This paper exploits the fact that the collapsing core of a massive star, at the endpoint of its thermonuclear life, rapidly becomes hydrostatic after bouncing at nuclear densities. The energy transferred by pdV work from the inner unshocked core as it becomes hydrostatic to the bounce shock in the outer core is, to a good approximation, the initial energy of the supernova. It can be shown semi-analytically that this energy is equal, with minor qualifications, to the binding energy of the hydrostatic remnant. The authors present analytical formulae for the structure and binding energy of a hydrostatic residue modeled as a composite of two nested polytropes. It is demonstrated that the results derived from considering the nested double polytrope are in fact very general and are only weakly dependent on the behavior of the nuclear equation of state.