  We calculate the orbits of a particle in Schwarzschild spacetime, assuming
that the dynamics is governed by a Snyder symplectic structure. With this
assumption, the perihelion shift of the planets acquires an additional
contribution with respect to the one predicted by general relativity. Moreover,
the equivalence principle is violated. If one assumes that Snyder mechanics is
valid also for macroscopic systems, these results impose strong constraints on
the value of the coupling parameter of the Snyder model.
