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Collisional Evolution of Minor Bodies: Modeling and Dynamics

Explore collisional evolution models of minor body populations in the solar system to understand fragmentation, dynamics, and family formation. The dream of a perfect fragmentation model awaits experimental validation for a deeper understanding.

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Collisional Evolution of Minor Bodies: Modeling and Dynamics

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  1. COLLISIONAL EVOLUTION OF MINOR BODY POPULATIONS

  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. LIFETIME OF BINARIES, LIMITS ON FAMILY YARKO-EXPANSION. INTRA-POPULATION FLUXES: interrelation among different populations in the solar system (MBAs – NEOs, Trojans – SPC, TNOs – Centaurus….)

  3. MBAs, Trojans, Hildas, KBOs The MODEL Observational constraints Initial population of Minor Bodies. GUESS Fragmentation models (Q*D, Q*S, r...) OUTPUT(Final size distriution, N. of families…) Dynamics (Vimp, <Pi>, Yarkowsky, PR drag…)

  4. FRAGMENTATION MODEL -1 THE DREAM Dp ρp, cp, sp Vimp Simple analytic equations Dt ρt, ct, st Size and velocity distribution of escaping fragments, cf, sf c = structure: porosity, rubble pile, monoliths.. s = spin rate Benz-Aspahug, 1999: Q*D (D), fl (Q*D , E) . Nf (Df, Q*D , E) ??

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

  6. DYNAMICAL EFFECTS: 1) Vi , <Pi> (Farinella, Davis, Dahlgren, Bottke, Marzari, Dell’Oro, Paolicchi, Greenberg, Vedder, Gil-Hutton…….) 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.

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

  8. THE ‘CLASSICAL’ NUMERICAL MODEL: 1) Bodies distributed in size-bins 2) <pi> vimp 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. 5) Families are treated as sub-populations 6) Tail control with interpolation (???)

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

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

  12. Number of families vs. completeness limit. 1) COLLISIONAL EROSION Number of bodies Marzari et al. 1999 Diameter 2) NO DYNAMICAL EROSION

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

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

  15. FUTURE DIRECTIONS: Testing different fragmentation models and scaling laws while waiting for the dream to come true (The perfect fragmentation model) 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

  16. FRAGMENTATION MODEL -3: LABORATORY EXPERIMENTS 1) Guns: • 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 2) Explosives Review: Holsapple et al. 2002 (Ast. III)

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