  We study the problem of relaxing a large cosmological constant in the
astrophysical domain through a dynamical mechanism based on a modified action
of gravity previously considered by us at the cosmological level. We solve the
model in the Schwarzschild-de Sitter metric for large and small astrophysical
scales, and address its physical interpretation by separately studying the
Jordan's frame and Einstein's frame formulations of it. In particular, we
determine the extremely weak strength of fifth forces in our model and show
that they are virtually unobservable. Finally, we estimate the influence that
the relaxation mechanism may have on pulling apart the values of the two
gravitational potentials Psi and Phi of the metric, as this implies a departure
of the model from General Relativity and could eventually provide an
observational test of the new framework at large astrophysical scales, e.g.
through gravitational lensing.
