Would a big enough manmade metal sphere have gravity?

[ZionsRodeVos]

According to the theories that discuss gravity, if humans were to create a solid metal sphere with the same mass as Earth would it have the same gravity as earth?

Would it have to be orbiting something and/or moving to have that same gravity? Or could it be stationary and have the same gravity as earth?

 

[mathman]

According to the theories that discuss gravity, if humans were to create a solid metal sphere with the same mass as Earth would it have the same gravity as earth?

Would it have to be orbiting something and/or moving to have that same gravity? Or could it be stationary and have the same gravity as earth?

Yes
No,Yes

The gravity due to a spherical object depends only on its mass and the distance from the center of any test object.

 

[Crazymechanic]

Rotation of an object actually has nothing to do with gravity , that is called centripetal force and it acts against gravity for example when a sphere rotates it has certain strength of gravity which is proportional to it's mass now the centripetal force which results from the spheres angular momentum acts against the spheres gravity for everything on and in the sphere.
As gravity tends to pull objects with mass closer (elementary particles including) but angular momentum tends to make things "fly away"

Now as for the metal sphere it is a yes and a no , because well to get the same strength of gravity you need the same mass as Earth yes that is correct , but the density of a metal like iron sphere would be much higher than that of Earth so the same mass would result in a sphere which is smaller , and gravity is a force which has it's strength related to the distance from the center of the object so an object which has the same weight as Earth but is smaller in size would have a higher surface gravity.

Just like a black hole , the black hole has the same mass as the star it collapsed from in the first moment but due to the different size than the previous star it's gravity is much much higher.

 

[WannabeNewton]

Rotation of an object actually has nothing to do with gravity

In the Newtonian regime yes this is true.

 

[technician]

In the Newtonian regime yes this is true.

Just for clarification for all students; what is the 'non-Newtonian' regime?

Is there any time when it is not true?

 

[A.T.]

Just for clarification for all students; what is the 'non-Newtonian' regime?

Is there any time when it is not true?

http://en.wikipedia.org/wiki/Lense–Thirring_effect

 

[Nugatory]

Just for clarification for all students; what is the 'non-Newtonian' regime?

Is there any time when it is not true?

Not true only in very extreme situations, such as close to a rotating black hole or neutron star. For reasonable densities and distances away from the gravitating object, Newton's laws work just fine for stars, planets, and anything smaller.

 

[technician]

http://en.wikipedia.org/wiki/Lense–Thirring_effect

Please... Do not send me to wiki !
If I wanted their explanation I would go there.
I think this may be against PF guidelines
Quote a textbook if any thing.

 

[HallsofIvy]

No, referring to Wikis NOT against PF guidelines. Insisting that a person not expect you to do any work yourself probably isn't either. But it is a little tacky.

 

[Drakkith]

Quote a textbook if any thing.

This would be extraordinarily difficult for those of us who have no textbook for every possible thing we post on.

 

[sophiecentaur]

Quote a textbook if any thing.

Unfortunately, if we only ever quoted from textbooks and we all bought the appropriate one to read, the cost would be ridiculous.
Despite what we say about Wiki, the majority of Wiki pages that deal with the majority of topics on PF are just fine - certainly for starters. When they're not, and you quote them here, someone will point out what's wrong. It is far more fruitful to go there first and as a question about what you found out than just to produce some vague question and to expect exactly the appropriate answer.
Showing that you have made some effort is courteous to other PF members and will get positive results.

 

[ZionsRodeVos]

I guessed that the size of the object would be smaller than Earth to have the same mass but hadn't thought that because you would be closer to the center the gravity would be stronger.

So to keep the gravity the same even though the material is different then in the case of this example the mass would need to be reduced for the sphere to have the same gravity as earth?

I read that wiki link and must admit that I don't understand a lot of it. I'll have to read it again. Initially I thought that the rotation of the Earth on its axis was what created gravity but it seemed to me that the rotation would be too slow for it to be able to generate gravity and then of course after listening to various documentaries and lectures it sounded more like mass was the only thing that determined if an object would have enough gravity for it to be felt.

And why is it that gravity pulls toward the center of an object that has gravity? It seems to me that if an object were traveling through a tunnel toward the center of the Earth at some point there would be more mass to either side of it than at the core and so wouldn't there then be a stronger gravitational pull to one side or the other that would slow or halt the objects movement toward the core of the earth?

