The fundamental processes of melting, the well known Stefan and Neumann problems, have been of great interest from a theoretical point of view as well as for their wide applications. The yet unmolten part of the material undergoing phase change within spherical containments is generally presumed to remain stationary, an unlikely occurrence in practice. The differing densities of the liquid and the solid may readily cause a force imbalance on the solid in gravitational and perhaps microgravitational environments, thereby moving the solid away from the center. In the present work, an approach related to the theories of lubrication and film condensation was employed and an approximate closed-form solution of melting within spheres was obtained. It was shown that a group of dimensionless parameters containing, Prandtl, Archimedes and Stefan numbers describes the melting process. Fundamental heat transfer experiments were also performed on the melting of a phase-change medium in a spherical shell. Free expansion of the medium into a void space within the sphere was permitted. A step function temperature jump on the outer shell wall was imposed and the timewise evolution of the melting process and the position of the solid-liquid interface was photographically recorded. Numerical integration of the interface position data yielded information about the melted mass and the energy of melting that support the theory.