Homework III

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Homework III
due Monday, March 30 LEVEL 3 DRAFT (worth 10
points) 1. Title page DONE (with Abstract on
it) 2. Abstract is effectively DONE
Introduction is effectively DONE Motivation
is effectively DONE 3/4. ALL Sections have
some sentences 5/6. Discussion has a few
sentences 7/8. TWO Tables are formatted and
have columns identified 9/10. TWO Figures are
outlined with captions
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Reading Homework
for Monday, March 23 READ CHAPTER 6, in
particular 1. Section 6.3, other terrestrial
bodies and moons 2. Section 6.4, gas and ice
giants
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Planetary Interiors I
observations mass, size, density
terrestrial ? 3.9 to 5.6 silicates Fe/X
core 7 dwarfs ? 1.8 to 3.5 silicates ices
Fe jovian ? 0.7 to 1.6 H He gas/liquid
ices small moons ? 0.3 to 1.9 icy,
porous rotation period, geometric
oblateness oblate spheroid is equilibrium
shape due to gravity rotation gravity
field spacecraft orbits periapse precession
rates of moons/rings
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Planetary Interiors Observations
observations magnetic field energy
output accretion/gravitational
differentiation Jupiter hot, He recently
unmixed Saturn cold, He raining out for long
time radioactive heating (50 of Earth
output) 235U (0.7 Gyr), 238U (4.5), 232Th
(13.9), 40K (1.4) composition of
atmosphere and/or surface seismic data (Earth
and Moon only) dig a hole (Earth and Moon
only) deepest on Earth 12 km in Russia
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Gravity vs. Pressure
hydrostatic equilibrium dP/dr
g(r) ?(r) assuming constant density Pc
3GM2 / 8pR4 lower limit works for objects like
the Moon which have nearly uniform density other
bodies have ?(r) increasing toward center, so Pc
higher accurate calculations require compositio
n mixing ratios and chemistry equation of
state (often quantum theory for gas
giants) temperature structure internal heat
sources heat transport heat loss mechanisms
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Equations of State
equation of state expression relating pressure
(P), density (?), temperature (T),
composition 1. ideal gas P ? k T / µ
m planetary atmospheres 2. electron
degeneracy P 0.049 (h2 / me) (Z? / Amp)5/3
(non-relativisitic) P independent of
T brown dwarfs, normal white dwarfs 3.
electron degeneracy P 0.123 (hc) (Z? /
Amp)4/3 (relativistic) massive white
dwarfs messy planet interior P
complicated function! phases, mixture
chemistry
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Earths Interior
1. thermal structure determines chemical
structure surface structure and
evolution mantle convection drives mountain
building, ocean formation short-term
earthquakes, volcanism convection in the Earths
fluid core maintains the magnetic
field navigation, communication, cosmic
radiation shield 2. geoid map
shows elevations/depressions relative to surface
of equal gravitational potential surface
features vs. geoid reveals how soft mantle
is Earth has minimal match between continents
and geoid
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Earths Geoid
from 100 m
(purple) to 85 m (red) mantle sinks/depressions
India, Hudson Bay, Antarctic/Pacific mantle
upwellings/plumes New Guinea, Icelandic ridge,
Yellowstone hotspot Hawaiian island chain pushed
up subduction zones dragged down
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Earths Interior
1. thermal structure determines chemical
structure surface structure and
evolution drives mantle convection mountain
building, ocean formation short-term
earthquakes, volcanism convection in the Earths
fluid core maintains the magnetic
field navigation, communication, cosmic
radiation shield 2. geoid map
shows elevations/depressions relative to surface
of equal gravitational potential surface
features vs. geoid reveals how soft mantle
is Earth has minimal match between continents
and geoid 3. paleomagnetic records
indicate magnetic field has existed for at least
3.0 Gyr polarity reversals common, averaging
every 200,000 yr reversal events take a few
thousand years
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Earths Magnetic Field
Convective Dynamo Model (Glatzmaier Roberts,
Los Alamos) input dimensions rotation
rate heat flow composition run
20 yr increments for 300,000 yr explains
intensity of magnetic field dipole structure
aligned with rotation non-dipolar drift at
0.2 deg/yr dipole reversals
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Flipping Magnetic Field!

