Gravity a question from a bus driver:-)

[bigalzz]

i may be in the wrong forum here and I'm sure I'm showing my ignorance. I'm not any kind of physicist,, geo, astro or otherwise.. but I'm curious.. if i weigh one "g" at the surface of the earth.. what would i weigh at the center of the earth?? my little brain is telling me i should weigh zero or negative.. there may even be a cavity at the center of the Earth caused by the 360 * of mass around that point... can anyone enlighten me? it's anoyinng me and I'm sure i must be wrong.

 

[Vorde]

The actual net gravitational pull at the exact center of the Earth (or the center of mass because Earth isn't a perfect sphere) is exactly zero. As I think you were thinking, the gravity from every direction would cancel out each other, leaving nothing.

However there is no cavity because there is immense pressure there because of the force of literally an entire planet pushing in on you from all sides, enough to heat up the core of the Earth to a liquid, hence the molten core.

 

[Nik_2213]

"...hence the molten core."

FWIW, IIRC, the Inner Core is solid, but the Outer Core *is* liquid...

Also, because of the Moon's gravity, the 'zero point' would be offset her way.

 

[DaveC426913]

Yup. As Vorde points out. Net gravitational force at the centre of the Earth is zero. If there were a cavity there, you would float around weightless.

I had never thought of it before but I suppose Nik is correct. At the centre of the Earth you'd still be about 400 miles from the barycentre of the Earth Moon system. You would apply Newton's shell theorem, meaning you would experiece a tiny force equivalent to standing on a rocky sphere 400 miles in radius.

 

[D H]

At the centre of the Earth you'd still be about 400 miles from the barycentre of the Earth Moon system. You would apply Newton's shell theorem, meaning you would experiece a tiny force equivalent to standing on a rocky sphere 400 miles in radius.

No, you wouldn't.

Suppose we somehow managed to make a hollow spherical shell centered at the center of the Earth and somehow managed to transport a person into this shell. A person at the very center of this shell accelerate toward the Moon with exactly the same acceleration experienced by the Earth as a whole. Net result: Zero acceleration with respect to the Earth.

Now suppose the person was a bit anti-moonward from the center of the shell. The gravitational acceleration of the person due to the Earth is still zero, but the acceleration of the person and the acceleration of the Earth toward the Moon will differ by a slight amount. Net result: The person will accelerate away from the center, eventually hitting the wall of the shell. It is only at this point that the person would "feel" a force, and this would be extremely small. This is a tidal (1/r³) force. A similar line of reasoning applies if the person is a bit moonward from the center.

On the other hand, if the displacement was orthogonal to the Earth-Moon line, the person would accelerate toward the center of the Earth. Tidal forces are weird.

 

[bigalzz]

Yup. As Vorde points out. Net gravitational force at the centre of the Earth is zero. If there were a cavity there, you would float around weightless.

I had never thought of it before but I suppose Nik is correct. At the centre of the Earth you'd still be about 400 miles from the barycentre of the Earth Moon system. You would apply Newton's shell theorem, meaning you would experiece a tiny force equivalent to standing on a rocky sphere 400 miles in radius.

i posted the following on another thread.. (i don't know how to drive these forums)

if we accept that there is zero gravity at the center of the earth. then this would be true for stars and even black holes.. and if you move from the center, at some point there will be an "event horizon" (for want of a better term) where the gravity is half G. and further, if a cold body such as the moon has zero gravity at the center, it may very well have a cavity at the center??
I'm sure I'm wrong and i don't know what difference it would make but i'd like to find out for sure and why not. i have the burden of a curious but uneducated mind.

 

[DaveC426913]

No, you wouldn't.

Suppose we somehow managed to make a hollow spherical shell centered at the center of the Earth and somehow managed to transport a person into this shell. A person at the very center of this shell accelerate toward the Moon with exactly the same acceleration experienced by the Earth as a whole. Net result: Zero acceleration with respect to the Earth.

Yeah, I'm having trouble wrapping my head around this.

The Earth rotates about the Earth-Moon barycentre, so why would that not be the centre?

You could consider the Earth-Moon system as a single solid spheroid including a 223,000 mile tall mountain on it. The gravitational centre would not be at the spherical centre of the Earthen-lobe.

 

[D H]

if a cold body such as the moon has zero gravity at the center, it may very well have a cavity at the center??

No, it can't. You are looking at the wrong quantity. It is pressure rather than gravitational force you should be looking at, and the pressure at the center of the Earth (and at the center of the Moon) is immense.

 

[bigalzz]

No, it can't. You are looking at the wrong quantity. It is pressure rather than gravitational force you should be looking at, and the pressure at the center of the Earth (and at the center of the Moon) is immense.

as I've made clear, I'm speaking from ignorance,so i apologise if it sounds foolish. but I'm proposing that the "event horizon would be the focus of the "pressure" not the center.. I'm naturaly drawn to your perspective, but I'm trying to think out of the box. (my "box" is very limited :-)

 

[D H]

The Earth rotates about the Earth-Moon barycentre, so why would that not be the centre?

Because it's irrelevant.

Look at it this way: Rephrase your question so that the third body is the Sun rather than the Moon: "The Earth rotates about the Sun-Earth barycenter, so why would that not be the center?" Note that the Sun-Earth barycenter is well outside the Earth; it is in fact very close to the center of the Sun.

 

[Vorde]

as I've made clear, I'm speaking from ignorance,so i apologise if it sounds foolish. but I'm proposing that the "event horizon would be the focus of the "pressure" not the center.. I'm naturaly drawn to your perspective, but I'm trying to think out of the box. (my "box" is very limited :-)

Not quite sure of the question, but even though the 'net' pressure would theoretically be zero at the center of the Earth, that doesn't equate to feeling no pressure like you would feel no gravity, instead it equates to feeling immense inward pressure from all sides.

