Precession shift in curvature based extended theories of gravity and quintessence fields

AbstractIn this paper we constrain the sizes of hypothetical new weak forces by making use the data coming from the precession of Planets. We consider the weak field approximation of Scalar–Tensor Fourth Order Gravity (STFOG), which include several models of modified gravity. The form of the corrections to the Newtonian potential if of the form of Yukawa-like potential (5th force), i.e. $$V(r)=\alpha \frac{e^{-\beta r}}{r}$$ V ( r ) = α e - β r r , where $$\alpha $$ α is the parameter related to the strength of the potential, and $$\beta $$ β to the range of the force. The present data on periastron advance allow to infer a constraint on the free parameter of the gravitational models. Moreo…