2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/179777The equation of motion for test particles in $f(R)$ modified theories of gravity is derived. By considering an explicit coupling between an arbitrary function of the scalar curvature, $R$, and the Lagrangian density of matter, it is shown that an extra force arises. This extra force is orthogonal to the four-velocity and the corresponding acceleration law is obtained in the weak field limit. Connections with MOND and with the Pioneer anomaly are further discussed.Revtex4 file, 5 pages. Version to appear in Physical Review DGeneral Relativity and Quantum CosmologyAstrophysicsHigh Energy Physics - Theorytext