2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231187The field equations of a generalized $f(R)$ type gravity model, in which there is an arbitrary coupling between matter and geometry, are obtained. The equations of motion for test particles are derived from a variational principle in the particular case in which the Lagrange density of the matter is an arbitrary function of the energy-density of the matter only. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the model is also considered. The perihelion precession of an elliptical planetary orbit in the presence of an extra force is obtained in a general form, and the magnitude of the extra gravitational effects is constrained in the case of a constant extra force by using Solar System observations.12 pages, no figures, accepted for publication in PLB. Some further references addedGeneral Relativity and Quantum CosmologyAstrophysicsHigh Energy Physics - Theorytext