No gravity at center of earth= no pressure?

[Malibuguy]

Of the four forces: electromagnetism , strong forces, weak forces and gravity - don't most physicists who have at least a phd believe that gravity is the most poorly understood?

 

[cragar]

We have general relativity and Newtonian gravity, but yes there is a lot more research to due on gravity. And we don't have a Quantum theory for gravity yet.

 

[willem2]

The mantle comprises 7/8 of the volume of the Earth and 2/3 the mass.

The core is obviously much more dense than the mantle.

If there were zero gravity in the center of the earth, why is the core so much more dense than the mantle ?

The heaviest stuff doesn't end up where gravity is biggest, but at the lowest point.

 

[Drakkith]

And I think another interesting question that should be asked is let's say I take an atomic clock to the center of the Earth in a hollow cavity. Will this clock tick the same as a clock way out in the vast emptiness of space where the field is zero. I think gravitational time dilation is related to the gravitational potential and not the field. Will my clock tick the same in a place where the field cancels to zero or where it is zero because nothing is there.

Your clock would have greater time dilation than both the surface of the Earth and deep space.

 

[Drakkith]

If there were zero gravity in the center of the earth, why is the core so much more dense than the mantle ?

Why did the most dense elements find their way into the core rather than stay in the mantle? Or near the surface where gravity is supposedly greatest according to the notion that gravity keeps getting smaller the further away from Earth surface either inward or outward.

Geologists say that the least dense materials are found on the Earth's surface.

Because the denser materials sank when the Earth was molten still. The gravity isn't zero at the center of the earth.

 

[Doc Al]

The gravity isn't zero at the center of the earth.

Why do you think this?

 

[sophiecentaur]

There are two 'Gravities'to consider.
1. The Force of gravity.
This is the sum of the attractions of every particle in the Universe on any object - mostly we only need to consider the effect of all the particles of the Earth. When at the centre, these forces will cancel out, because they are uniformly in all directions.

2. The Gravitational Potential
This is to do with the Energy needed to move an object around 'against gravity'. Arbitrarily, the GP at a point is defined as the energy required to bring an object from Infinitely far away so, for an attractive force, it is a negative quantity. The graph of GP against distance has zero at infinity and forms a 'well' (we've all seen the rubber sheet model).
The shape of the graph follows a 1/d law (d = distance from the centre) as you approach the surface but, once below the surface, the graph still continues down but it follows a d² law with a zero at the centre. This means that (of course) you need to supply energy to get up to the surface and even more to escape. As it happens, it requires the same energy to get from the centre (uniform Planet - the simplest model) to the surface as from the surface to the same distance outwards. (see attachment)

So there is no force at the centre but you still need to Work to get away from the centre. You are at the bottom of a flat bottomed potential well.

I need to put to bed a statement that someone made that "you are attracted to the Centre of Mass". This is an approximation and is only true for all objects when you are far enough away.
e.g. The CM of the Earth/Moon combination is a point below the surface of Earth. If you are standing on the Moon, however, you are attracted towards the Moon (more or less, to the centre of it) - which is NOT the CM of the Earth/Moon.

 

[sophiecentaur]

Of the four forces: electromagnetism , strong forces, weak forces and gravity - don't most physicists who have at least a phd believe that gravity is the most poorly understood?

But the level of 'not understanding' is way beyond what is being discussed here. There is no need to leave the Classical realm to discuss this stuff.

 

[Drakkith]

Why do you think this?

Why wouldn't I? The gravitational force doesn't simply disappear to my knowledge. You would be in the center of a large gravity well.

 

[cjl]

You're in the center of a large gravitational well, but the gradient of the potential is zero.

 

[Drakkith]

You're in the center of a large gravitational well, but the gradient of the potential is zero.

Ok? That doesn't mean that gravity doesn't exist there.

 

[cjl]

It means the gravitational force is zero.

 

[Drakkith]

It means the gravitational force is zero.

The force is equalized yes, but gravity still affects you.

 

[sophiecentaur]

Ok? That doesn't mean that gravity doesn't exist there.

Try to make sense of the graph in that earlier post of mine and appreciate the difference between Force and Potential.

