Short distance non-perturbative effects of large distance modified gravity

In a model of large distance modified gravity we compare the non-perturbative Schwarzschild solution of [G. Gabadadze, A. Iglesias, Phys. Rev. D 72 (2005) 084024, hep-th/0407049] to approximate solutions obtained previously. In the regions where there is a good qualitative agreement between the two, the non-perturbative solution yields effects that could have observational significance. These effects reduce, by a factor of a few, the predictions for the additional precession of the orbits in the Solar system, still rendering them in an observationally interesting range. The very same effects lead to a mild anomalous scaling of the additional scale-invariant precession rate found by Lue and Starkman.