• normal flip minus 500
  yr mid-flip flip
  plus 500 yr
• (blue in, yellow out / Earth rotation is
  vertical / transition is at core-mantle boundary)
• 36,000 yr into simulation, flip!
• field intensity drops by a factor of 10 and then
  recovers
• matches what is seen in paleomagnetic record
• convection in fluid outer core continually tries
  to reverse field, but
• solid inner core inhibits reversals because it
  changes on long diffusion timescale
• 3. a reversal is successful only occasionally,
  therefore 200,000 yr

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Earth Structure
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Earth Layers
upper mantle 6-65 km to 700 km primarily
olivine (Mg,Fe)2SiO4 and pyroxene
(Mg,Fe)SiO3 lower mantle 700 km to 3000
km olivine under high P ? periclase MgO
perovskite MgSiO3 pyroxene under high
P ? garnet fluid outer core 3000 km to 5200
km primarily Fe in composition convective
dynamo present core temp too high for permanent
mag field (decay in 20,000 yr) as Earth cools,
Fe solidifies and sinks, lighter element(s)
rise rising fluid Earth rotation Coriolis
forces cause helical flow ? VOILA! magnetic
field generated solid inner core 5200 km to
6400 km primarily Fe in composition (some
Ni) ? is 5-10 less than pure FeNi S? O?
H? size of Moon temp of Sun!
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Other Terrestrial Worlds
Moon moment of inertia indicates nearly uniform
density core is 13-26 R (compare Earth 19
inner and 53 outer) gravity geoid attributable
to different crustal thicknesses (0 to 107
km) had magnetic field 3-4 Gyr
ago Mercury 60 of planet mass is Fe core
extends to 75 R Venus 3 less dense than
Earth missing some heavy element? no magnetic
field core frozen or lack of rotation? no
tectonics heat loss low (hot mantle?), but
through volcanism Mars no tectonics heat
lost in past via volcanism geoid highly
correlated with topography, so thick, rigid
lithosphere ancient magnetic field evidence now
shattered far more FeO than on Earth Fe-Ni
core or Fe-FeS core?
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Jovian Interiors
Jovian type 1 Gas Giants Jupiter 80 R
below H2 He Saturn 55 R below H2
He Jovian type 2 Ice Giants Uranus 85 R
below H2 He CH4 Neptune 85 R below H2
He CH4
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Jovian Interiors H
hydrogen behavior temp range 50-150K at
tropopause to 10000-20000K at center pressure
range 0 bar to 20-80 Mbar at center lt 1
Mbar hydrogen is H2 solid or liquid gt 1
Mbar hydrogen is mixed molecular/atomic in
Jovians fluid particles closely packed
molecules overlap e swap molecular metallic
hydrogen deeper H2 dissociated H2 ? 2H
occurs 0.95 R to 0.80 R in Jup atomic metallic
hydrogen convection leads to magnetic fields
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Jovian Interiors He and H2O
helium behavior temp and pressure never high
enough to go to metallic form He not fully
mixed in Jupiter and Saturn Saturn has less
pressure than Jupiter, so even less mixed water
behavior 15 different crystalline forms (P,T)
conditions mixtures with trace molecules
conductive fluid explains magnetic fields of
Neptune and Uranus
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Solar System Explorers 2009-5
Write an equation from Chapters 2-5 on the board
(no cheatsheet). Explain it and give an example
of where you would apply it. (P2 a3, KBO at
100 AU) 1. Youll be writing on the board
without a piece of paper in your
hand. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
14. 15. 16. 17. 18. 19. 20.
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Solar System Explorers 2009-6
Describe any observation made of an extrasolar
planet or planetary system that is NOT a radial
velocity measurement. Give the name of the star
system, the technique used, and the science
result. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
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