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In this paper we use the latest corrections to the Newton-Einstein secularperihelion rates of some planets of the Solar System, phenomenologicallyestimated with the EPM2004 ephemerides by the Russian astronomer E.V. Pitjeva,to put severe constraints on the range parameter lambda characterizing theYukawa-like modifications of the Newtonian inverse-square law of gravitation.It turns out that the range cannot exceed about one tenth of an AstronomicalUnit. We assumed neither equivalence principle violating effects nor spatialvariations of $\alpha$ and $\lambda$. This finding may have importantconsequences on all the modified theories of gravity involving Yukawa-typeterms with range parameters much larger than the Solar System size. However,caution is advised since we, currently have at our disposal only the periehlionextra-rates estimated by Pitjeva: if and when other groups will estimate theirown corrections to the secular motion of perihelia, more robust and firm testsmay be conducted.

Constraints on the range lambda of Yukawa-like modifications to the Newtonian inverse-square law of gravitation from Solar System planetary motions