EART 160: Planetary Science

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EART 160 Planetary Science
11 February 2008
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Last Time

• Paper Discussion Stevenson (2001)
• Mars Magnetic Field
• Planetary Interiors
• Pressure inside Planets

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Today

• Midterm graded
• Projects Have you talked to me yet?
• Homework 4 here (due Friday)
• Planetary Interiors
• Temperature inside Planets
• Heat Sources and Cooling Mechanisms
• Rheology

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Mean 30.2 S.D. 3.63 Max 37 Min 25 Median 31
Mean 35 St. Dev. 8
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Midterm Info

• Short Answer Questions
• What happens if Earths mass cut in half?
• Moons orbit becomes unbound! Moon Escapes!
• Common refractories Si, Mg, Fe, S
• H, He, C, O are volatile elements
• Everybody did problem 3
• Only two people did problem 2

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Pressures inside planets

• Hydrostatic assumption (planet has no strength)

• For a planet of constant density r (is this
  reasonable?)

• So the central pressure of a planet increases as
  the square of its radius
• Moon R1800km, P7.2 GPa
• Mars R3400km, P26 GPa

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Pressures inside planets

• The pressure inside a planet controls how
  materials behave
• E.g. porosity gets removed by material compacting
  and flowing, at pressures few MPa
• The pressure required to cause a materials
  density to change significantly depends on the
  bulk modulus of that material

The bulk modulus K controls the change in density
(or volume) due to a change in pressure

• Typical bulk modulus for silicates is 100 GPa
• Pressure near base of mantle on Earth is 100 GPa
• So change in density from surface to base of
  mantle should be roughly a factor of 2 (ignoring
  phase changes)

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Real planets

• Notice the increase in mantle density with depth
  is it a smooth curve?
• How does gravity vary within the planet?

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Phase Transitions

• Under pressure, minerals transform to different
  crystal structure
• How do we detect this?
• Transition zone can sore a LOT of water!
• How do the depths change on other planets?

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Temperature

• Planets generally start out hot (see below)
• But their surfaces (in the absence of an
  atmosphere) tend to cool very rapidly
• So a temperature gradient exists between the
  planets interior and surface
• We can get some information on this gradient by
  measuring the elastic thickness, Te
• The temperature gradient means that the planet
  will tend to cool down with time

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Heat Sources

• Accretion and Differentiation
• U Eacc
• Eacc m Cp DT
• Cp specific heat
• Radioactive Decay
• E H m
• H 5x10-12 W kg-1
• K, U, Th today
• Al, Fe early on
• Tidal Heating in some satellites

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Specific Heat Capacity Cp

• The specific heat capacity Cp tells us how much
  energy needs to be added/subtracted to 1 kg of
  material to make its temperature
  increase/decrease by 1K
• Energy mass x specific heat capacity x temp.
  change
• Units J kg-1 K-1
• Typical values rock 1200 J kg-1 K-1 , ice 4200 J
  kg-1 K-1
• E.g. if the temperature gradient near the Earths
  surface is 25 K/km, how fast is the Earth cooling
  down on average? (about 170 K/Gyr)
• Why is this estimate a bit too large?
• Atmosphere insulates

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Energy of Accretion

• Lets assume that a planet is built up like an
  onion, one shell at a time. How much energy is
  involved in putting the planet together?

In which situation is more energy delivered?
early
later
If accretion occurs by lots of small impacts, a
lot of the energy may be lost to space If
accretion occurs by a few big impacts, all the
energy will be deposited in the planets
interior So the rate and style of accretion (big
vs. small impacts) is important, as well as how
big the planet ends up
Total accretional energy
If all this energy goes into heat, what is the
resulting temperature change?
Is this a reasonable assumption?
Earth M6x1024 kg R6400km so DT30,000K Mars
M6x1023 kg R3400km so DT6,000K What do we
conclude from this exercise?
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Next Time

• Planetary Interiors
• Cooling Mechanisms
• Rheology
• Planetary Atmospheres
• Structure
• Dynamics