| Abstract: | Basing on the author's work a review of the possibilities as well as the limits of treating the problem of the collisional history of the asteroids by analytical methods is given. Using empirical data on rock fragmentation and general principles like symmetry and mass conservation the distribution function of the fragments arising from a single collision is analytically formulated. The size distribution of asteroids adjusting when crushing collisions have taken place a sufficiently long time can be obtained as the solution of an integrodifferential equation with partial derivatives (equation of fragmentation). Quasi-stationary solutions of the equation of fragmentation are discussed for particular cases. The problem of the steady state is reduced to the solution of a transcendental equation. The results obtained show that analytical methods already offer a good theoretical understanding of the observed size distribution of the asteroids. They should be, therefore, a useful basis of carrying out numerical calculations. |