 

[Drakkith]

Try to make sense of the graph in that earlier post of mine and appreciate the difference between Force and Potential.

I completely understand the two. The force of gravity from everything around you is equal, so you don't experience any net pull in a direction. You obviously are contributing to the mass and gravity of the center of the earth, as gravity is still working and doesn't suddenly just disappear.

 

[Studiot]

The question of is there a difference between zero resultant or net force and zero force?

is actually a pretty deep philosophical one.

We are asking the question: If A-B=0 is there a difference beween when A\neq0 & B\neq0 and A=B=0?

I contend that there are certainly circumstances when there is a real difference.

Take for instance the situation of my wallet.

I have a £10 (B=£10) note in my wallet an I go into a restaurent and eat a meal. I then pay £10 for the meal (A=the bill). I now have zero money left

so A-B=0

But I have had a meal and I once had £10, much better than for the beggar outside for whom A=B=0

 

[I like Serena]

But I have had a meal and I once had £10, much better than for the beggar outside for whom A=B=0

Wouldn't the beggar beg for money and get say €40.
And then, rather than saving it, he would go to an expensive restaurant and eat even better than you did, spending the €40 and making sure he had nothing left, spending left overs on extras, like booze.

So he started with nothing, didn't really do anything for it, and ended with nothing.
A - B = 0 - 0 = 0
But he did have a better meal!

 

[sophiecentaur]

I completely understand the two.

Umm?
I think that, if you did, you would not be viewing this as some sort of a paradox (that is what comes over in your posts). There is none but the rather sloppy use of the word Gravity can lead to confusion.

If you regard Potential as the basic quantity (energy is the way forward for understanding most things) then there is a scalar field of GPE in a region. The force is just the gradient of that field. A gradient can be zero so the force can easily be.
If you lay a spring on a flat surface and fix one end, there is no force on the other end until you try to displace it. The spring is still there - along with its 'springyness' even if it's not pulling or pushing anything.

 

[Drakkith]

I don't see anything complicated about this. The attraction of gravity doesn't cease to exist simply because you are in the center of something. The mass in your body attracts all the mass around you and vice versa. Just like being in a hollow sphere you don't experience any net force in a direction, but it is still there. There is no philosophical anything here.

Edit: Sophie, I have absolutely no idea what you are trying to say. How can I put it any simpler than "Gravity exists in the center of the earth"?

 

[rcgldr]

You're in the center of a large gravitational well, but the gradient of the potential is zero.

Ok? That doesn't mean that gravity doesn't exist there.

It means the gravitational force is zero.

Choosing to use the example of a hollow (empty) shell at the center of the Earth that is supporting all of the weight of the mass outside the shell, there is no compressive force inside the shell (I'm assuming there is a vacuum inside the shell). There is no gravitational force within the shell. The gravitational potential all points inside the shell is the same, so the gradient is zero, but the potential at all points within the shell is a large negative value (not zero), the same as any point on the inner surface of the shell.

 

[Drakkith]

Choosing to use the example of a hollow (empty) shell at the center of the Earth that is supporting all of the weight of the mass outside the shell, there is no compressive force inside the shell (I'm assuming there is a vacuum inside the shell). There is no gravitational force within the shell. The gravitational potential all points inside the shell is the same, so the gradient is zero, but the potential at all points within the shell is a large negative value (not zero), the same as any point on the inner surface of the shell.

Of course. But if you put an object inside this shell then it still attracts everything else outside the shell. I don't know which terms to use. Force? Net force? Attraction? Every time I've used something it apparently is taken completely wrong and I don't know why.

 

[cragar]

something I've always wondered was, when they say the E field is zero inside a hollow charged cavity. Sure it cancels mathematically but how does it cancel physically, it seems the fields would have to interact somehow to cancel. I don't know if what i said sounds right. And also time dilation is different in the middle of the Earth then out in deep space where the field is zero. So some how the clock can tell the difference.

 

[Studiot]

Wouldn't the beggar beg for money and get say €40.
And then, rather than saving it, he would go to an expensive restaurant and eat even better than you did, spending the €40 and making sure he had nothing left, spending left overs on extras, like booze.

