gravity at center of the earth

[billwald]

Shouldn't the force of gravity at the center of the earth be zero because all the mass would balance and cancel out? If so, then there should also be zero pressure due to overlaying matter?

 

[Aeschylus]

Yes the gravity is approximately zero at the cnetre of the Earth. What's even more inetresting though is that when you are inside the Earth the gravity gets less and less until you reach the centre (actually that's assuming perfect sphericity and uniform density so it might not be quite true) where it is approx. zero.

The pressure at the cnetre of the Earth is termndous as even though there is no garvity there you still have the weight of all the matter above pushing from all sides.

 

[billwald]

But it is gravity that causes the push. No gravity, no push.

Consider a 100 mile hollow iron asteroid with a one mile thick shell and man hole access to the interior. There will be a small effect of gravity if you were on the outside of the shell. If you were on the inside of the shell you would still be attracted to the shell but slightly less because of the counter force from the opposite wall.

If your belly button was at the exact center of the sphere your belly button would feel no "gravity" (you would't drift toward either wall) because the the "gravity" from the shell would be balanced. There would be a very small TENSION between your head and feet because your head was closer to one side and your feet closer to the opposite side.

Now say the walls are 45 miles thick and your belly button is still at the center of the sphere (now a 10 mile dia space). Nothing has changed except the TENSION - not compression - in your spinal column.

 

[michabo]

billwald,

Aeschylus is agreeing with you! The gravity at the centre will be zero. He's just pointing out that the rocks around you will not have the same property, and they will be pulled into you, creating an enormous pressure.

 

[billwald]

What will pull the rocks into me?

 

[Aeschylus]

What will pull the rocks into me?

Gravity! Even though the gravity at the centre of the Earth is zero the rocks above are affected by the Earth's gravity and that gravity pulls them towards the centre (infact if you are inside the Earth r metres away from the centre th gravitional pull you feel will be that of the sphere at the cntre of the Earth of radius r, of course that assume things like uniform density and that the Earth is a perfect sphere).

 

[billwald]

I think the problem is complicated by the fact that in engineering "statics" it is assumed for purposes of calculation tha all mass is concentrated at the "center of gravity" but this is only appropriate when dealing with an object as part of a larger system. It is meaningless when the object IS the system. For example, if the sphere - or an irregular shaped object - was the ONLY object in the universe. It has no center of gravity because this concept requires an outside reference point. Or, where is the cg of the universe? A meaningless question.




As I illustrated, consider a hollow sphere as the entire system. It has no center of gravity because it has a shell of gravity and the only gravitational force is toward the shell, not toward the center of the sphere.

 

[Aeschylus]

I think the problem is complicated by the fact that in engineering "statics" it is assumed for purposes of calculation tha all mass is concentrated at the "center of gravity" but this is only appropriate when dealing with an object as part of a larger system. It is meaningless when the object IS the system. For example, if the sphere - or an irregular shaped object - was the ONLY object in the universe. It has no center of gravity because this concept requires an outside reference point. Or, where is the cg of the universe? A meaningless question.

I assure the approximation to point masses is only made when the shape of the object is unimportant. In the case of a sphere it is an important theorum that gravitionally a rigid, uniform sphere behave just like all it's mass was concentrated at the centre. Even considering the sphere in total isolation it still has a centre of gravity which is easy to find (also note the centre gravity is the point at which we can consider it's weight to act, which is not the way I think you are using the term).

As I illustrated, consider a hollow sphere as the entire system. It has no center of gravity because it has a shell of gravity and the only gravitational force is toward the shell, not toward the center of the sphere.

The force of gravity of the shell acting on objects outside it will be directed towards the centre of the shell (the thing about classical physics is that even when we are consdiering an object in isolation we are still allowed to introduce hypotehtical test particles), for objects inside the shell, the shell will exert no net graivtional force on them (this is another well-known theorum).

 

[billwald]

Please Direct me toward the "shell" theorum.

 

[Aeschylus]

Please Direct me toward the "shell" theorum.

http://scienceworld.wolfram.com/physics/SphereGravitationalForce.html

 

[billwald]

Thanks. Unfortunately the math is beyond me. I'll work on it.

 

[The3rdhero]

Shouldn't the force of gravity at the center of the earth be zero because all the mass would balance and cancel out? If so, then there should also be zero pressure due to overlaying matter?

i see where your coming from, but is there proof of gravity? other than dropping things?

i don't think there's anything "pulling us down"
i just think space has something that makes you float, and earth doesnt

 

[billwald]

If mass warps space then there isn't any force except the tendency to seek the lowest energy level?

