How to justify the shell theory by using Gauss Law?

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SUMMARY

The discussion centers on the justification of the shell theorem using Gauss's Law. It establishes that as an object descends beneath the Earth's surface, only the mass located beneath it contributes to gravitational force, while the mass above exerts no influence. This principle, rooted in Newton's work, is effectively demonstrated through Gauss's Law, which states that the gravitational field inside a spherical shell is zero. Thus, the gravitational effects can be analyzed solely based on the mass contained within a Gaussian sphere.

PREREQUISITES
  • Understanding of Newton's Law of Universal Gravitation
  • Familiarity with Gauss's Law in electrostatics and gravitation
  • Basic knowledge of spherical symmetry in physics
  • Concept of Gaussian surfaces in mathematical physics
NEXT STEPS
  • Study the derivation of the shell theorem in classical mechanics
  • Explore applications of Gauss's Law in gravitational fields
  • Investigate the implications of gravitational potential inside spherical shells
  • Learn about the mathematical formulation of gravitational fields using Gaussian surfaces
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Physics students, educators, and professionals interested in gravitational theory and its applications in classical mechanics.

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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