  In a model of large distance modified gravity we compare the nonperturbative
Schwarzschild solution of hep-th/0407049 to approximate solutions obtained
previously. In the regions where there is a good qualitative agreement between
the two, the nonperturbative 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.
