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Physics, Astronomy & Cosmology / Re: Which bit of the Shell theorem is not working?
« on: 16/10/2023 07:58:30 »
Hi.
Wikipedia gives a short definition or explanation of the shell theorem:
1. A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its center.
2. If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell.
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So the shell is made of some material and that material does gravitate - it attracts other stuff to it. When you're outside that shell it behaves exactly as you would expect . You would have a force of attraction identical to the force of attraction you would have if you imagine all of the shell was just squahed down into one really small ball and placed at the centre position of that shell.
It's only when you're inside the hollow shell where it may seem you get an unexpected result. You are still attracted to each part of that shell. If you happen to be at the centre of the shell then you are equally attracted in all directions and there is no net force, as you may expect. However, even when you move away from that centre and toward one piece of the shell, you still feel no net force of attraction in any direction. Provided you stay inside the shell, you find no net force acts on you.
There are many articles and YT videos that provide explanation in varying levels of detail and sophistication. The simplest explanation is merely suggestive or hand-wavy: When you move toward one piece of the shell, the distance between you and that piece decreases, so by Newton's law the force of attraction to that piece (the bit infront of you) should increase. That does happen. However, since you have moved off-centre, there is now a bit more of the shell behind you rather than infront of you. That tends to increase the attraction to the direction behind you. It just so happens that both things happen in the right proportion and the net (or total) force stays at 0.
The acceleration can be determined in various ways, you could use any inertial reference frame you want OR you can just identify that acceleration more directly by giving the person insde the shell an accellerometer. To get the right result with an accelerometer in the real world you'd need a really, really big shell and a person who is actually floating in outer space so that they weren't experincing any forces other than the gravitational attraction of the shell.
Best Wishes.
Has my post been deleted, and Paul's?I don't know.
If an object within a shell has no gravitational effect on any object within it, surely that is from the point of view of the outside Observer? One would assume that the shell would indeed have gravitational attraction, if the she'll where 100, 000km thick and 10 million in diameter?There may be some minor errors in the English in that question. I think I know what you're asking.
Wikipedia gives a short definition or explanation of the shell theorem:
1. A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its center.
2. If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell.
- - - - - - - - - -
So the shell is made of some material and that material does gravitate - it attracts other stuff to it. When you're outside that shell it behaves exactly as you would expect . You would have a force of attraction identical to the force of attraction you would have if you imagine all of the shell was just squahed down into one really small ball and placed at the centre position of that shell.
It's only when you're inside the hollow shell where it may seem you get an unexpected result. You are still attracted to each part of that shell. If you happen to be at the centre of the shell then you are equally attracted in all directions and there is no net force, as you may expect. However, even when you move away from that centre and toward one piece of the shell, you still feel no net force of attraction in any direction. Provided you stay inside the shell, you find no net force acts on you.
There are many articles and YT videos that provide explanation in varying levels of detail and sophistication. The simplest explanation is merely suggestive or hand-wavy: When you move toward one piece of the shell, the distance between you and that piece decreases, so by Newton's law the force of attraction to that piece (the bit infront of you) should increase. That does happen. However, since you have moved off-centre, there is now a bit more of the shell behind you rather than infront of you. That tends to increase the attraction to the direction behind you. It just so happens that both things happen in the right proportion and the net (or total) force stays at 0.
The acceleration can be determined in various ways, you could use any inertial reference frame you want OR you can just identify that acceleration more directly by giving the person insde the shell an accellerometer. To get the right result with an accelerometer in the real world you'd need a really, really big shell and a person who is actually floating in outer space so that they weren't experincing any forces other than the gravitational attraction of the shell.
Best Wishes.
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