 

[sophiecentaur]

And why is it that gravity pulls toward the center of an object that has gravity? It seems to me that if an object were traveling through a tunnel toward the center of the Earth at some point there would be more mass to either side of it than at the core and so wouldn't there then be a stronger gravitational pull to one side or the other that would slow or halt the objects movement toward the core of the earth?

This idea turns up regularly. The bits of the sphere at a greater distance from the centre than you are have no contribution to the gravitational field there. The field, in fact, is proportional to the distance from the centre, once you are below the surface, and zero at the centre.
Google Newton's Shell Theorem to find out about it. He even had to invent his own form of Calculus in order to prove that theorem I believe.
Also Google "Hole through centre of the Earth". There's loads about it.

 

[ZionsRodeVos]

This idea turns up regularly. The bits of the sphere at a greater distance from the centre than you are have no contribution to the gravitational field there. The field, in fact, is proportional to the distance from the centre, once you are below the surface, and zero at the centre.
Google Newton's Shell Theorem to find out about it. He even had to invent his own form of Calculus in order to prove that theorem I believe.
Also Google "Hole through centre of the Earth". There's loads about it.

I've read Newton's Shell Theorem on Wikipedia, twice. Of course that was only the first part which explains it pretty well. It isn't going to do me any good to get into the math yet, but I did recognize some of the notation from calculus.

What is puzzling is that if all mass no matter its size has gravity then why would I think that all the gravity would be focused at the center of a sphere? And what was harder for me to understand, and maybe I still haven't, is what you said above and the theorem I read that once I get to the center of the solid sphere the gravity is zero. Does that mean I would feel no gravity at the center of the earth, assuming I could actually get there and survive? If that is true that doesn't make sense to me because I would have so much mass around me at all sides I would think that I'd feel gravitational pull from all sides and if it were strong enough then it should pull me apart.

Does this theorem mean that if there was a planet with the same mass as the Earth but bigger so that the core was hollow, say about a half mile diameter hollow space that anyone in the center would feel no gravity but people on the surface would still feel gravity close to what we feel on earth?

 

[sophiecentaur]

Potential is more reliable than force in these discussions, I think.
No g at the centre. BUTTTTTT the Potential is still at its lowest at the centre. The potential well, instead of going down to an infinitely negative point for a point mass, bottoms out at a very finite value. See this link. and the pretty 3D plot at the top.
They would 'feel' no gravity, of course, because there would be no floor pushing up at them.

 

[technician]

This would be extraordinarily difficult for those of us who have no textbook for every possible thing we post on.

But i think I am correct in saying that posts and explanations should conform to standard textbook explanations...or peer reviewed journals.
I think that is made clear in forum rules!

 

[technician]

Unfortunately, if we only ever quoted from textbooks and we all bought the appropriate one to read, the cost would be ridiculous.
Despite what we say about Wiki, the majority of Wiki pages that deal with the majority of topics on PF are just fine - certainly for starters. When they're not, and you quote them here, someone will point out what's wrong. It is far more fruitful to go there first and as a question about what you found out than just to produce some vague question and to expect exactly the appropriate answer.
Showing that you have made some effort is courteous to other PF members and will get positive results.

I did look at the wiki link...hence my response. Wiki is a reasonable source of facts but, in my opinion, is not a teaching medium.
it is the equivalent of using a dictionary to learn a foreign language.
Regarding textbooks...you know i have raised this before...I understand from forum rules that posts and explanations should conform to standard textbook explanations and we should all make certain we know what these are before we post something to the contrary.

 

[micromass]

But i think I am correct in saying that posts and explanations should conform to standard textbook explanations...or peer reviewed journals.
I think that is made clear in forum rules!

If the topic is mainstream and not controversial, then wiki links are allowed. Do take them with a grain of salt however, they're not always reliable. But they're good to get a general overview.

Personally, I think quoting from a textbook is always better than linking to wiki. But sometimes we just don't have the time or the resources to do this.

 

[ZionsRodeVos]

Potential is more reliable than force in these discussions, I think.
No g at the centre. BUTTTTTT the Potential is still at its lowest at the centre. The potential well, instead of going down to an infinitely negative point for a point mass, bottoms out at a very finite value. See this link. and the pretty 3D plot at the top.
They would 'feel' no gravity, of course, because there would be no floor pushing up at them.

