How do we calculate gravitational force when an object is inside a shell?

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    Shell Theorem
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Discussion Overview

The discussion revolves around calculating the gravitational force on an object located inside a shell of thickness R(earth)/2, specifically when the object is positioned between the inner and outer radii of the shell. Participants explore the implications of the shell theorem in this context.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant proposes applying the shell theorem to determine the gravitational force acting on an object located inside the shell.
  • Another participant suggests considering the scenario as having two shells, advocating for the application of the shell theorem to each shell separately.
  • A participant questions whether the gravitational force can be calculated using the same formula as for an object outside the larger shell, noting that the distance from the mass to the center is r.
  • Another participant acknowledges the need to account for the mass of the smaller shell and emphasizes that the gravitational force formula must reflect the mass below the object.
  • A later reply expresses gratitude for the clarification regarding the mass consideration.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the exact method for calculating the gravitational force when the object is inside the shell, with multiple viewpoints and interpretations presented.

Contextual Notes

Participants discuss the dependence on the definitions of the shell's mass and the distances involved, but these aspects remain unresolved.

anhchangdeptra
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Imagine all the mass of the Earth is in a shell of a thickness of R(earth)/2. So if the object is inside the shell or outside the shell, I know I can apply the shell theorem to solve the gravitational force acting on it. But, what if the object is IN the shell, in another words R(earth)/2<r<R(earth), how do we calculate the gravitational force?
 
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so its like you have two shells. The object is outside one shell and inside the other. Apply the shell theorem to each one and what do you get.
 
Oh! So we only care about the smaller shell with radius= R/2. The distance from mass m to the center is r so basically we have the same formula as for an object outside the bigger shell= (GMm)/r^2 (only the r is different is the two cases)?
 
anhchangdeptra said:
Oh! So we only care about the smaller shell with radius= R/2. The distance from mass m to the center is r so basically we have the same formula as for an object outside the bigger shell= (GMm)/r^2 (only the r is different is the two cases)?
M is also different. After all, you don't care about the part of the shell above the object.
 
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Oh yes! I really forget the M. Thank you very much!
 

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