How would shell theorem act in a hollow sphere?

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Discussion Overview

The discussion revolves around the implications of the shell theorem when applied to a hollow spherical object, particularly focusing on gravitational effects both inside and outside the sphere. Participants explore theoretical aspects related to gravity, mass, and the characteristics of such a hollow sphere.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that the shell theorem indicates gravity is focused at the center of a spherical object, questioning how this applies to a hollow sphere with Earth's gravity.
  • Questions are raised about the mass required for a hollow sphere to exert gravitational force equivalent to that of Earth.
  • Participants inquire about the gravitational effects inside the hollow sphere and how it interacts with other objects within it.
  • There are mentions of two shell theorems: one describing the gravitational field outside the shell and another for inside the shell, with some participants expressing familiarity with only one of them.
  • One participant summarizes the two theorems, stating that outside the shell, the gravitational field behaves as if all mass were concentrated at the center, while inside the shell, the gravitational field is zero.

Areas of Agreement / Disagreement

Participants generally agree on the basic principles of the shell theorem but express uncertainty regarding the specific implications for a hollow sphere and the mass required to replicate Earth's gravity. Multiple competing views remain regarding the effects of the hollow sphere on gravitational interactions.

Contextual Notes

Limitations include assumptions about the uniformity of mass distribution in the shell and the dependence on the definitions of gravitational effects inside and outside the shell.

Joseph King
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What I understand is this: Shell theorem states that the force of gravity is focused at the center of an object. But, say that there is a large planet with a gravitational force equal to that of earth's. It is perfectly round… and hollow. Since it is hollow, how large would it be to have Earth's gravity? Stranger yet, what would the effects be inside and outside of the sphere?
 
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To have Earth gravity what would be its mass?

What is the gravity inside any shell of a given mass?

How large the planet is depends on the size of the shell and the density of mass composing it, right?
 
Exactly. And what effects would it have on other objects inside the sphere.
 
There are two shell theorems that describe the field from a spherically symmetry shell of mass. One describes the field outside the shell, the other describes the field inside the shell. Are you familiar with both of those?
 
I only know of the one focused inward.
 
Joseph King said:
I only know of the one focused inward.
And what does that theorem say? (In post #1 you mentioned the theorem that deals with the field outside the shell.)
 
Well, basically, it states that if you have an object (ie earth) then the force of gravity is focused at the center. So, if you are underground, the mass above you does not have any gravitational effect on you.
 
Joseph King said:
Well, basically, it states that if you have an object (ie earth) then the force of gravity is focused at the center. So, if you are underground, the mass above you does not have any gravitational effect on you.
Here's how I would put the two theorems:

(1) Outside the shell, the field is that of a point mass equal to the mass of the shell and located at the center of the shell.

(2) Inside the shell, the field is everywhere zero.
 
That makes sense, thanks!
 

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