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[ Technical Notes > Melting the Inner Earth > References and Notes ]

References and Notes

1. See, for example, Frank D. Stacey, Physics of the Earth (New York: John Wiley & Sons, Inc., 1969), pp. 281–282.

2. The mass expelled from Earth during the flood was probably less than 2.8  × 1024 grams, less than 1/2,000 the mass of the Earth. [See Table 108 on page 340.] Therefore, that lost mass can be neglected. Even if it could not be neglected, it would have only a secondary effect, because the loss of that mass would not alter Earth’s spin rate.

For example, the ice skater shown in Figure 84 on page 154 will spin faster as she pulls her arms in toward her spin axis. However, if her arms ever flew off her spinning body, her spin rate would immediately stop increasing.

3. Only a very small fraction of the preflood Earth’s potential energy was expended in increasing the Earth’s rotational kinetic energy.  The Earth’s angular velocity today is

  

This faster spin rate increased the Earth’s rotational kinetic energy despite Earth’s lower polar moment of inertia. However, this increase was relatively trivial and can be neglected

.

4. This factor of 5 can be estimated by calculating the ratio of the energy released by gravitational settling just within the outer core (Dr  g  V  h) to the energy expended in melting (L  V  rav), where

Dr = the average density difference between particles that sink to the particles that float,

g  = the average acceleration of gravity in the core,

V = the volume of melted rock in the outer core,

h = the average “fall distance” (about half the radius of the outer core),

L = the heat of fusion in the outer core, and

rav = average density of the melted particles.

If           g ª 500 cm/sec2                    h  ª  1,750  × 105  cm

             L ª 4  × 109 ergs/gm            

then this dimensionless ratio is about 5. 

Any ratio that is much greater than 1.0 will produce runaway heating near the center of the Earth. (Other minor effects are being omitted.) Clearly, this factor is large because h (the “fall distance”) is so large. With about 5 times more heat in the core than it takes to melt the outer core, heat within the outer core should be conducting today into and melting the base of the mantle and the top of the inner core.

5. As shown in “Forming the Core” on page 160, the runaway melting diminishes, because the solid mantle’s radial movement diminishes as the core’s radius increases. At the exact center of the Earth, that movement—and the resulting friction, melting, and shrinkage of magma—was a maximum.

6. To understand why most of this heat was released within months, see “Why Did the Flood Water Drain So Slowly” on page 510.

7. Don L. Anderson, Theory of the Earth (Boston: Blackwell Scientific Publications, 1989), p. 68.

8. “The kinetic energy (~5 x 10  38 ergs) released in the largest impacts (1.5 x 10  27 g at  9 km/sec) would be several times greater than that required to melt the entire Earth.”  George W. Wetherill, “Occurrence of Giant Impacts during the Growth of the Terrestrial Planets,” Science, Vol. 228, 17 May 1985, p. 879.

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