Impact Cratering on Small Bodies a well-posed problem? Erik Asphaug • Earth Sciences Department, UCSC [email protected].
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Impact Cratering on Small Bodies a well-posed problem? Erik Asphaug • Earth Sciences Department, UCSC [email protected] Chapman et al. 2001 Gaspra Galileo SSI Oct 29, 1991 Craters or Facets? Keith: “The Siren of CPU Power” Benz and Asphaug 1994,95: rock fracture model is resolution independent and simulates the available laboratory data (Nakamura and Fujiwara 1991; Rubin and Ahrens 1993; Housen and Holsapple 1999) Just so you know… catastrophic disruption is far easier to model than cratering. High strain rates can typically be assumed; outcome is typically well defined; simple EOS can often be adequate. Large Rocks are More Easily Disrupted Housen and Holsapple (1999); simulated in SPH by Bruesch and Asphaug (2002) Q*D R-3/m (Farinella et al. 1982; Fujiwara 1980) Q *D Q*D is the specific energy (erg/g) required to catastrophically disrupt a target (fragmentation and dispersal of 50% of the original mass) Keith: “The Siren of CPU Power” Benz and Asphaug 1994,95: rock fracture model is resolution independent and simulates the available laboratory data (Nakamura and Fujiwara 1991; Rubin and Ahrens 1993; Housen and Holsapple 1999) Just so you know… catastrophic disruption is far easier to model than cratering. High strain rates can typically be assumed; outcome is typically well defined; simple EOS can often be adequate. Structural Clues from Meteorites? ordinary chondrite meteorite Meteorites are highly selected! saddle of Himeros on Eros What about shapes? Shapes by Scott Hudson, Steve Ostro, et al. 6489 Golevka <1 km diameter One is a “rock”, one is clearly “something else” 216 Kleopatra >200 km across Hints from Asteroid Spins • Barrier at crit • Do asteroids larger than 150 m lack cohesion ? • Conversely, are smaller asteroids monolithic? crit2 = 4/3 G Pravec et al. 2002 required strength is small, ~R22 Size distribution of the fragments follow a size distribution ~1.56, similar to the comet distribution as a whole and to the size distribution of asteroids (Weissman et al. 2003) If fragments are formed in disruptions… where are the small comets? Comet LINEAR 1999 S4 Comet Shoemaker-Levy 9 and the Catenae of Ganymede and Callisto From Asphaug, Schenk and Zahnle (in prep) Asteroids as Experiments 1996: The advent of realistic shape models for code simulations Can begin to seek detailed agreement between modeling and experiments - asteroids as experiments - crater diameter Thomas et al., Science 2001 - crater distal rupture - ejecta and block distribution Quic kTime™ and a TIFF ( Unc ompr ess ed) dec ompres s or ar e needed to s ee this pic tur e. Can learn target geology from their observed response to impacts 3D Eros SPH model with Shoemaker Regio “repaired” And pure forward modeling: can predict outcomes of collisions if we know the target geology! Castalia Ostro et al. 1990 shape model Asphaug and Scheeres 1999 Phobos and Stickney Crater Asphaug and Melosh (1993) concluded that Stickney formed in the gravity regime, and that shattering is much easier to achieve than dispersal. t=12min (Note: radial fractures modeled in 3D SPH) We also found that an incoherent or porous Phobos would not have antipodal fractures, as anticipated from laboratory experiments (e.g. Love, Brownlee and Hörz 1991) Homogeneous Porous Asphaug and Benz 1994; Asphaug et al. 1996 Can we reproduce tectonic features associated with specific impacts? QuickTime™ and a SGI decompressor are needed to see this picture. White = Fractured Ida Asteroid Ida Conclusions (from Asphaug et al. Icarus 1996) • Ida propagates impact stresses coherently. It may be shattered, but it is not a rubble pile. • Gravity regime starts at ~1 km diameter for craters forming on Ida More General Analysis: Cratering or Disruption Outcome Depends on Asteroid Structure Impact modeling of two asteroids, of identical shape and mass, hit by identical smaller asteroid. Mass loss and v differ by more than a factor of 2. Left: monolith Right: rubble-pile Bottom: xy, yz slices Color: fracture damage Momentum and Energy Deposition Vary Widely rubble pile monolith 5 km/s 16m diameter rock impacting from top into equal-mass targets For contact binary asteroids, the shock is confined to the impacted lobe Just as geology is affected strongly by impacts… … so impacts are affected strongly by geology! space spuds Why is this shape so common? Gradual Shape Evolution of Asteroids? 3D Model: • Gravity-regime ejection • Werner (1994) polygon gravitation • Local angle of repose maintained • Analyze time evolution of rotation and shape • Do asteroids evolve, through shape instability, into “peanuts”? So far, the process appears to make “muffins” rather than “peanuts” Koycansky and Asphaug (in press) QuickTime™ and a Y UV420 codec decom pressor are needed to see this picture. Eros: One might say an aeolian landscape Closest Image of Eros Consider a simple assumption: Cohesion contact area / volume ~ (grain size)-1 Quic kT ime™ and a T IFF (Unc ompres sed) dec ompres sor are needed to see this pic ture. Small bead coated with particles of Xerox® toner How would sand behave on a 1 km asteroid? Sand exhibits the ability to sustain ~33° slopes. There is also some cohesion, which for dry sand in 1G is minimal. . Let’s assume a 1 km asteroid, g = 10-5 G, and ask how cohesive, relative to gravity, is sand? (dgrain300m) If cohesion 1/dgrain we expect scale-equivalent behavior in 1G by