No gravity at center of earth= no pressure?

[BobG]

But the idea that gravity gets smaller once you move from the surface in either direction (towards space or towards the center) doesn't make sense. Gravity pulls toward the center of a mass. If you are beneath the surface it makes sense for gravity to pull the same or more. Not less

It makes perfect sense if you look at the Earth's gravitational field as the sum of the gravitational field of each little piece of the Earth, which it actually is.

Saying gravity pulls towards the center of mass is a simplified generality. It only literally applies if the mass you're talking about is a perfect sphere.

When you start talking about real planets, the force of gravity will always point close to the center of the Earth, regardless of where you are, but not necessarily towards the exact center of the Earth because the mass of the Earth isn't distributed in a perfect sphere (which is one reason why geostationary satellites require constant stationkeeping to keep them in their proper location relative to the Earth; why a sun-synchronous orbit is possible; why satellites in a Molniya orbit always have inclinations of 63.4 degrees, and so on).

 

[Malibuguy]

We know that gravity decreases the farther one moved from the center of the mass.
If we move into the substance of the mass, some say it gets weaker.
But if the mass were very small and very dense, so that the center and the surface were very close together, if we follow the idea that the center is zero, how could you have such a high degree of gravity go to zero in such a small movement inward while the force would be quite strong and extend quite far from the surface outswards into space?

 

[Drakkith]

Look, the issue here is about WEIGHT. From time you start digging at the surface until you get all the way to the center of the earth, your WEIGHT is lessening. Weight is caused by gravitational attraction in a net direction. In the core you have equal amounts of gravity pulling every direction, so there is no net force to cause the effect of Weight. You ARE still within a gravitational field and would experience effects such as Time Dilation just like you would anywhere else on the earth.

But the idea that gravity gets smaller once you move from the surface in either direction (towards space or towards the center) doesn't make sense. Gravity pulls toward the center of a mass. If you are beneath the surface it makes sense for gravity to pull the same or more. Not less

Gravity pulls towards the center of mass of an object, yes, but that is a result of the additive gravitational force from everything that makes up that object. As you get UNDER the ground you now have the gravity of the layers above you pulling you opposite of the ones below you. This reduces your weight, but does not reduce or increase the gravity.

This idea that gravity gets smaller when you approach the center of the Earth until it goes to zero makes no sense at all.

Do you weigh more or less when you are on top of mount Everest cOmpared to the bottom of the grand canyon?

The gravity does not get smaller as you approach the center, but your weight does.

 

[Malibuguy]

A summary of what I've seen posted.

Although gravity is zero at the center of the earth, pressure will be greatest at the center of the Earth unless there is some solid shell surrounding the center of the Earth that is supporting some or all of the weight outside that shell, in which case the pressure inside the shell could be anything.

If there is a shell supporting all the weight outside the shell, and the inside of the shell is a vacuum, then depending on the Earth's mass distribution (such as a uniform sphere, or a sphere made of continuous uniform spherical shells), there would be no gravity at any point within that hollow shell.

If an object were placed inside inside the hollow shell with zero gravity, then the object would create it's own gravitation field. I'm not sure about interaction between the object and the mass outside the shell, other than the object's gravitational field would increase the pressure on the shell.

Gravity is produced by mass, yes? Gravity pulls towards the mass, yes?. If gravity is pulling you one way and gravity is pulling the other way , you might get stretched a little or compressed.

Being surrounded by mass cannot mean that gravity no longer exists. Wherever there is mass gravity exists.

 

[Drakkith]

Gravity is produced by mass, yes? Gravity pulls towards the mass, yes?. If gravity is pulling you one way and gravity is pulling the other way , you might get stretched a little or compressed.

Being surrounded by mass cannot mean that gravity no longer exists. Wherever there is mass gravity exists.

Inside a perfectly symmetrical sphere, no matter how much you increase the gravity of the sphere, you will never experience a net force in any direction. The increase in attraction of your hand towards the closer side of the sphere is perfectly counteracted by there being MORE matter on the other side of your hand. The gravity equals out in both directions. (This is what is meant by "cancels out", not that the gravity simply dissapears.)

 

[Subductionzon]

As has been said, the shell theory explains rather nicely how gravity inside a uniform shell is zero. That means as you go down you can ignore the gravitational forces of all of the mass further away from the center of the Earth than you are. You are effectively on a smaller planet. Now even though the force of gravity goes down the pressure goes up. No matter what depth you are at you have to support all of the weight above you. So pressure goes up, but it goes up slower as you go deeper.

Now to make matters worse the Earth is not of uniform density. The core is much denser that the mantle. As a result the force of gravity at first goes up as you approach the center of the Earth. It will continue to slowly rise for the first half of your trip to the center until you hit the outer core/mantle boundary. There the acceleration due to gravity would be about 10.8 m/s^2.

ETA: I almost forgot, here is a Wikipedia article on the shell theory:http://en.wikipedia.org/wiki/Shell_theorem"

 

[cragar]

@ malibu guy: Now suppose I go into the Earth a little bit. So now I have some Earth above my head and some below. You might ask well the mass above my head is closer than the mass on the farther side of the Earth so it should be stronger. But in your field of view you see a smaller section that is closer, but the mass far away you see r^2 more of it because of surface area of a sphere.
and the field falls of as 1/r^2, so the r^2 perfectly cancels. This may not answer your question but might help you understand Gauss's law. When we use Gauss law for E fields and gravity we only consider the mass or charge enclosed to add to our field in symmetric cases.
Gauss's law is pretty deep and elegant

 

[cragar]

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.

 

[Malibuguy]

Ok so I did a little more probing about the composition of the Earth. Scientist believe that core of the Earth is made out of molten iron which is at very high temperature thousands of degrees C and under very intense pressure. Pressure is force per surface area. The volume of the core is only 1/8 the volume of the Earth But the core accounts for 1/3 the mass.

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 ?

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.

 

[cragar]

suppose a heavy rock is in free-fall towards Earth . what is harder to stop a heavy rock or a lighter object. Maybe that's why the denser elements ended up in the core. Not sure tho.
I am not sure how planets form but if they were in some liquid or plasma state, the heavier elements might punch through the surface because they have more momentum and end up in the core. Maybe.

 

[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.