We consider a family of holomorphic embeddings K f : C 3 → CP(M f ) of nondegenerate quadric C 3 in C 4 into complex projective Hilbert space CP(M f ) parametrized by functions f ∈ F 3 ⊂ C∞ (R + , R). We show that there is a natural correspondence between this and the Kepler system. Taking this into account we give a complete classical as well as quantum description of the system in terms of the map K f . In this way we illustrate in the paper a nontrivial application of the theory developed in our earlier publications