percent of their mean radii (R m ), but the roughness of the latter as a class (''planetary bodies'') is below 0.01R m .
A variety of techniques have demonstrated that some of the solid bodies of the Solar System have distinct irregular shapes, Furthermore, the maximum topographic relief of small while the rest have sphere-like equilibrium shapes; a sharp bodies increases along with the mean radius, whereas the transition exists between the two. Such an abrupt, mass-depenmaximum surface relief of planetary bodies decreases as dent transition may be explained by the yield strength of matethe mean radius increases (Thomas 1989, Croft 1992). Firial at low temperatures. Gravitational forces in nonequilibrium nally, when both classes of bodies are considered in terms figures produce structural stresses, and if a body is sufficiently of increasing radius, we can observe a well-defined differmassive to produce differential stresses above the yield strength, ence between them. Finally, a sharply defined boundary then the shape of the body will relax into an equilibrium, spherebetween the small and planetary bodies can be defined on like figure. A solution is obtained herein that allows estimation the basis of radius for both icy bodies (Hyperion and Miof the critical size and mass of a body of any composition or, mas, which are irregular and spherical in shape, respecconversely, estimation of the strength properties of real icy and tively) and rocky bodies (2 Pallas and 1 Ceres).
rocky bodies. By use of available data on strength properties of chondrites, the critical radius of an ordinary chondritic body
We suggest that this sharp transition may be explained is estimated to be 756 km. The critical radius of a body with simply by the fundamental or ultimate strength of a body's the composition of select terrestrial basic rocks is estimated to material at a given temperature. The only force that can be 582 km. Each of these figures is between the diameters of overcome the ultimate strength of an irregular body and Vesta (small body) and the Moon (planetary body). At the force it into the figure of an equilibrium ellipsoid is gravity, temperature of the saturnian system (70 K), the yield strength which, in turn, is dependent on the body's mass. Our soluof icy Hyperion and Mimas (both of which are in the transitional tion is based on a plastic-body model [Saint-Venant body size range) is between 0.38 and 1.4 MPa. The yield strength of (Handing 1990)] that is not deformed until the differential Proteus in the neptunian system (30-40 K) is estimated to stress equals the yield strength, after which deformation be 1.62 MPa, illustrating the well-known dependence of yield proceeds. Two major mechanisms form the basis of this strength on temperature and corresponding well to available ''critical mass'' theory: gravitational compression and plasexperimental data on the strength properties of water ice. The asteroids 2 Pallas and 1 Ceres, occupying the transitional size tic deformation. The derived solution yields an exact value range between small and planetary bodies, have estimated yield of the required critical mass or a critical transition size for strengths of 16.0 to 60.2 MPa. These values are much lower any material whose yield strength is known.
than those for ordinary chondrites (about 250 MPa) and are perhaps more appropriate for carbonaceous chondrites.