I'm going to have to spend more time looking at this potential you speak of. I've read the first paragraph of few times and everything else in the link at least once and I don't see how it relates and am not understanding it right now. It seems there is a difference between potential theory and everything else I have been learning so far and I don't see where potential fits in.

Why would a floor be pushing up at someone? Does the Earth push up at us? I didn't intend for both my threads to be talking about the same thing but they seem to be converging to that point whereas if gravity is as Einstein envisioned it then it would seem to me that the reason you would feel no gravity at the center of the Earth is that the amount of mass warping space time is less.

 

[sophiecentaur]

I'm going to have to spend more time looking at this potential you speak of. I've read the first paragraph of few times and everything else in the link at least once and I don't see how it relates and am not understanding it right now. It seems there is a difference between potential theory and everything else I have been learning so far and I don't see where potential fits in.

Why would a floor be pushing up at someone? Does the Earth push up at us? I didn't intend for both my threads to be talking about the same thing but they seem to be converging to that point whereas if gravity is as Einstein envisioned it then it would seem to me that the reason you would feel no gravity at the center of the Earth is that the amount of mass warping space time is less.

If it did not, we would sink right in, wouldn't we? If you jump off a cliff, exactly the same force of gravity is acting on us but the situation is noticeably different when we stand at the top of the same solid cliff.

If you approach problems from the Energy point of view, rather than the Forces point of view, it can often be relied on to yield a more reliable answer. Hence, I introduced potential. Consider the work you can get out of a mass, hanging on a rope, at some height (out near the Moon, perhaps - not practical but worth the thought). Every metre the mass gets nearer the Earth, some work can be got out of that falling mass. Its Potential is decreasing (that -1/radius curve, which would go off to -∞ if the Ezrth's mass was all at the centre). Once the mass reaches the surface, it will still be pulled down (work can be got out, so the potential is still decreasing) but by less and less of the Earth's mass until it reaches the centre, when the Potential is at a minimum and the force is zero.

It might be better to get your classical stuff sorted out first, before you launch into GR. Certainly, Einstein did it that way and he was probably smarter than you (). But, if you must, you could say that the warping is zero when you get into the centre (ignoring other objects in space, of course).

 

[D H]

Does the Earth push up at us?

Yes, it does, even in Newtonian mechanics. It's called the normal force.

 

[ZionsRodeVos]

I'm guessing GR stands for general relativity and I do believe I am understanding small portions of it. I'm sure my questions make it quite obvious that I am no where near the level of understanding of Einstein.

Does both Newton's theory and Einsteins theory include the premise that the Earth pushes up at us? I didn't think either did.

We don't sink into the Earth because on the surface it is solid. Unless I am mistaken the Earth is not expanding so why or how would it be pushing up at me?

 

[D H]

Does both Newton's theory and Einsteins theory include the premise that the Earth pushes up at us? I didn't think either did.

Both do.

We don't sink into the Earth because on the surface it is solid.

Exactly.

Let's look at things from a Newtonian perspective. I'll ignore the Earth's rotation about it's axis and it's orbit about the Sun. This makes an Earth-based frame of reference a Newtonian inertial frame: Newton's laws apply. A person standing still on the surface of the Earth is not moving and hence is not accelerating. The net force must be zero. We know there's a downward force acting on the person; it's gravity. There must be some other force that counterbalances this gravitational force. That other force is the normal force, the force that keeps you from sinking into the Earth.

The same thing happens when you lean against a wall or when you climb a ladder to push up on the ceiling. The wall or ceiling pushes back against you. The force that keeps you from falling into the Earth, falling into the wall, or punching up through the ceiling is normal to the surface in question. That's why it's called the normal force.I don't think it's a good idea to explain the relativistic point of view to you. You are obviously having difficulties understanding Newtonian mechanics. You need to understand that fully before moving on to more advanced topics.

 

[sophiecentaur]

I'm guessing GR stands for general relativity and I do believe I am understanding small portions of it. I'm sure my questions make it quite obvious that I am no where near the level of understanding of Einstein.

Does both Newton's theory and Einsteins theory include the premise that the Earth pushes up at us? I didn't think either did.

We don't sink into the Earth because on the surface it is solid. Unless I am mistaken the Earth is not expanding so why or how would it be pushing up at me?

