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Pressure and Gravitational Field at Earth's Center
Name: Bob
Status: student
Age: N/A
Location: N/A
Country: N/A
Date: N/A
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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Update: June 2012
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