2. WHY DO WE WANT TO MODEL THE COLLISIONAL EVOLUTION OF MBPs? SOLAR SYSTEM FORMATION : what was the primordial distribution of the minor body population before the collisional evolution begins? Constraints on the planetesimal accretion process. COLLISIONAL PHYSICS: to understand the formation of families and family erosion. Statistical testing of scaling laws on many events. INTRA-POPULATION FLUXES: interrelation among different populations in the solar system (MBAs – NEOs, Trojans – SPC, TNOs – Centaurus….) LIFETIME OF BINARIES, LIMITS ON FAMILY YARKO-EXPANSION.

3. GUESS Initial population of Minor Bodies. GUESS Fragmentation models (Q * D, Q * S, .) Dynamics (V imp,, Yarkowsky, PR drag…) Observational constraints The MODEL MBAs, Trojans, Hildas, KBOs

4. Size and velocity distribution of escaping fragments, c f, s f D p ρ p, c p, s p D t ρ t, c t, s t V imp c = structure: porosity, rubble pile, monoliths.. s = spin rate Simple analytic equations FRAGMENTATION MODEL -1 THE DREAM Benz-Aspahug, 1999: Q * D (D), f l (Q * D, E). N f (D f, Q * D, E) ??

5. FRAGMENTATION MODEL -2: THE SINERGY Impact experiments Scaling laws Hydrocodes Asteroid families Size distribution of minor bodies Craters on planets and asteroids Binary asteroids Meteorites

6. DYNAMICAL EFFECTS: 2) Resonances cause outflow from the belt 3) Dissipative forces (Yarkowsky, PR drag) ( O’Brien & Greenberg, 2001 ): the small body tail problem. Penco, Dell’Oro, La Spina, Paolicchi, Cellino, Campo Bagatin., in press. 1) V i, (Farinella, Davis, Dahlgren, Bottke, Marzari, Dell’Oro, Paolicchi, Greenberg, Vedder, Gil-Hutton…….)

7. Initial population guess Time (yr) Planetesimal accretion ( about 1 Myr) Giant impacts – Mass depletion, stirring of orbital elements ( about 100-200 Myr) Collisional evolution models (about 4.5 Gyr) MBAs Trojans Resonance sweeping, Endogenic dynamical excitation

8. THE ‘CLASSICAL’ NUMERICAL MODEL: 1) Bodies distributed in size-bins 2) v imp input from the dynamics of the population 3) Montecarlo method: computation of representative collisions and distribution of new generated fragments in the bins (the fragmentation model is used here). 4) Time evolution controlled by relative changes in each bin. 6) Tail control with interpolation (???) 5) Families are treated as sub-populations

9. PREDICTIONS OF THE MODEL THAT CAN BE COMPARED TO OBSERVATIONS (The Main Belt case) 1) Size distribution of Main Belt Asteroids 2) Number of families and their slope (Marzari and Davis, 1999) 3) Basaltic crust of Vesta (Davis et al. 1984) 4) Rotation rates (difficult to implement, physics not yet clear) 5) CRE ages of stony meteorites (O’Brien and Grenberg, 2001) 6) Fraction of rubble-piles among asteroids (Bagatin et al. 2001)

10. N(>D) = K D -b 0.4 1.5 Gaspra 20 200 Ida -3.40 5 SDSS -1.30 20 3 Durda -2.34 SDSS -3.00 40 PLS -1.95 SIZE DISTRIBUTION - 2.70

11. Bumps, waves…. what is the origin? 1)Transition regimes in scaling laws or dishomogeneity 3) Different populations  S = 2.7 g cm -3 por: 30%  C = 1.4 g cm -3 por: 40% (from Britt et al. 2002: Ast III) 2) Small size cutoff (non-gravitational forces) ?? Maybe. too gradual to produce waves.

12. D l (km)ModelObservedN. asteroids 5029214.1 10 3 4079641.3 10 4 20325?8.2 10 4 10503?5.4 10 5 5544?3.2 10 6 Number of families vs. completeness limit. Marzari et al. 1999 Number of bodies Diameter 1) COLLISIONAL EROSION 2) NO DYNAMICAL EROSION

13. VESTA: basaltic crust almost intact. The body was not disrupted over the solar system age.

14. Different populations and families Yarkovsky effect, PR drag CPU time MODEL

15. FUTURE DIRECTIONS: Include all dynamical effects and handle the problem of the small body tail Derive strong constraints on the primordial populations of minor bodies, study the history of families Testing different fragmentation models and scaling laws while waiting for the dream to come true (The perfect fragmentation model)

16. –High shot repetition rate (1 shot / 25 min) –Velocity 2-5.5 km/s (200 m/s step) –Projectiles 0.4 - 3 mm –Target temperature control 150-370 K –4 shadowgraphs up to 1 MHz –Shock accelerometers up to 200000g. Resonant freq. 1.2 MHz 1) Guns: FRAGMENTATION MODEL -3: LABORATORY EXPERIMENTS 2) Explosives Review: Holsapple et al. 2002 (Ast. III)