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We solve the Einstein equations in the Randall-Sundrum framework with astatic, spherically symmetric matter distribution on the {\it physical brane}and obtain an approximate expression for the gravitational field outside thesource to second order in the gravitational coupling. This expression whenconfined on the {\it physical brane} coincides with the standard form of theSchwarzschild metric. Therefore, the Randall-Sundrum scenario is consistentwith the Mercury precession test of General Relativity.Comment: 17 pages, plain Tex, references added, typos correcte

Recovery of the Schwarzschild metric in theories with localized gravity beyond linear order