Collisional breakup of particles in a planetary ring

Jeffreys (1947) estimated the size of fragments resulting from breakup of a satellite inside the Roche limit, obtaining a result of about 100 km. This result does not allow for the further breakup of the fragments due to collisions among themselves, which should reduce the maximum size to less than about 3 km for rock, or less than about 1 km for ice. This result affects not only Jeffreys' speculations as to the origin of Saturn's rings, but also recent speculations on the origin of the moon by capture and the possible tidal destruction of satellites of Mercury or Venus.