So he started with nothing, didn't really do anything for it, and ended with nothing.
A - B = 0 - 0 = 0
But he did have a better meal!

New month's resolution


Change my profession.

 

[rcgldr]

And also time dilation is different in the middle of the Earth then out in deep space where the field is zero.

Time dilation is related to gravitational potential, not gravitational field strength. Again using the hollow shell at the center of the Earth example, then all points within that hollow shell experience the same large negative gravitational potential and time dilation.

http://en.wikipedia.org/wiki/Gravitational_time_dilation

 

[sophiecentaur]

I don't see anything complicated about this. The attraction of gravity doesn't cease to exist simply because you are in the center of something. The mass in your body attracts all the mass around you and vice versa. Just like being in a hollow sphere you don't experience any net force in a direction, but it is still there. There is no philosophical anything here.

Edit: Sophie, I have absolutely no idea what you are trying to say. How can I put it any simpler than "Gravity exists in the center of the earth"?

I am saying that there is no Force but there is Potential. If there is no gradient of Potential, there is no Force. Just using the word "gravity' is too unspecific to mean anything.

You can only say that 'gravity exists at the centre of the Earth' in the same sense that gravity exists everywhere - because it goes with the existence of all the matter in the Universe. You can't have one without the other. The gravitational energy is just very 'patchy'; in some places it is a lot lower (i.e. more negative) than in others.

 

[rcgldr]

center of Earth ... there is no Force ... there is potential.

There is no field either, just a potential. If you put an object inside a hollow shell at the center of the earth, the only field there is due to the object itself. The objects field does interact with the surrounding mass.

 

[cragar]

Time dilation is related to gravitational potential, not gravitational field strength. Again using the hollow shell at the center of the Earth example, then all points within that hollow shell experience the same large negative gravitational potential and time dilation.

http://en.wikipedia.org/wiki/Gravitational_time_dilation

Isn't potential a man made invention, the fields are what we experience and interact with,
how would my clock sense a potential if there is no field for it to interact with?

 

[sophiecentaur]

There is no field either, just a potential. If you put an object inside a hollow shell at the center of the earth, the only field there is due to the object itself. The objects field does interact with the surrounding mass.

Natch - Field is Force on a Unit Mass, by definition.

The object in the middle will, as usual, be interacting with the sum total of masses in the Universe.

 

[sophiecentaur]

Isn't potential a man made invention, the fields are what we experience and interact with,
how would my clock sense a potential if there is no field for it to interact with?

That is a deep philosophical point. Isn't it all a man-made invention? Fields are only a way of interpreting what we see happening to things. The whole thing can be looked at in terms of Energy just as well. You can never say what things 'really' are. You can only use models and the Force model may have its appeal to you because it sort of feels right - nothing more.

Try some QM using forces alone - that could prove tricky.

 

[Drakkith]

I am saying that there is no Force but there is Potential. If there is no gradient of Potential, there is no Force. Just using the word "gravity' is too unspecific to mean anything.

You can only say that 'gravity exists at the centre of the Earth' in the same sense that gravity exists everywhere - because it goes with the existence of all the matter in the Universe. You can't have one without the other. The gravitational energy is just very 'patchy'; in some places it is a lot lower (i.e. more negative) than in others.

That is exactly what I've been saying. Did you bother to read my other posts explaining what I meant? I thought it was pretty clear exactly what I meant by "Gravity". I have no idea how I could possibly explain it in terms that you would agree with, so sorry.

 

[Malibuguy]

Okay can anyone tell me what is the upper limit of gravity? Obviously if you are in space away from any mass than gravity can be zero. But how large can it get? And what are the conditions?

 

[Drakkith]

Okay can anyone tell me what is the upper limit of gravity? Obviously if you are in space away from any mass than gravity can be zero. But how large can it get? And what are the conditions?

Ever heard of a Black Hole? That's about as high as you can get as far as I know.

 

[Malibuguy]

Hmm but what is the strength of gravity of the black hole?

 

[sophiecentaur]

That is exactly what I've been saying. Did you bother to read my other posts explaining what I meant? I thought it was pretty clear exactly what I meant by "Gravity". I have no idea how I could possibly explain it in terms that you would agree with, so sorry.

