Cassini and extra force constraints to nonminimally coupled gravity with a screening mechanism

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