nano-powders 0.003m diameter. These are bizarre substances. For reference, Xerox® toner particles have diameter 12.7m, so the desired behavior of sand on a 1 km asteroid would be >103 times more cohesive. • To get behavior like Xerox® toner, you’d need grain sizes one meter diameter! Add to that UV ionization at 1AU without an atmosphere (Lee et al. 1996; Sickafoose et al. 2000) Surveyor image of the western lunar horizon shortly after sunset. The white arrow is pointing at a layer of dust levitated ~ 1 meter above the surface. (LASP) Granular segregation salt and sand rotating inside of a clear lucite cylinder become self-segregated QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Blocks littering the surface of Eros. NEAR image 0153130598 Choo et al., Phys. Rev. Lett., 79 (1997) Upon repeated shaking or other periodic disturbance, granular media can undergo sorting by size, density, or elastic properties. “How do we know that the creations of worlds are not determined by falling grains of sand?” - Victor Hugo, Les Miserables Quic kT ime™ and a T IFF (Unc ompres sed) dec ompres sor are needed to see this pic ture. Largest blocks are 2 to 3 m Descent Image Feb 12 2000 “Ponds” imaged from low-altitude flyover Explosion Cratering Experiments • Mechanics of asteroid and comet surfaces • Spectroscopy beneath the surface materials • A relatively fail-safe way to poke and prod geologic structures • Seismology • By filming these events, can create simulation chambers back home for constructing more ambitious landers, hoppers, rovers and excavators Asteroid Surface Probe designed by Ball Aerospace for the Deep Interior spacecraft proposal Faults and Joints on Eros NLR Science Team (L. Prockter) • Is Eros competent? • Or is it fragmental? “… a well-defined base or thickness of regolith may not exist on this object.” - Robinson et al., The geology of 433 Eros (MAPS 2002) normal stress across a fault hydrostatic stress center of Mohr circle + Equations of fault and joint mechanics projected deviatoric stress traction across a fault Mohr-Coulomb Slopes on Eros NLR Team Eros is not mountainous: Only 2% is steeper than 40° QuickTime™ and a Only 5% is steeper than 33°are neededdecompressor to see this picture. Angle of Repose Glass beads ~20o Average for common unconsolidated materials ~33o Steepest stable angle for highl angular, poorly sorted rocks (talus) ~40o-50o Water-rich soils up to 90o Zuber et al. (2000); Asphaug et al. (2002) Low-Velocity Impacts Hypothesis Check: 700m diameter crater Four ~100m diameter rocks Original impactor mass: 2·1013g Impact speed: use vorbit ~1000cm/s Pi-group scaling: assume dry sand Dcrater~ 300m Assume constant deceleration 1000cm/s=√(2ax) x~10000cm a=-50cm/s2 Stress = 2·1013g · 50cm/s2 / (1000cm)2 = 108dyn/cm2 This is about the expected strength of competent rocks NEAR Image 0136819148 “These things tend to come in pairs” -- Woody Allen 1999 KW4 (Ostro et al. 2001 radar) Merline et al. 2002 (Asteroids III): About 15% of all asteroids have satellites! Known from doublet crater statistics (Stansberry and Melosh 1990 Do they form by impact? Galileo Image Dactyl Satellite of Ida Gradient Image Mathilde An Asteroid that Shouldn’t Exist? • Mathilde is more than 30% “crater void” • The rest of Mathilde is ~50% pore space • No evidence for structural damage from impacts (!) • No evidence for ejecta emplacement, either: The gravity regime won’t work • And a very puzzlingly slow rotation (17.4 days) Second image mosaic of Mathilde, at NEAR’s closest approach: Perfect targeting, but of what? Strength regime does not apply to Mathilde… Asphaug and Thomas 2000 but gravity regime does not apply either! (no ejecta blankets) Compaction Cratering to the Rescue? Housen and Holsapple, Nature, 1999 • Primitive asteroids begin as porous crushable material • Mascons will form at the craters • Angular momentum of impactors will be conserved “At the early stage existence of dense solar nebula gas keeps relative velocity of the solid bodies lower. This results in low impact velocity and weak impact process. But highly porous material also has a quite low acoustic velocity and low impact velocity yields high Mach state and resultant compaction is induced.” - Kurita et al. LPSC 1999 Inelastic Collisions: A Random Walk in 3-Space 120 100 Percent with Lower Angular Momentum 80 Cumulative Angular Momentum after Seven Giant Impacts on Mathilde 60 40 Present Angular Momentum of Mathilde = 1.5·1020 Probability = 1.5% 20 0 0.00E+00 1.00E+20 2.00E+20 3.00E+20 4.00E+20 5.00E+20 -20 Angular Momentum (kg m2/s) 6.00E+20 7.00E+20 8.00E+20 9.00E+20 Mass of Planet Angular Momentum Spin Axis Spin Period Agnor, Canup and Levison (1999) This is a familiar problem to accretion theorists: Under inelastic accretion, planets start to spin themselves to pieces! Stalled Shock Cratering Asphaug et al. 2002 • Nearly all crater ejecta is accelerated to escape velocity • The impact deposits less angular momentum to the asteroid • No mascons are anticipated at the craters Survival of the Weakest? • Initial bombardment, if non-catastrophic, will produce a rubble pile • Low crushing strength and rapid shock attenuation allow rubble piles to withstand further bombardment So, are rubble piles the natural end state of asteroids? ©Scientific American 2000 Conclusions: 1) Asteroids and meteorites as benchmarks for impact models 2) SPH with explicit Weibull fracture is a good framework for understanding radial fracture (+ gravity, + Mohr-coulomb) 3) Vesta, the V-type asteroids, and the HED meteorites