  We consider a nonminimally coupled curvature-matter gravity theory at the
Solar System scale. Both a fifth force of Yukawa type and a further
non-Newtonian extra force that arises from the nonminimal coupling are present
in the solar interior and in the solar atmosphere up to interplanetary space.
The extra force depends on the spatial gradient of space-time curvature R. The
conditions under which the effects of such forces can be screened by the
chameleon mechanism and be made consistent with Cassini measurement of PPN
parameter $\gamma$ are examined. This consistency analysis requires a specific
study of Sun's dynamical contribution to the arising forces at all its layers.
