How to justify the shell theory by using Gauss Law?

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The discussion centers on justifying the statement that as an object descends into the Earth, only the mass beneath it influences gravitational force, while the mass above exerts no force. This concept is rooted in Newton's shell theorem, which states that a uniform spherical shell of mass exerts no net gravitational force on objects located inside it. Gauss's law supports this by indicating that only the mass enclosed within a Gaussian surface contributes to the gravitational field. Therefore, as one goes deeper, the gravitational effects of the layers above cancel out, leaving only the mass below to exert force. This illustrates the relationship between Gauss's law and the shell theorem effectively.
Negi Magi
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"As the ball gets deeper under the surface of the Earth, the layers above it stop exerting gravitational force, and all that matters is the mass underneath."

How to justify this sentence is true?
 
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Negi Magi said:
"As the ball gets deeper under the surface of the Earth, the layers above it stop exerting gravitational force, and all that matters is the mass underneath."

How to justify this sentence is true?

Well it was proven in general by Newton a few hundred years ago: http://en.wikipedia.org/wiki/Shell_theorem

Using Gauss' law, it's manifest in that you only consider the mass inside the Gaussian sphere. In a sense, Gauss' law embodies the shell theorem.
 
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