This paper presents a detailed study of $ f(R,T) $ gravity, a modified theory of gravity where the gravitational Lagrangian is an arbitrary function of the Ricci scalar $ R $ and the trace $ T $ of the stress-energy tensor. The field equations are derived using a variational principle, and the equations of motion for test particles are obtained. The model is shown to depend on the nature of the matter source, and several particular cases are analyzed, including scalar field models where the trace $ T^\phi $ is the stress-energy tensor of a self-interacting scalar field. The Newtonian limit of the model is analyzed, and the effect of an extra acceleration on the motion of test particles is discussed. The paper also considers the perihelion precession of Mercury as a test of the model, providing a constraint on the magnitude of the extra-acceleration. The results show that the model can reproduce the observed precession of Mercury, and that the extra-acceleration is small compared to the expected values for dark matter or the Pioneer anomaly. The paper concludes that $ f(R,T) $ gravity is a viable alternative to general relativity, with potential applications in cosmology and astrophysics.This paper presents a detailed study of $ f(R,T) $ gravity, a modified theory of gravity where the gravitational Lagrangian is an arbitrary function of the Ricci scalar $ R $ and the trace $ T $ of the stress-energy tensor. The field equations are derived using a variational principle, and the equations of motion for test particles are obtained. The model is shown to depend on the nature of the matter source, and several particular cases are analyzed, including scalar field models where the trace $ T^\phi $ is the stress-energy tensor of a self-interacting scalar field. The Newtonian limit of the model is analyzed, and the effect of an extra acceleration on the motion of test particles is discussed. The paper also considers the perihelion precession of Mercury as a test of the model, providing a constraint on the magnitude of the extra-acceleration. The results show that the model can reproduce the observed precession of Mercury, and that the extra-acceleration is small compared to the expected values for dark matter or the Pioneer anomaly. The paper concludes that $ f(R,T) $ gravity is a viable alternative to general relativity, with potential applications in cosmology and astrophysics.