Gravitational conceptual problem

[Johnny5]

Suppose that we have two enormous spheres, and let each of them be a rigid body.

 

 

 

Let one be the size of the earth, but far more dense, and let the other be the size of the moon, and also much more dense.

 

Now, let them be touching, the smaller one on top of the bigger one.

 

Would gravity cause the smaller one to start rolling around the bigger sphere, or would it just sit on top?

[ydoaPs]

it depends where the second is located.

[Johnny5]

it depends where the second is located.

 

 

The two are in vaccum, and in an inertial reference frame, and nothing else in the universe is exerting a force on either object.

 

The only force either object experiences is the gravitational attraction of the other.

 

So I don't see why it would depend on where the second is located. The second is at rest, on top of the first. Does it start rolling, without a nudge?

 

I am assuming both things are symmetrically shaped. They are rigid spheres.

[ydoaPs]

spheres aren't entirely sphereical. if you're assuming they are perfect spheres, then it wouldn't move.

[Johnny5]

spheres aren't entirely sphereical. if you're assuming they are perfect spheres, then it wouldn't move.

 

Right.

 

Now, suppose that I give one of them a nudge. What's gonna happen?

[ydoaPs]

it will go until friction stops it. what happens when you roll a ball on earth?

[Johnny5]

it will go until friction stops it. what happens when you roll a ball on earth?

 

It goes until friction stops it. But would there be friction if the spheres were perfectly rigid, and truly spherical? Or wouldn't the surfaces be so smooth, that there would be no friction?

[ydoaPs]

they would still be touching at at least one point, so there would be friction.

[Johnny5]

they would still be touching at at least one point, so there would be friction.

 

In theory, they would be touching yes, but lets make this problem slightly more realistic, let there be electrons located at the surface of both spheres.

 

Now what?

 

wouldn't there be an electrostatic force of repulsion? So that the spheres wouldn't really be touching?

[ydoaPs]

yes they would. that is how you don't fall through your chair.

[mezarashi]

If you have a configuration of two spheres whose surfaces' are just touching each other and none have any velocity relative to each other, then I can confidently say that there will be no motion. Orbital motion is due to some initial velocity component perpendicular to the direction of the gravitational force.

 

And about your hypothesis of electrons on the surface. In actuality, did you know that the reason your table top feels hard is because the electrons of the atoms of your hand repel the electrons of the atoms comprising the table . We've taken the word "touch" for granted without really thinking about it. Depending on your application you would assign different definitions (touching distance: the distance where the grav force and electromag force reach a balance of equilibrium...maybe). In anycase, the electromagnetic force is probably the principle force in making solid objects seem...solid. So with this in mind, the notion of electrons of the first sphere repelling the second isn't anything mysterious at all is it

[Johnny5]

If you have a configuration of two spheres whose surfaces' are just touching each other and none have any velocity relative to each other' date=' then I can confidently say that there will be no motion. Orbital motion is due to some initial velocity component perpendicular to the direction of the gravitational force.

[/quote']

 

Given that nothing else in the universe exists, I agree. Of course there are no two such spheres capable of existing, so the question is rather academic. But out of curiousity, if you give one of them a tap, what happens?

[Johnny5]

 

And about your hypothesis of electrons on the surface. In actuality' date=' did you know that the reason your table top feels hard is because the electrons of the atoms of your hand repel the electrons of the atoms comprising the table . We've taken the word "touch" for granted without really thinking about it. Depending on your application you would assign different definitions (touching distance: the distance where the grav force and electromag force reach a balance of equilibrium...maybe). In anycase, the electromagnetic force is probably the principle force in making solid objects seem...solid. So with this in mind, the notion of electrons of the first sphere repelling the second isn't anything mysterious at all is it [/quote']

 

It is mysterious actually, given that photons mediate the electric force of repulsion. At least thats what QFT says, but I can't get Mr. Mattson to teach it to me. Not to mention, I never did like Feynman diagrams, the approach doesn't seem rigorous. Furthermore, QED has SR built into it, and I have problems with SR.

