Recent analysis of the Milky Way's satellite galaxies reveals that these objects share a common central mass density, even though their luminosities range over five orders of magnitude. This observation can be understood in the context of galaxy formation theory by quantifying the factors which restrict the central mass density to a small range. The satellite central mass is bracketed between two limits. The upper limit is set by the maximum mass that can collapse into a given region by the hierarchical growth of structure in the standard cold dark matter cosmology. The lower limit comes from natural temperature thresholds which exist for gas to be able to cool and form a galaxy. The wide range of luminosities in these satellites reflects the effects of supernova feedback on the fraction of cooled baryons which are retained.