Is there really no gravitational force at the center of a massive object?

[DaveC426913]

Please explain. What is this graph supposed to represent? It doesn't look to me like the gravitational potential for either a solid sphere with a small hole drilled through it, or like a spherical shell, which are the two cases that we've discussed so far.

It is the potential for a sphere with a hollow centre where:
1] the diameter of the sphere is shown by the change in curvature from positive to negative. This can be seen to occur at the contour line second from the bottom.
2] the hollow centre is too small to be seen at this scale (the "me" dot eclipses it). At that tiny point, the curvature is flat (and parallel to the flat space outside the well).

 

[Loren Booda]

How do this thread's symmetry arguments for gravity compare to those for electromagnetism?

 

[DaveC426913]

Please explain. What is this graph supposed to represent?

I have updated the graphic for clarity. Happier?

 

[belliott4488]

I have updated the graphic for clarity. Happier?

Yes! Thanks.
Now that I get the figure, though, I'm still wondering what your question is. This shows the parabolic curve for the interior that I mentioned in an earlier post. It's flat at the center (where "me" is), so there's no gradient, i.e. no force. Is that a problem?

 

[belliott4488]

How do this thread's symmetry arguments for gravity compare to those for electromagnetism?

If you're referring to the arguments for the cancellation of the field, they're the same. For example, there is no E-M field inside a uniformly charged hollow sphere.

 

[capnahab]

No, because an atom is a fuction of the uncertainty principle. I was talking about being at the center of the singularity of a black hole. A very small space but I can visualize it. Let's get to the bottom of it. If you are at the center of the singlarity of a black hole, does it make any difference? Maybe I misunderstand the terminoligy. To the newbies, even the singlarity has over the diameter of the Plank length, no matter if the black hole has the weight of of three Suns or a three billion Suns.

I dare you to ask the astrophysictists the diameter of a 3 billion Sun black hole singularity. It is smaller than the diameter of the nucleas (can't spell it) of any atom.

 

[Andre]

At the centre of a very massive object, the gravitational force is zero. Is that net zero or is it gross zero?

What I mean is: If two people are pulling on my limbs with equal force in opposite directions, my net movement is zero, but I am under great stress. The net forces on me sum to zero, but the gross forces are that of two people pulling on me.

Is it the same with gravity? If I were at the center of the Earth, is there a test I could do to measure the absolute gravitational pull on me?

It seems counterintuitive, Dave? No force and hence no stress? But there is. Change that pulling in pushing. There is no net force but there is pressure. If you would be at the centre of the Earth there is no gravity indeed but you would still be under a tremendous amount of stress too, due to the sum of pressures of all overlying masses times their indivual gravity constant. That's why the 'iron' inner core is solid, despite the high temperatures, due to the shear pressue.

 

[Doc Al]

It seems counterintuitive, Dave? No force and hence no stress? But there is. Change that pulling in pushing. There is no net force but there is pressure. If you would be at the centre of the Earth there is no gravity indeed but you would still be under a tremendous amount of stress too, due to the sum of pressures of all overlying masses times their indivual gravity constant. That's why the 'iron' inner core is solid, despite the high temperatures, due to the shear pressue.

But that's not what's being discussed here. The scenario under discussion is: What's the gravitational field within a hollow cavity at the center of a spherically symmetric planet. There is none. (There's none even if you get rid of the cavity, of course--but then you have other effects: the weight of that mass pushing down on you.)