In modern thought, the orbits of the planets are viewed as the paths of those planets through mostly empty space. Ancient and medieval thinkers, however, considered the celestial orbs to be thick spheres of rarefied matter nested one within the other, each one in complete contact with the sphere above it and the sphere below. When scholars applied Ptolemy's epicycles, they presumed that each planetary sphere was exactly thick enough to accommodate them. By combining this nested sphere model with astronomical observations, scholars calculated what became generally accepted values at the time for the distances to the Sun: about , to the other planets, and to the edge of the universe: about . The nested sphere model's distances to the Sun and planets differ significantly from modern measurements of the distances, and the size of the universe is now known to be inconceivably large and continuously expanding.