Gravitomagnetic effects in Palatini f(R) theories of gravity

We explicitly worked out the orbital effects induced on the trajectory of a test particle by the the weak-field approximation of the Kerr-de Sitter metric, which is a solution of vacuum f(R) field equations, in the Palatini formalism. It results that the node, the pericentre and the mean anomaly undergo secular precessions proportional to k, which is a measure of the non linearity of the theory. We used such theoretical predictions and the latest observational determinations of the non-standard precessions of the perihelia of the inner planets of the Solar System to put a bound on k getting k ≤ 10 m. The node rate of the LAGEOS Earth’s satellite yields k ≤ 10 m. The periastron precession of the double pulsar PSR J0737-3039A/B allows to obtain k ≤ 3× 10 m. Subject headings: Classical general relativity–Approximation methods; equations of motion–Experimental tests of gravitational theories–Orbit determination and improvement