The approximately spherical shape of the C60 molecule permits the calculation of an analytic potential that describes the physical interaction between molecules. This potential was used to study the molecular properties of C60 by computing the second virial coefficient, the compressibility, the lattice vibrational specific heat, the vacancy formation energy, and the energy of the separation of two close packed surfaces. These calculations provide a theoretical framework for the molecular properties of C60 that is consistent with the limited experimental data available. Also, the calculations provide a potential for the interaction of carbon atoms on different molecules which can be used when the spherical approximation is inadequate, as in the solid at low temperatures.