  We study the ground state and the first three radially excited states of a
self-gravitating Bose-Einstein- Condensate with respect to the influence of two
external parameters, the total mass and the strength of interactions between
particles. For this we use the so-called Gross-Pitaevskii-Newton system. In
this context we especially determine the case of very high total masses where
the ground state solutions of the Gross-Pitaevskii- Newton system can be
approximated with the Thomas-Fermi limit. Furthermore, stability properties of
the computed radially excited states are examined by applying arguments of the
catastrophe theory.
