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

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To calculate gravitational force when an object is inside a shell, the shell theorem can be applied to both the inner and outer shells. When the object is within the inner shell, only the mass of the inner shell contributes to the gravitational force, while the mass above it does not affect the force experienced by the object. The gravitational force can be expressed using the formula (GMm)/r^2, where r is the distance from the object's position to the center of the shell. It's crucial to adjust the mass M to reflect only the mass of the shell that is below the object. Understanding these principles allows for accurate calculations of gravitational force in complex shell configurations.
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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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