If, when you mean Gravitational Force, you mean that an, when you mean Gravitational Potential , you say that then there can be no confusion. But "gravity" is generic, like "electricity" and is too vague for nitty gritty discussion.
"Gravity" is everywhere in the same way that "time" is.
You mustn't mind my being picky but so many people take such liberties with poor old Science. It's a wonder she let's us know anything about her.

 

[Malibuguy]

The core of most planets is much denser material than the outer layers. Surface gravity doesn't correlate well with the diameter, since the mass of the core is more important. So again standing on mount Everest you weigh less because you are further away from the core. And digging down at least to the surface of the core which is 7/8 to the center may not mean that gravity is decreasing.

 

[Malibuguy]

someone raised the point that gravity might not be the reason why the core of the Earth is made out of dense molten iron.

lets consider the moon. most scientists believe the moon came about from a collision where part of the Earth's crust was knocked off the earth. The moon therefore did come about with a metal core from birth. But that core formed. The moon was very hot due to the energy of the collision This heat would allow iron to be molten and flow. If gravity were zero in the center then wouldn't the iron reside as a shell not on the inside but on the surface according to those who believe that gravity decreases as you move in either direction from the surface until it reaches zero at the center.

 

[Subductionzon]

There was a lot of energy released in the formation of the Earth. As the Earth cleared its orbit of matter the potential energy that the matter had would be changed to heat. I believe it was enough to liquify the Earth. The heat is maintained by the radioactive decay of radioactive isotopes of uranium, thorium, rubidium, potassium and others. There is enough heat released by these to maintain the liquid core. It was calculated by Lord Kelvin from the known heat flux of the Earth that it was roughly 100 million years old. This answer was not pleasing to either fundamentalist Christians or geologists. The discovery of radioactivity resolved that problem, at least for geologists. So the Earth lost almost all of its heat of formation in the first hundred million years or so.

The Moon on the other hand is much smaller than the Earth an has a much higher surface area to mass ration and it long since cooled all the way through.

And the surface of the outer core is roughly half way to the center. But since volume has a cubed relation to the radius that means that the outer core/mantle boundary is roughly at half of the way to the center, not 7/8. And until you do hit that boundary the force of gravity slowly goes up. At the outer core/mantle boundary the acceleration due to gravity would be about 10.8 m/s^2.

And lastly, no, just because gravity is zero at the center does not mean that dense materials would avoid the core for any reason. . The heaviest materials are still attracted to the center more than lighter material would be.

 

[Doc Al]

those who believe that gravity decreases as you move in either direction from the surface until it reaches zero at the center.

That's only true for the idealized case of a uniform sphere of mass. Obviously, if the material has a denser layer below the surface, you may well increase the gravitational force on a test mass that is brought below the surface. (The case of moving the test mass above the surface is too trivial to discuss.) Of course, as you get to the center the gravitational field strength will go to zero for any spherically symmetric mass distribution, even one with denser layers. (Let's leave out special cases like black holes. )

 

[Malibuguy]

Why would the iron move to the center of the moon.
The moons rotation and orbit would exert forces greater than the zero gravity center so that one would expect a metal shell not a solid center

 

[sophiecentaur]

Why would the iron move to the center of the moon.
The moons rotation and orbit would exert forces greater than the zero gravity center so that one would expect a metal shell not a solid center

Could you put some figures to that assumption? We're not talking fairground rides here. What difference would you expect in the effective gravitational forces on different parts of the Moon due to the Earth c/w its local distributed masses?

 

[D H]

Mailbuguy, you have been given several pointers to read. Have you read any of them? Please read:

• Newton's shell theorem, http://en.wikipedia.org/wiki/Shell_theorem
• Gauss' law, http://en.wikipedia.org/wiki/Gauss'_law_for_gravity
• Preliminary Earth Reference Model, http://geophysics.ou.edu/solid_earth/prem.html

You (and others) are confusing force and energy. These are related but different concepts. Gravitational force is zero at the center of the Earth. Gravitational energy is a different story. It is energy, not force, that explains why planets become differentiated. Nature seeks a minimum energy configuration.

