Modeling the YORP Effect

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Modeling the YORP Effect

• Radiative Spin-up and Spin-down of Small
  Asteroids D. Rubincam
• And
• YORP-Induced Long-Term Evolution of the Spin
  State of Small Asteroids and Meteoroids
  Rubincams Approximation
• - D. Vokrouhlicky and D. Capek
• Presented by David Riethmiller
• 26 September 2007

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Yarkovsky OKeefe Radzievskii Paddock Effect

• Asteroids rotate with some angular velocity
• YORP is a radiation recoil effect that puts a
  net torque on the asteroid
• We are interested in how the asteroids spin rate
  evolves with time, due to the YORP effect.

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Yarkovsky OKeefe Radzievskii Paddock Effect
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Directed Radiation

• Observed radiant intensity proportional to
  cos(?)
• Consequence area element viewed from any angle
  measures same radiance

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Surface Modeling

• Surface of asteroid modeled as triangular facets,
  based on Gaussian Random Sphere method
• Each facet absorbs sunlight and reradiates
  immediately

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How to Use the Model

• Power deposited on surface element dA

• rs unit vector from asteroid to sun
• N unit vector normal to surface element
• S insolation
• FS incident solar flux

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More How to Use It

• Assume each surface element in radiative steady
  state with respect to insolation
• (all energy absorbed gets re-radiated immediately
• Surface elements act as blackbodies

• Lamberts Law gives the recoil force per unit
  area on dA

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The Important Part

• If r is the vector from the asteroid center of
  mass to the area element, the torque on each area
  element is given by

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Obliquity

• Unlikely that the net torque will maintain the
  asteroids spin axis orientation
• How will torque components change the orientation
  over time?

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Obliquity Evolution Type I
Stable e at 90 (Eros)
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Obliquity Evolution Type II
Stable e at 0 and 180 (Deimos)
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Obliquity Evolution Type III
Stable e at 35 and 150 (Geographos)
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Obliquity Evolution Type IV
Stable e at 90 and 180 (Golevka)
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Conclusions

• YORP is a radiation recoil effect that puts a
  net torque on an asteroid.
• This net torque changes the spin axis orientation
  (obliquity) and rotation period of the asteroid
  over time.
• Asteroid shape influences its evolution type,
  characterized by points of stable obliquity.

Got roids?
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Extra Slide 1 Spherical Harmonic Surface Modeling

• The models used are spherical harmonic expansions
  on known asteroid shapes

• Plm(cos ?) Legendre polynomial of degree l and
  order m
• ? co-latitude
• ? east longitude
• Almi shape coefficients derived from inner
  products of spherical harmonics with numerical
  shapes

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Extra Slide 2 Gaussian Random Spheres

• Original model called for spherical harmonic
  expansion on known asteroid shapes
• Improved model uses Gaussian Random Spheres
• The radii of a large sample of objects satisfy
  log-normal statistics with a variance s and a
  characteristic dimensional factor a, and the the
  radius r in the direction given by spherical
  angles ? and f may be expressed as

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Extra Slide 3 Long-Term Obliquity Evolution