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Physics of Earth's Evolution
However the Earth came to its presently
differentiated form, it must have obeyed our
known physics:
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Conservation of energy and momentum
The laws of thermodynamics
The laws governing electromagnetism
EPSC 666 November 4, 2009
... Olivia
Energetics
About 4.6 billion years ago, the primordial
Earth condensed from a cloud of planetesimals
with a composition not unlike that of the
chondritic meteorites we find that have fallen to
Earth.
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The gravitational potential energy available in this
collapse could have brought the mass of Earth to a
temperature exceeding 30000K –- a plasma primordial
Earth?
Early Earth
Early Earth surely didn't exist in a gravitybound plasma state; internal temperature
was probably pretty much as it is today –
perhaps a little cooler, perhaps a little hotter.
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Al 26Mg (t½ ~ 700k years; 1000K)
The “Big Splat” (deep magma ocean)
U, Th, K (long-lived; current sources)
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Heat budget
Losses:
1.
2.
Measured global cooling rate: ~30TW → 44TW* and
probably higher during the ancient past.
Geomagnetic field loss (external): ~1 → 4TW
Sources:
Radioactive decay: crust (6 → 9TW), upper mantle
(12 → 21TW), lower mantle (3 → 14TW)
2. Entropy increase in mantle: (~3TW)
3. From core into mantle: ( > 8.6TW + ~1 → 2TW)
4. Remnant primordial gravitational energy: (~9 → 14TW)
1.
* In 2008, average rate of human energy consumption – all forms: 15
→ 16TW
New Theory of the Earth, Anderson, D.L, 2007, Cambridge
Earth model and T
Mao, H-K and Hemley, R, 2007 www.pnas.org cgi doi 10.1073 pnas.0703653104
Modes of cooling
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Inner core: conduction cooling, freezing
surface (an interior source 40K?)
Outer core: very vigorous convection
D'' layer (lowermost mantle): conduction
Lower mantle ( > 660km depth): vigorous
convection
Upper mantle ( < 660km): convection
Lithosphere ( upper 0 – 200km): conduction
Convection
Convection continues to differentiate,
reorganize the Earth's mantle.
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to
Requirements for convection:
Locally, the temperature gradient, dT(z)/dz, must
exceed the adiabatic gradient:
dT(z)/dz > g αP T / CP

The observed “vigour” of mantle convection
suggests that the adiabatic gradient must be
“substantially” exceeded:
The Rayleigh number, Ra, the ratio of bouyant to
viscous forces: Ra ~ 106
Temperature
Mao, H-K and Hemley, R, 2007 www.pnas.org cgi doi 10.1073 pnas.0703653104
PREM
Dziewonski and Anderson (1981)