Authors :
Tanvin Chowdhury
Volume/Issue :
Volume 10 - 2025, Issue 12 - December
Google Scholar :
https://tinyurl.com/yprjrf6e
Scribd :
https://tinyurl.com/d9ttw96w
DOI :
https://doi.org/10.38124/ijisrt/25dec1337
Note : A published paper may take 4-5 working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and ResearchGate.
Abstract :
We present a reverse dynamical derivation of the shell theorem by assuming, hypothetically, that a particle
inside a hollow spherical shell experiences a nonzero gravitational force. Such an assumption, constrained by spherical
symmetry, necessarily leads to simple harmonic motion about the center. We demonstrate that this motion is incompatible
with Newtonian gravity through multiple independent arguments, including violations of Gauss’s law and Laplace’s
equation, contradictions with energy conservation and momentum conservation, and the absence of any physical
mechanism capable of supporting a restoring force inside an empty cavity. This backward approach shows that the
vanishing of the gravitational field inside a hollow shell is not merely a result of symmetry or integration, but a
fundamental requirement imposed by the internal consistency of gravitational theory.
References :
- Newton, Philosophiæ Naturalis Principia Mathematica, 1687.
- D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics, Wiley.
- H. Goldstein, C. Poole, J. Safko, Classical Mechanics, Addison- Wesley.
- J.D. Jackson, Classical Electrodynamics, Wiley.
- R. Fitzpatrick, Introduction to Classical Mechanics: With Problems and Solutions, CRC Press.
We present a reverse dynamical derivation of the shell theorem by assuming, hypothetically, that a particle
inside a hollow spherical shell experiences a nonzero gravitational force. Such an assumption, constrained by spherical
symmetry, necessarily leads to simple harmonic motion about the center. We demonstrate that this motion is incompatible
with Newtonian gravity through multiple independent arguments, including violations of Gauss’s law and Laplace’s
equation, contradictions with energy conservation and momentum conservation, and the absence of any physical
mechanism capable of supporting a restoring force inside an empty cavity. This backward approach shows that the
vanishing of the gravitational field inside a hollow shell is not merely a result of symmetry or integration, but a
fundamental requirement imposed by the internal consistency of gravitational theory.
