Solar System planetary orbital motions and f(R) Theories of Gravity
  In this paper we study the effects of $f(R)$ Theories of Gravity on Solar System gravitational tests. In particular, starting from an exact solution of the field equation in vacuum, in the Palatini formalism, we work out the effects that the modifications to the Newtonian potential would induce on the Keplerian orbital elements of the Solar System planets, and compare them with the latest results in planetary orbit determination from the EPM2004 ephemerides. It turns out that the longitudes of perihelia and the mean longitudes are affected by secular precessions. We obtain the resulting best estimate of the parameter $k$ which, being simply related to the scalar curvature, measures the non linearity of the gravitational theory. We use our results to constrain the cosmological constant and show how $f(R)$ functions can be constrained, in principle. What we obtain suggests that, in agreement with other recent papers, the Solar System experiments are not effective to set such constraints, if compared to the cosmologically relevant values. 
Matteo Luca Ruggiero, Lorenzo Iorio