Original abundance of asteroids from their present rotational properties

Mathematics – Probability

Scientific paper

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Asteroids, Mass Distribution, Planetary Rotation, Angular Momentum, Collisions, Size Distribution, Solar System

Scientific paper

A long-standing problem in Solar System evolution is the strong mass depletion that occurred in the asteroid zone. Recent collisional evolution models (Davis et al., 1985) suggest that comminution due to destructive impacts is responsible only for a small part of the mass loss, implying that at the end of the accretionary phase the belt mass was no more than several times the present mass. A similar conclusion can be independently reached by another line of evidence, relying on the present rotational properties of asteroids. The abundance of objects having unusually large angular momenta of rotation in the diameter range 200-300 km implies that, if these angular momenta have a collisional origin, approximately one third of these objects have been hit by projectile asteroids larger than about 65. About 450 such projectiles are currently available in the belt, yielding a 16 per cent impact probability against a 250-km-sized target over the Solar System's lifetime. Hence a moderate mass depletion (by a factor of the order of 5) is consistent with the present abundance of asteroids with rapid spins and elongated shapes.

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