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COLLISIONAL EVOLUTION
OF MINOR BODY POPULATIONS
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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.)
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The MODEL
MBAs, Trojans, Hildas, KBOs
Observational constraints
Initial population of Minor Bodies. GUESS
Fragmentation models (QD, QS, r...)
OUTPUT (Final size distriution, N. of families)
Dynamics (Vimp, ltPigt, Yarkowsky, PR drag)
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FRAGMENTATION MODEL -1 THE DREAM
Dp ?p, cp, sp
Vimp
Simple analytic equations
Dt ?t, ct, st
Size and velocity distribution of escaping
fragments, cf, sf
c structure porosity, rubble pile,
monoliths.. s spin rate
Benz-Aspahug, 1999 QD (D), fl (QD , E) .
Nf (Df, QD , E) ??
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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
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DYNAMICAL EFFECTS
1) Vi , ltPigt (Farinella, Davis, Dahlgren,
Bottke, Marzari, DellOro, Paolicchi, Greenberg,
Vedder, Gil-Hutton.)
2) Resonances cause outflow from the belt
3) Dissipative forces (Yarkowsky, PR drag)
(OBrien Greenberg, 2001) the small body tail
problem.
Penco, DellOro, La Spina, Paolicchi, Cellino,
Campo Bagatin., in press.
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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)
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THE CLASSICAL NUMERICAL MODEL
1) Bodies distributed in size-bins
2) ltpigt 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 (???)
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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 (OBrien and
Grenberg, 2001)
6) Fraction of rubble-piles among asteroids
(Bagatin et al. 2001)
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Ida
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SIZE DISTRIBUTION
N(gtD) 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
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Bumps, waves. what is the origin?

1. 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)
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Number of families vs. completeness limit.
Dl (km) Model Observed N. asteroids
50 29 21 4.1 103
40 79 64 1.3 104
20 325 ? 8.2 104
10 503 ? 5.4 105
5 544 ? 3.2 106
1) COLLISIONAL EROSION
Number of bodies
Marzari et al. 1999
Diameter
2) NO DYNAMICAL EROSION
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VESTA basaltic crust almost intact. The body was
not disrupted over the solar system age.
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Yarkovsky effect, PR drag
CPU time
MODEL
Different populations and families
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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
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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)