Natural systems tend to minimize their energy. Hence an important problem in astrophysics is the parametrization of the ground state. In this context a quantum statistical approach is very useful. The problem of the variational approximation of the density matrix is extended towards a parametrization of the ground state. With an analogy to the semiclassical approach, a classical approach to the variational principle in the parametrization of the ground state is elucidated and its applications are discussed. We find that planetary systems tend to have circular orbits in an effort to attain the ground state. The results of this paper may be useful for the modern problem of detecting planets around bright stars.