I think you are being a bit optimistic in that statement. The conclusions you are coming to rather suggest that you may be 'familiar' with some of the terms but your use of them suggests that they don't fit together quite right. This is hardly surprising as you are still struggling with the Classical approach. It is very unlikely that you will suddenly 'get it' by some sort of fast track process, which by-passes the grind of Maths and Classical Mechanics. You are in company with a lot of people in this and I blame the media and some of modern teaching approaches for this. I wouldn't go as far as the blessed Mr Gove but I see where he's coming from. haha.

 

[ZionsRodeVos]

I very much appreciate all of you for your patience with me and for helping me understand even though I am not approaching things the way many of you have/do. Or did some of you also start out asking questions before bothering with the math? Do you mean that I must get into the mathematics to be able to understand these theories? Is there no way to discuss them without math or is it that I am simply not getting it yet even though you are telling me this is the way it is?

It would seem to me then the type of push you are referring to is not the same as when one person pushes another.

Why must there be a force to counterbalance gravity? Is it not enough that these objects are solid and so even with a force such as gravity we simply don't penetrate them?

 

[WannabeNewton]

If there was no reaction force from the ground due to you standing (or walking) on the ground, then the only force acting on you would be gravity and Newton's 2nd law would indicate that you are accelerating downwards, which is a contradiction. There must be some reaction force from the ground due to you standing (or walking) on it that manages to counteract gravity so that your path stays tangential to the ground; this constraint force is the so called normal force. Part of the origin of the normal force comes from the Pauli exclusion principle, which in part shows why ordinary bulk matter is stable and occupies volume.

 

[Nugatory]

Is it not enough that these objects are solid and so even with a force such as gravity we simply don't penetrate them?

"Solid" is just another way of saying "when you push on it, it pushes back on you".

It might be easier to see this if you imagine a coil spring between your feet and the ground. The spring compresses under your weight, and pushes back as it compresses because that's what springs do. Now imagine that the spring becomes stiffer and stiffer, so it compresses less and less under your weight... If the spring were stiff enough that the compression was unnoticeable, you'd say that it was "solid".

Even a block of steel, something that we all agree is about as solid as solid can be, actually behaves like a very very stiff spring when you stand on it - it compresses by maybe .0001" or thereabouts.

 

[sophiecentaur]

I very much appreciate all of you for your patience with me and for helping me understand even though I am not approaching things the way many of you have/do. Or did some of you also start out asking questions before bothering with the math? Do you mean that I must get into the mathematics to be able to understand these theories? Is there no way to discuss them without math or is it that I am simply not getting it yet even though you are telling me this is the way it is?

It would seem to me then the type of push you are referring to is not the same as when one person pushes another.

Why must there be a force to counterbalance gravity? Is it not enough that these objects are solid and so even with a force such as gravity we simply don't penetrate them?

In the case of a star, it's pressure, due to the momentum of the mobile atoms at high temperature (kinetic theory) and with a solid planet it is more pedestrian electric repulsion of the positive nuclei of all the atoms. Just another of the fundamental forces.

Regarding the Maths, I think you either have to take what you are told as a done deal or you have to learn the Maths which will take you down a level or two in depth of understanding. Of course, the Maths is not the ultimate model, so you can say that no one has arrived there (or ever will, imo). At least, if you can use Maths to help you, you can rely on coming to slightly better founded conclusions than you can by arm waving and the risk of Science Fiction ideas creeping when you don't know better.
No one said it would be easy, dear boy.

 

[ZionsRodeVos]

"Solid" is just another way of saying "when you push on it, it pushes back on you".

It might be easier to see this if you imagine a coil spring between your feet and the ground. The spring compresses under your weight, and pushes back as it compresses because that's what springs do. Now imagine that the spring becomes stiffer and stiffer, so it compresses less and less under your weight... If the spring were to stuff enough that the compression was unnoticeable, you'd say that it was "solid".

Even a block of steel, something that we all agree is about as solid as solid can be, actually behaves like a very very stiff spring when you stand on it - it compresses by maybe .0001" or thereabouts.

This is very helpful to me understanding the push of the Earth from me standing/walking on it. Another thing to look at is a sponge which has much less of a push than the Earth and so it gives more and compresses more than the Earth would but at a certain point the sponge does not compress more and that is like it pushing back finally.

And so I am seeing that it is not easy. And reading about the Pauli exclusion principle gets me into quantum physics.