A careful discussion of the interaction of the inner electron with the nucleus of the helium atom allows for the reduction to a one-dimensional Hamiltonian describing the frozen planetary atom configuration. This is obtained by cancelling the angular momentum of each electron, even though it is only their sum which is guaranteed to be constant. The true oscillatory nature of the angular momenta in the full two-dimensional Hamiltonian can be included in a time-periodic model that correctly accounts for the finite lifetime of the frozen planetary atom. This system can be further simplified by averaging over the motion of the inner electron so as to define an oscillatory Hamiltonian with a single degree of freedom.