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 solar system scale, which can explain Pioneer anomalous acceleration. We use the potential coming from this hybrid action in weak field limit to test its impacts on Solar system dynamics, by comparing the theoretical precession of perihelion of a test particle, $\dot{\varpi}$ with corrections to the standard Newtonian - Einsteinian precession of perihelia of some planets, recently estimated by Pitjeva. Here we show that obtained results of the asymptotic behavior of hybrid action, are 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 obtain the stability condition of planetary orbits.

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