Do%20100%20km%20asteroids%20spin-fission%20into%20binaries?

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Do 100 km asteroids spin-fission into binaries?
Keith Holsapple University of Washington Seattle,
WA
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Really The theories of shape v. spin limits
implications for binary fission

• What guidance do theories give us on
  interpretation of observations?
• What guidance on expectations of code
  calculations?

Binaries may form when spin limits are exceeded
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Hierarchy of Theories

• Ellipsoidal shapes
• Fluids
• Idealized Rubble piles
• Real Rubble piles
• Cohesive bodies
• Other shapes
• Fluid Dumb-bells,
• Fission,
• Binaries and other multiple bodies

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Permissible states must satisfy

1. Equilibrium throughout
2. Stress-free on surface
3. Any material constraints (strength)
4. And stability

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Ellipsoidalfluid and rubble piles

• Fluid no shear stresses, Maclaurin and Jacobi
  shapes
• Idealized rubble pile pressure dependent
  strength

Shear strength
Tan(?)
pressure
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Range of spin limits
2.3 hr
Rigid, surface spin-off
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Summary Ellipsoids, fluids and ideal RP

• Fluids limited in shape
• RP have much larger, but definite range of spins
  at any given shape
• There is no size scale to the problem same
  solutions at any scale

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The data
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So there is a size dependence

• why do the observed spins fall off at large
  sizes??

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Why do all gt30 km asteroids have a lower limit
spins than the smaller ones??

• Their strength is lower?

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Is everything big required to be on the Jacobi
curve??

• Astronomers routinely ASSUME Jacobi shapes are
  required, and solve for things like mass density
• 2003 EL61
• Or infer density profiles
• E.g. Ceres

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Why?

• All materials relax over time???
• So asteroids would, if they lasted long enough,
  all become the Jacobi ellipsoids?
• But they don't last that long??
• Or a certain pressure threshold must be exceeded
  for relaxation?
• Or is there another reason?

• The strength is constant in time, but smaller for
  large bodies?

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Recall that

• The spin limit does depend on friction angle ?

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Spin limits versus Friction angle.. ??????
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• Maybe large asteroids have a lower friction
  angle??

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Data
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The real strength of rocks(not the Mohr-Coulomb
idealized model)
Effective friction angle decreases with size..
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So

• The effective angle of friction does decrease
  substantially as the body size (and pressure)
  increased, and that would account for a
  decreasing spin limit

So does this idea work? Well, sort of, with a
little encouragement
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The Hoek Brown strength model for "rock masses"
?50
?43
600 km asteroid
?40
?17
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So if the friction angle changes from about 40
to 17, then

• There could well be a difference approaching 21
  in the spin limits as the asteroid diameter
  approaches 600km or larger

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So, (by reaching a little) we could get a limit
curve that looks like
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Ellipsoids, Cohesivecan spin a lot faster..
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Other shapes

• Known for fluids (binary stars), remember there
  is no size scale in the theory..

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Equilibrium Shapes of Fluid bodies
10 hr
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The dumb-bell -gt binary branch
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The pear-shaped sequence (terminates in mass
shedding)
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The binary sequence
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The hamburger sequence
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Code calculations

• The challenge can they reproduce the known
  fission mechanisms for fluid bodies?
• Should not RP bodies admit those solutions (as
  well as others)??

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More study required..

• (If we knew what we were doing, it wouldn't be
  called research..

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Range of spin limits
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