A well-behaved f(R) gravity model in planetary motions

In this paper we consider asymptotic behavior of a hybrid action of f(R) gravity model which proposed by Saffari and Rahvar (2008), in the Solar system scale, which can explain Pioneer anomalous acceleration. We use the resultant weak field gravitational potential which comes from the hybrid action to test its impacts on the Solar system dynamics, by comparing theoretical precession of perihelion of a test particle, ϖ ˙ , with corrections to the standard Newtonian–Einstenian precessions of perihelia of some planets, which recently estimated by Pitjeva (2005a,b, 2006, 2008). Here we show that the asymptotic behavior of hybrid action is in more accordance with observation relative to the other modifications such as power law and logarithmic corrections (Iorio, 2008). We also show that an extra additional lensing of the prediction of General Relativity is reproduced. Finally we consider the stability condition of planetary orbits in the presence of the hybrid action.