 

[D H]

Not quite sure of the question, but even though the 'net' pressure would theoretically be zero at the center of the Earth

What do you mean by "'net' pressure"?

The pressure at the very center of the Earth is immense. It is in fact the point where pressure is at its maximum.

 

[bigalzz]

that's what I'm questioning.. if you go down on an elivator to the center of the Earth (ignoring the heat etc.) as you decent, the mass above you will increase.. the mass to either side of you would be canceled by oposite forces.. eg i will have "x" gravitational force to my right and equal to my left etc, so i will be unaware of any lateral forces...but the forces benieth me and above me will be changing.. at some point the above forces and the below forces will cancel each other.. the center.. as you move away from the center you will reach a point i call nomonaly the "event horison" this would be the "spherical" center of gravity.. the point to which all the mass of the Earth (and stars and black hloles) attracted.. again, it is counter intuitive and i surely expect to be shot down.. but i'd like to understand.

 

[D H]

You are still looking at the wrong perspective. Instead of gravitational acceleration it would be better to look at things from the perspectives of pressure (the weight of everything above you) and gravitational potential energy (the energy change involved in moving to even closer to the center of the Earth).

 

[Vorde]

What I meant by net pressure was that I thought the OP might have been thinking that in the thought transition from 'gravity' to 'pressure' the OP may have been under the impression that all the pressure canceled each other out, and I wanted to try and explain that it didn't.

I apologize for the confusion and/if I misread the thoughts of the OP.

 

[mesa]

However there is no cavity because there is immense pressure there because of the force of literally an entire planet pushing in on you from all sides, enough to heat up the core of the Earth to a liquid, hence the molten core.

I thought the majority of the heat in the Earth was from radioactive decay of things like Uranium?

 

[Steely Dan]

I thought the majority of the heat in the Earth was from radioactive decay of things like Uranium?

What you are thinking of is the heat that escapes from the Earth (that is, radiated away). Naturally there are high temperatures in the inner Earth that exist simply because of the high densities and pressures.

 

[Vorde]

I don't have anything to substantiate myself on this, but that seems very unlikely. First of all the percent uranium in the Earth is very, very small. Second of all I know how immense the pressure at the core is so I am very skeptical about it being anywhere close to even a fraction of the responsibility for the heating of the Earth's core compared to pressure heating.

I'd love for someone to show me otherwise though.

 

[D H]

I thought the majority of the heat in the Earth was from radioactive decay of things like Uranium?

Yep. Nowadays, at least. Sources of the heat (better said: enthalpy; objects don't contain heat) inside the Earth are radioactive decay; residual heat (enthalpy) from the differentiation of the Earth into core, mantle, and crust; residual heat from the initial formation of the Earth; and continued tidal stresses from the Moon and the Sun. Depending on who you read, radioactive decay is currently responsible for somewhere between 45% to 90% of the thermal energy that is being lost by the Earth.

 

[Vorde]

Well I feel like an idiot, does pressure really do that little? Though I guess this belongs in the geology section.

 

[mesa]

Well I feel like an idiot, does pressure really do that little? Though I guess this belongs in the geology section.

You should feel smarter, we just learned something new ;)
Thanks for the clarification D H!

 

[Drakkith]

that's what I'm questioning.. if you go down on an elivator to the center of the Earth (ignoring the heat etc.) as you decent, the mass above you will increase.. the mass to either side of you would be canceled by oposite forces.. eg i will have "x" gravitational force to my right and equal to my left etc, so i will be unaware of any lateral forces...but the forces benieth me and above me will be changing.. at some point the above forces and the below forces will cancel each other.. the center.. as you move away from the center you will reach a point i call nomonaly the "event horison" this would be the "spherical" center of gravity.. the point to which all the mass of the Earth (and stars and black hloles) attracted.. again, it is counter intuitive and i surely expect to be shot down.. but i'd like to understand.

At the exact center the NET FORCE of gravity does cancel out on all sides, resulting in no feeling of weight. If we hollowed the Earth's core out slightly and teleported you inside it, you would not fall anywhere. However, the rest of the Earth is not at the center and IS feeling a net force which is always inward. What's holding that material up against the pressure? You are. Until you are crushed by unimaginable force.

To elaborate a bit, consider a slice or section of the Earth about 1/3 of the way up from the core. This section has more of the Earth on the coreward side of it than on the outward side. In addition, the matter above it is also being pulled down, so it has the weight of all the matter above it as well. Overall everything is feeling a net force towards the center.

 

[Lsos]

Despite the gravity at the center being zero, the pressure is immense because all that ~4000 miles of rock on one side of the Earth is not so much attracted to the center of the earth, but to the ~4000 miles of rock on the OTHER side of the earth. So yeah, in the very center all the forces might cancel out, much like the forces from two cars colliding head on can "cancel" each other out...but nevertheless you DO NOT want to be in the center of those two cars. Unless, of course, you are inside this magical shell that keeps getting mentioned.

 

[mesa]

So yeah, in the very center all the forces might cancel out, much like the forces from two cars colliding head on can "cancel" each other out...but nevertheless you DO NOT want to be in the center of those two cars.

That cracked me up, good analogy

 

[Drakkith]

Despite the gravity at the center being zero, the pressure is immense because all that ~4000 miles of rock on one side of the Earth is not so much attracted to the center of the earth, but to the ~4000 miles of rock on the OTHER side of the earth.

To avoid confusion of some readers, I would just like to clarify that "Gravity Itself" doesn't cancel out, but the net force from it does, as all the mass is pulling all of you equally from all sides.