  We explore local consequences of a non-zero cosmological constant on
astrophysical structures. We find that the effects are not only sensitive to
the density of the configurations but also to the geometry. For non-homogeneous
configurations, we calculate the effects for a polytropic configurations and
the isothermal sphere. Special emphasis is put on the fact that the
cosmological constant sets certain scales of length, time, mass and density.
Sizable effects are established for non spherical systems such as elliptical
galaxy clusters where the effects of $\Lambda$ are growing with the flatness of
the system. The equilibrium of rotating ellipsoids is modified and the
cosmological constant allows new configurations of equilibrium.