[DavidAngelMX]

Look, we all know that friction doesn't have to do with imperfect surfaces, but with electromagnetic interactions between the surfaces of the materials, so, if these spheres are made of matter, there should be some interaction, and as a consequence, there should be friction.

 

So, if the friction is great enough to force the small sphere to roll and not slide, and assuming that there is no energy loss when a determined point of the surface of the small sphere is separated from the surface of the other one, then the ball should roll forever, since there is no air friction to stop it, just like the imaginary case of a ball rolling on earth without any friction except for that with the floor.

 

Well... I don't get the idea, I don't think this is a thrilling gravitational event.

[Ophiolite]

The spheres will deform, or was 'rigid' meant to cover that?

[mezarashi]

Given that nothing else in the universe exists, I agree. Of course there are no two such spheres capable of existing, so the question is rather academic. But out of curiousity, if you give one of them a tap, what happens?

 

 

If you give it a tap, then of course, the spheres will roll around each other's barycenter. As you have given hypothetically, there is no friction, so there is nothing to stop an eternal orbit. As with the photons, the photons used to "carry" the electromagnetic force are distinctly different. If I'm not wrong, they are known as virtual photons, with some other fancy denotation I have forgotten. I don't think it'll require quantum physics to see the general picture for this concept though

[Johnny5]

they would still be touching at at least one point, so there would be friction.

 

You know what, no two real solid objects touch, because of the repulsion of electrons at the surface of each object, yet there is still friction.

[Johnny5]

Look' date=' we all know that friction doesn't have to do with imperfect surfaces, but with electromagnetic interactions between the surfaces of the materials, so, if these spheres are made of matter, there should be some interaction, and as a consequence, there should be friction.

[/quote']

 

Yes.

 

Friction is, as far as I know, considered to be the result of an electromagnetic interaction between surface electrons of two objects (someone correct me if there is any other explanation of friction out there).

[Johnny5]

So' date=' if the friction is great enough to force the small sphere to roll and not slide, and assuming that there is no energy loss when a determined point of the surface of the small sphere is separated from the surface of the other one, then the ball should roll forever, since there is no air friction to stop it, just like the imaginary case of a ball rolling on earth without any friction except for that with the floor.

 

Well... I don't get the idea, I don't think this is a thrilling gravitational event.[/quote']

 

That's exactly what I wanted to know. Does anyone else agree with David, I think he's right.

 

You have gravitational attraction of the two spheres towards one another, and electric repulsion, these 'two' different forces bring the centers of inertia of both spheres into static equilibrium. But any tiny perturbation whatsoever, would cause the center of inertia of the small sphere to start orbiting the center of inertia of the larger sphere, in the rest frame of the larger sphere.

 

Then, either the small sphere rolls without slipping, or slips without rolling.

 

Any corrections to this? I am not using mathematics as much as I should.

 

PS: I said two forces, but there really just may be the one

superforce S of nature. I'm not certain yet.

[Bob182]

If the frictional force causes the smaller ball to roll without slipping, there will also be an equal and opposite force on the larger ball, causing it to rotate also.

[Johnny5]

If the frictional force causes the smaller ball to roll without slipping, there will also be an equal and opposite force on the larger ball, causing it to rotate also.

 

Hmm, so they would start spinning like umm gears ?

 

Let's say that there is friction between them.

 

I am having some trouble picturing what happens.

 

I'm not using math by the way.

 

Let the two spheres have identical masses and radii.

 

They are gravitationally attracting each other, and electrically repelling each other.

 

They are in deep space away from all other external fields, other than their own.

 

You are viewing the motion in the center of mass frame.

 

Since the spheres are equally massive, and have identical radii, the center of mass of this two body system is located at the point of contact.

 

Let the spheres be rigid.

 

Right now, they are at rest in this frame.

 

Someone then gives the one on top a gentle tap.

 

Now what happens?

 

I think conservation of energy comes into play here.

 

Anyone?

 

It will help to talk about what happens to rigid vectors drawn from the center of each sphere to a fixed point on the surface, because as Bob says, each sphere is going to start spinning in the center of mass frame.

 

oh oh oh, and one more question before I forget, is the center of mass frame an inertial reference frame?

 

Regards