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Name: Bob
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Question:
Regarding pressure at the center of the earth, it seems that the comments by Argonne reviewers that gravity is zero or near zero and that things would float contradicts statements that the pressure is high. If you consider a spherical surface at the center, all the material on the outside of the surface is under no force, i.e., it is floating in a zero gravity field. Therefore the force on any material at the surface is also near zero--in other words no pressure. I would guess that at the maximum estimated temperature at the center, even iron would be a solid, if the pressure estimates of 380 Gpsl's were correct. From seismic surveys it appears the center is in a liquid state which is consistent with iron at 2000 degrees C at a relatively low pressure. What is the model used to calculate the pressure at the center?



Replies:
Hi Bob,

Just to be thorough, it appears you're citing a 1999 source (or similar information) summarized in this link:

http://hypertextbook.com/facts/1999/PavelKhazron.shtml

I think your confusion stems from the difference between gravity and pressure. Gravity is a body force, which means it acts uniformly on a mass, not on any surface or point of the mass. This is unlike pressure, which only acts on a surface of an object, not its interior -- pressure-type forces must be transferred to the interior of a body intermolecularly.

When gravity nets out to zero, because it is a body force, the effect is that a mass experiences no force. This is in contrast with surface forces (pressures), which can also net out to zero (zero linear acceleration and/or zero rotational acceleration), but the body itself still experiences forces that are transferred from point to point and part to part. For example, a person in a space ship would still experience air pressure around them, but would not experience (appreciable) gravity. The person feels "weightless" even though his body is being acted on by air pressure. As evidence of this, the person does not "fall" (no gravity), but the air dissolved in their blood also stays dissolved (because it is still under pressure).

I would like to comment on some of the assumptions of the post you referenced.

http://www.newton.dep.anl.gov/askasci/env99/env002.htm

These posts are correct, but they make some substantial assumptions which are fine for illustrating a physics idea, but are not intended to be rigorously correct in a practical sense. Suppose for simplicity, the Earth were a solid, hard sphere, not rotating, uniformly comprised, and static, and suppose you could drill a tunnel through it (a clear line from pole to pole). If you were to fall into that hole, you would fall toward the center of the earth, and neglecting any practical considerations like wind resistance and magnetic fields and such, you would oscillate up and down through the tunnel, just as the previous answer describes. If you stopped yourself at the center, the gravitational forces would balance to zero, and you would have quite a gravitational well (ha!) to climb out of to get back to the surface. This what the posters describe, and within the confines of those assumptions, is correct. I cannot emphasize enough the importance of being clear about assumptions. Now, obviously there are lots of practical considerations that make this scenario unrealistic -- you have listed many of them, and there are a lot more too.

In a practical scenario, the earth is not uniform, and so there may not be any actual zero-gravitational field point (although near the mass-center of Earth, the gravity will be close to zero). But that supposes that you can get there (which the previous answers point out is challenging). And, in a practical sense, there are many physical problems -- heat, pressure, magnetic fields, etc. -- that would make the experience anything but "steady".

I hope this helps,

Burr Zimmerman


The Earth's gravitational field at its center is zero -- that is, ignoring that the "center" moves around due to mass movement over time and space. Your mistake is the assertion that a spherical surface has zero gravitation. That only occurs at the very (hypothetical) center. Otherwise, the force of gravity is: F = G x m x M /R^2. So it is only 1 / |R|^2 that determines the strength of the gravitational force. The statement: "all the material on the outside of the surface is under no force, i.e., it is floating in a zero gravity field." is not true. All of these concepts derive from Newton's gravitational laws, q.v.

Vince Calder



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