 

[Deamiter]

Um... gravity exerts forces whether it's root cause is the warping of space or not! All we know about it now is that it DOES exert forces. Also there's atomic forces and magnetic forces...

No force forces things to the lowest energy level. That's just a product of many interactions between particles where a high concentration of particles tends to exert a net outward force...

I get the feeling there's a basic understanding here, but if you ask more specific questions, I'm sure we can come up with more specific (and comprehensible) answers!

 

[CookieThief]

I think that at the center of the earth there is gravity. Here's why i belive there may be. Matter is made up atoms, and atoms are made up of subatomic particles; up qurks, down qurks, gluons, boson's etc... each atom has an atomic mass, thus each patricle has a specific value. (unfortunitlly until the large hardon colider is finshed, mankind will not have proof of the gravitaional values of different materials) This is why some hydrocarbon componds float ontop water.

That having been said, we see things on a 3 deminsonal plane. (x,y,z) So again it only seems logical that atoms would have 3 deminsions and form 3D structers; like a sphear. taking all of this into consideration (along with the fact that our earth has molten lava at it's center) we begin relize that there is a great deal of energy and presure in the planets core. (an inverted example of this would be the bubeles in a soda glass) all the pressure holds the planet togeather squeezing so hard that they cancel eachother out well still maintaing gravetaional energy

 

[michabo]

That having been said, we see things on a 3 deminsonal plane. (x,y,z) So again it only seems logical that atoms would have 3 deminsions and form 3D structers; like a sphear. taking all of this into consideration (along with the fact that our earth has molten lava at it's center) we begin relize that there is a great deal of energy and presure in the planets core. (an inverted example of this would be the bubeles in a soda glass) all the pressure holds the planet togeather squeezing so hard that they cancel eachother out well still maintaing gravetaional energy

Huh? What does any of that have to do with gravity at the centre of the earth?

 

[billwald]

Gravity can cause frictional heat by compacting loose material but pressure produced by the static force of gravity can not. The only difference between a large pressure and a small pressure is magnitude. Consider a large iron ball inside a perfect insulator out in space. If static pressure could produce heat, then the ball would get hotter and hotter and hotter.

Why doesn't Venus have a magnetic field? It is almost the same mass as the earth, is closer to the sun, and has a higher surface temperature. Because the core is NOT liquid? Because it doesn't have a laarge moon to cause tidal heating?

Ignoring the theoretical math, no one has explained what is producing the pressure at the core of the earth if there is no effect of gravity on the individual particles at the core.

 

[michabo]

Gravity can cause frictional heat by compacting loose material but pressure produced by the static force of gravity can not.

If you see the Ideal Gas Law you will see there is a direct relationship between pressure and temperature. This is not exactly the same as heat, but I think it addresses your concerns.

If static pressure could produce heat, then the ball would get hotter and hotter and hotter.

If the ball was large enough, the interior would be warmer than the exterior

Why doesn't Venus have a magnetic field? It is almost the same mass as the earth, is closer to the sun, and has a higher surface temperature.

I don't know. I don't think this is a simple relationship, judging by how our magnetic field varies over time, including regular reversals of the poles. This is not due to the interior of the planet thretching.

Ignoring the theoretical math, no one has explained what is producing the pressure at the core of the earth if there is no effect of gravity on the individual particles at the core.

Yes, it has been explained several times. If you wish, when you dive down twenty metres, you have not substantially affected the gravitational attraction the earth exerts on your body, but you have increased the pressure on your body by an order of magnitude. Why do you suppose that is? Instead of having a column of water 20m pressing down on you, what do you suppose would happen if you have a "column"(*) 6,000,000m pressing down on you?

(* Really, it would not be a column, but the entire earth)

 

[Kant]

There is no gravity at Earth's "center of gravity" by definition. However, the pressure is enormous: several million atmospheres. This is due to the weight of the overlying material, whereupon gravity is not zero, but quite finite.

Force balance is the key. F=m*a, and a=0 for a static Earth. So all the forces (F) need to balance each other and cancel to zero, and in a sphere they balance one another by a pressure gradient that increases at a rate proportional to rho*g, where rho is the density and g is the gravitational acceleration.

Pressure is not related to the gravity at one's position, but rather the gravity of all the surroundings which exert contact with one another to put pressure upon any given position.

 

[Kant]

Also, Venus and Mars do not have a big magnetic field right now because they are not cooled quickly enough to induce convection in their metallic cores. This convection acts against rotation and magnetic forces to create the dynamo that comprises Earth's field. This is commonly accepted.