosmology;High Energy Physics - Theory