On astrophysical bounds of the cosmological constant

Astrophysical bounds on the cosmological constant axe examined for spherically symmetric bodies. Similar limits emerge from the hydrostatical and gravitational equilibrium and the validity of the Newtonian limit. The methods in use seem to be disjoint from the basic principles, however they have the same implication regarding the upper bounds. Therefore we will compare different inequalities and comment on the possible relationship between them. These inequalities are of relevance for the so-called coincidence problem and for the bound of the cosmological constant which comes surprisingly close to the "experimental" value.