The semiclassical quantization of classically stable planetary atom configurations (the so called frozen planet configurations) is discussed in some detail. The existence of (approximate) integrals of motion allows for a torus quantization procedure, the semiclassical limit of which is the Gutzwiller periodic orbit formula reduced to fundamental orbits only. We show that the multi-dimensional torus quantization yields accurate semiclassical energies for the planetary atom states. We compare our results with those obtained by a multipole model of the electron- electron interaction which has been proposed as a more transparent model for describing the frozen planet configurations. We give evidence that this model fails in predicting the energies for large quantum numbers.