2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227714We show that any analytic $f(R)$-gravity model, in the metric approach, presents a weak field limit where the standard Newtonian potential is corrected by a Yukawa-like term. This general result has never been pointed out but often derived for some particular theories. This means that only $f(R)=R$ allows to recover the standard Newton potential while this is not the case for other relativistic theories of gravity. Some considerations on the physical consequences of such a general solution are addressed.5 pagesGeneral Relativity and Quantum CosmologyCosmology and Nongalactic Astrophysicstext