 

[Malibuguy]

Just looking at the fact that a lot of planets have a dense core of metal and are not homogeneous.

The other perspective is that it is the surface pushing in on all sides.
But then this will produce a center that is more dense. A denser center produces gravity too.
The surface of this denser center pushes in on all sides too and then this creates more pressure. Then you get an inner core which is hotter and more dense Which is exactly what we have with the earth. This center also produces gravity. If one follows this idea then there will always be gravity at the center of the earth.

 

[Malibuguy]

Newtons shell assumes homogenious shell. Newtons shell seeks to explain our world one aspect .

But our world is not a homogenious shell. Neither is the moon Jupiter and a lot of other planets.

Please find a large body in the universe which produces significant gravity and is homogenious without a dense core

 

[Doc Al]

The other perspective is that it is the surface pushing in on all sides.
But then this will produce a center that is more dense. A denser center produces gravity too.
The surface of this denser center pushes in on all sides too and then this creates more pressure. Then you get an inner core which is hotter and more dense Which is exactly what we have with the earth. This center also produces gravity. If one follows this idea then there will always be gravity at the center of the earth.

Nope, still wrong. Any mass at the center of the Earth (say within some small radius r) only contributes to the gravity for distances from the center greater than r. At the very center the gravitational field strength is zero.

 

[sophiecentaur]

Newtons shell assumes homogenious shell. Newtons shell seeks to explain our world one aspect .

But our world is not a homogenious shell. Neither is the moon Jupiter and a lot of other planets.

Please find a large body in the universe which produces significant gravity and is homogenious without a dense core

The fact that a planet gets more dense towards the centre doesn't invalidate the assumption that it can be (more or less ) spherically symmetrical). Newton's shell theory deals with one uniform shell at a time. Its result is not affected by the density increasing with depth.;

But why not take one thing at a time? The original question was addressed using the most simple assumption (uniform density). People seemed to have enough difficulties dealing with that basic model but I think we got there more or less.
The next step is to allow the more dense stuff to gravitate towards the centre. That gives a more complicated result - slightly counter to the original but makes sense.

If you want to have asymmetry too then you'd have to modify the result further but, to what end? The basic principles tend to get lost in the specific instances in the end. But, whatever you suggest as a possible model, there will be somewhere 'in there' where the Potential is at a minimum and the force is zero.

 

[Malibuguy]

At the very center? What is that a point of one dimension? A place that has no volume That's not even a place. Hmm but maybe you mean that the net gravitational force is zero. What about the field of gravity around a volume located at the center?

 

[Doc Al]

Newtons shell assumes homogenious shell. Newtons shell seeks to explain our world one aspect .

But our world is not a homogenious shell. Neither is the moon Jupiter and a lot of other planets.

Please find a large body in the universe which produces significant gravity and is homogenious without a dense core

Sure, if a spherical mass has a lopsided mass distribution, there may well be a non-zero field at the geometric center. This has nothing to do with a 'dense core'.

 

[Doc Al]

At the very center? What is that a point of one dimension? A place that has no volume That's not even a place. Hmm but maybe you mean that the net gravitational force is zero. What about the field of gravity around a volume located at the center?

Again, for a spherically symmetric mass distribution, the field around some volume at the center is due to the mass contained within that volume. Regardless of the density of the core, as you get closer to the center the field goes to zero.

 

[sophiecentaur]

At the very center? What is that a point of one dimension? A place that has no volume That's not even a place. Hmm but maybe you mean that the net gravitational force is zero. What about the field of gravity around a volume located at the center?

For a small volume, the range of potential would be small, If you want to be picky, you could call it a situation of 'microgravity' rather than zero gravity - similar to that experienced in an orbiting spacecraft , in which objects are only weightless around the CM of the craft and payload. On either side of this, there is not zero weight but a finite force.

The way it's been approached in this thread is consistent with the normal way of getting to grips with basics - start with the simplest model and add complications later.

 

[Drakkith]

How's this sophie? The net force of gravity is zero at the center of the earth. The FORCE of gravity combines to equal out in every direction, just like pushing in on all sides of a box with equal force results in no net force in a direction.