  The effects of a nonminimally coupled curvature-matter model of gravity on a
perturbed Minkowski metric are presented. The action functional of the model
involves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$.
This work expands upon previous results, extending the framework developed
there to compute corrections up to order $O(1/c^4)$ of the $00$ component of
the metric tensor. It is shown that additional contributions arise due to both
the non-linear form $f^1(R)$ and the nonminimal coupling $f^2(R)$, including
exponential contributions that cannot be expressed as an expansion in powers of
$1/r$. Some possible experimental implications are assessed with application to
perihelion precession.
