Internal structure and densities of the solid worlds II - physical evidence


Deformation of solids: Suppose we have a bar of stiff nylon suspended by one end. If we suspend weights from the free end, the force of the weights pulling on the bar is stress. When the bar responds by stretching slightly, the change in its length is strain.

Stiffness: A graph of this relationship shows a line whose slope is Young's modulus, which represents the solid's stiffness.

Strength: The amount of stress required to make the solid break, its tensile strength, represents the solid's strength.

Note: Stiffness and strength are not necessarily linked.
Objects can be strained in three different ways:

Yield strength: In a typical trial, a solid would deform elastically up to a point, then ductility, then brittlely (it would break.) This gives us two measures of strength:

The real fun is that all of these parameters can vary depending on:

Crater Glacier on Mt. St. Helens from Wikipedia
Thus in the planets we see: On a human scale, we see this transition in glacial ice (right). On a larger, scale, the same relationship holds for planets' rocky crusts.

Earthquakes result from the quick release of energy when brittle deformation occurs. As a result, they occur within a few tens of km of the surface.

Earthquakes and Seismology:

Types of energy released when earthquake occurs - waves

Link to video of August 23, 2011 Virginia Earthquake seismic waves.

Wave speed: Each wave type travels with a characteristic speed.

Thus, if you stand some distance from an earthquake epicenter, you feel P waves first, then S waves, then surface waves. The farther away you are, the longer the lag time between these waves. This lag can be used to locate the epicenter, provided three observers at separate locations keep track.

Seismic waves as emmissaries to Earth's interior: Early study of seismic waves revealed that they were both reflected and refracted by inhomogeneities within the Earth. The foremost observation, however, was that they didn't travel at uniform speed. The image at right indicates changes of wave velocity with depth for P and S waves. Note:

Some items of interest:

Shadow zones: The presence of a molten substance starting at 2900 km is demonstrated by the S wave shadow that it casts. Moreover, refraction of P waves at the solid liquid interface "focuses" them so that a ring-shaped P wave shadow also exists.

Moment of Inertia

This is a rotating object's tendency to resist changes in its rate of rotation and reflects the distribution of its mass around its rotational axis. You know about the effect that folding your arms has when you are spinning. This happens because when you move the mass of your arms closer to your axis of rotation, you alter your moment of inertia. Observations of how celestial bodies interact with one another gravitationally enable us to determine their moments of inertia and make inferences about the distribution of their mass.

The moment of inertia (I) of a rotating object is given by:

I = C M R2

where M is the object's mass, R is its radius, and C, the moment of inertia coefficient, is a parameter that depends on the object's internal distribution of mass.

The example at right contrasts C for hypothetical planets of identical mass and radius but different mass distributions.Observed C for some planets include:

Thus, the moon is nearly uniform in density whereas the Sun is massively self-compressed. Earth has a significant concentration of mass at its center, in agreement with the other lines of evidence we have discussed.

The differentiated Earth

The stratified Earth from Prentice Hall via Purdue University.
At this point, we have a developing picture of Earth's interior, divided into distinct physical and compositional regions: So, what might the inner and outer core be made of?

Magnetic fields

Model of Earth's magnetic field from DKimages.
When an electric current travels in a circuit, it generates a magnetic field. Similarly, when a magnetic field moves or changes intensity, it induces current in nearby electrical paths. These two processes feed back on one another in active cores to sustain a planetary magnetic field. The energy to keep it going comes from movements in the fluid metallic core, driven by convection and the planet's rotation. This process requires that the core be metallic, because metals conduct electricity well. (Indeed, no known solid could support a magnetic field at deep Earth temperatures.) Thus, we know that the outer core is made of a substance that is: Moreover, it is probably made of something that is: The most likely candidate is iron. Every line of evidence, including laboratory studies, points at the mantle being made of silicate rocks and the core of an iron alloy. specifically:

Gravitational anomalies

A final source of information about the structure of the deep Earth comes from variations in Earth's gravitational field. These indicate variations in the density of rock, as in the example at right. Their study reveals details of Earth's subsurface structure on large and small scales. For us now, they confirm that:

And for fun, on 9/9/11, NASA's GRAIL Mission launched a pair of lunar satellites that created a detailed map of the moon's gravitational field before their mission ended in 2012.

Key concepts and vocabulary: