Asteroids: equilibrium shapes of rotating gravitational aggregates

Many evidences lead us to think that a significant portion of asteroids are aggregates of boulders kept together by gravity, with little or no contribution from cohesive forces. The standard hydrodynamics results for a self-gravitating and rotating cohesionless body would impose it to stay close to one of the well-known equilibrium sequences of MacLaurin and Jacobi; yet, when we compare the shapes of known asteroids, we find the bulk of the shapes far away from the classical equilibrium case. In this work an analysis of the preferential shapes that a gravitational aggregate tends to assume is presented. Our approach considers the evolution of a variety of initial shapes, free to evolve towards their own shape of equilibrium. The results show that actual asteroid shapes are consistent with the evolution, under the action of gravity alone, of aggregates of free components tending towards states of minimum free energy.