Greatest Pressure Point of Gravity

[ParanoiA]

In Greene's Elegant Universe, he describes gravity as a sort of pressure, or at least that's how I inferred it. That objects can be thought of as being "squeezed" into this vacuum of spacetime. So the larger the object, the more it warps spacetime having been pseudo-squeezed into the fabric.

 

With that predictably oversimplified analogy, that got me wondering where the greatest point of pressure can be found. For instance, is the pressure greater on the surface of the earth, or at it's core? I'm assuming the pressure decreases as you travel away from the surface of the earth toward space, but I'm not sure how that pressure changes when traveling away from the surface toward the center of the earth.

[insane_alien]

well, gravity isn't anything like pressure really. and gravitational field strength decreases as you approach the core, roughly linearly from the surface.

 

pressure on the other hand rises as you approach the center.

[iNow]

Why does the field strength decrease as you approach the core? Doesn't gravity fall off with the square of the distance? Does it have something to do with more mass being above you than below as you get closer to the center?

[insane_alien]

yes, the you can pretty much ignore the mass above you as that all cancels out so its only the sphere below your point that pulls you down.

[ParanoiA]

Does it have something to do with more mass being above you than below as you get closer to the center?

 

That is precisely why I asked the question. It would seem like the field strength would decrease.

 

So...I wonder how the gravitational field from the surface effects me as I move closer to the core. It wouldn't begin to pull me back would it?

 

well' date=' gravity isn't anything like pressure really. and gravitational field strength decreases as you approach the core, roughly linearly from the surface.

 

pressure on the other hand rises as you approach the center. [/quote']

 

hmm, but don't we interpret the feeling of gravity as pressure? I'm obviously confused on pressure and gravity.

 

Oh wait...do you mean that pressure is what I would feel because of the gravity acting upon the material above me as I descend toward the core? That would make sense. I suppose though, that I would interpret this pressure as "gravity", since it is caused by gravity acting on the material.

 

But the gravitational field strength would be less since there's less material, relative to my position anyway, to act on. Is that close?

 

So, is the surface the greatest point of gravitational field strength?

[D H]

hmm, but don't we interpret the feeling of gravity as pressure? I'm obviously confused on pressure and gravity.

We can't feel gravity. Suppose you are standing upright with your arms hanging at your sides. You can feel forces other than gravity, including the upward normal force of the ground on your feet (which keeps you from sinking into the ground) and the upward tensile force of your shoulders on your arms (which keeps your arms from falling off).

 

Oh wait...do you mean that pressure is what I would feel because of the gravity acting upon the material above me as I descend toward the core? That would make sense. I suppose though, that I would interpret this pressure as "gravity", since it is caused by gravity acting on the material.

Thought experiment: Imagine a tunnel (walls made of unobtanium) that goes all the way from the surface to the center of the Earth, evacuated of all air. This serves to separate the concepts of pressure and gravity. Now imagine taking an elevator that slowly descends to the center of the Earth. The Earth's gravitational force will drop off roughly linearly with depth as one descends, becoming zero at the center of the Earth. Now suppose you take pressure readings through the unobtanium walls as you descend. The pressure will rise because the material is (nearly) in hydrostatic equilibrium. The downward force of the weight of the material above is balanced by an upward force of the compression of the material below.

[Kyrisch]

and gravitational field strength decreases as you approach the core, roughly linearly from the surface.

 

[math]F_g \propto \frac{1}{R^2}[/math]

 

[math]V_{sphere} \propto R^3[/math]

 

So, the force of gravity of each smaller sphere is proportional to [math]\frac{R^3}{R^2} = R[/math], hence the rough linearity.

 

(Just some maths to clarify)

[Baby Astronaut]

hmm, but don't we interpret the feeling of gravity as pressure? I'm obviously confused on pressure and gravity.

In an indirect way, gravity is helping cause the pressure. If you're trapped under one million empty 1-liter bottles pressing down on you, the severity of your predicament would be less on the moon than on Earth, due to gravity.

 

Of course, there's no air on the moon so that's all a matter of perspective.

[ParanoiA]

In an indirect way, gravity is helping cause the pressure. If you're trapped under one million empty 1-liter bottles pressing down on you, the severity of your predicament would be less on the moon than on Earth, due to gravity.

 

Of course, there's no air on the moon so that's all a matter of perspective.

 

I guess that's how I'm thinking about it too. I guess the pressure is a reaction to gravity, not gravity itself.

 

Is that an accurate conclusion?

 

Thought experiment: Imagine a tunnel (walls made of unobtanium) that goes all the way from the surface to the center of the Earth, evacuated of all air. This serves to separate the concepts of pressure and gravity. Now imagine taking an elevator that slowly descends to the center of the Earth. The Earth's gravitational force will drop off roughly linearly with depth as one descends, becoming zero at the center of the Earth. Now suppose you take pressure readings through the unobtanium walls as you descend. The pressure will rise because the material is (nearly) in hydrostatic equilibrium. The downward force of the weight of the material above is balanced by an upward force of the compression of the material below.

 

That makes sense to me, as I descend the force of the weight of the material above me becomes greater and greater since the upward force of the material below is becoming less and less - all relative to where I am in the tunnel. While the gravitational force decreases as I get to the core since, again, the material below is becoming less and less. I hope I'm saying that right.

[D H]

I guess that's how I'm thinking about it too. I guess the pressure is a reaction to gravity, not gravity itself.

 

Is that an accurate conclusion?

That is an accurate conclusion. For more, google "hydrostatic equilibrium". The wikipedia article: http://en.wikipedia.org/wiki/Hydrostatic_equilibrium.