An Internal Heating Model to Elucidate the Shape of a Small Planetary Body

Small planetary bodies usually have irregular shapes. If they are large enough to be heated to a partial melting status, the deforming force of gravity could overcome the internal forces and make the shape transfigure from potato-like to spherical. We have developed a model to calculate the thermal history of a planetoid and apply the model to asteroids, since ample evidence has shown that many asteroids could have undergone differentiation. After revealing the relation between the shape and the ratio of the melt part, we also examine the surface roughness of these asteroids and suggest that 280 km would be a critical radius for an asteroid to develop a virtually globular contour.