# Why Newton's G is not a universal Constant of Nature A reanalysis of Cavendish's experiment to determine the density of the Earth

Heinrich, Werner F. (2021) Why Newton's G is not a universal Constant of Nature A reanalysis of Cavendish's experiment to determine the density of the Earth. [Preprint]

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## Abstract

A careful analysis of the methodology of Cavendish's classical experiment to determine the density of the Earth, [1], shows how G is constructed from realizations of Newton's definitions and axioms built into the methodology of the experiment. Therefore, as the physical constructs in these definitions and axioms are interrelated, Cavendish's methodology leads to three different but equivalent algebraic quantitative expressions, A, B, and C, each identified with G. This gives G/A=G/B=C/G=1, and its inverses. This can be considered the historical starting point of constructing a quantitative philosophy of nature based on mathematical principles.
Each of the three equivalent expressions represents a realization of a combination of different physical constructs in the definitions and axioms used. The realization of the relevant physical constructs and axioms built into Cavendish's methodology define what I call homogeneous gravitating spheres, HGS, for which the Earth is the quantitative reference standard. Realized in this reference standard are: Newton's operational definition 1 of mass in his Principia, his definition of centripetal acceleration, which implies the inverse square law for the centripetal surface acceleration of HGS, and his 2nd law of motion; the latter realized in a tangent space of the Earth. Taken together this defines a gravitational based standard of force for any arbitrary choice of a standard of mass. There is nothing universal in this. That this state of affairs has not been made clear since Cavendish read his report to the Royal Society of London on June 21 1798 is rather surprising, as the facts laid out here have far ranging consequences, particularly for the philosophy of science and nature w.r.t. constructing the Weltbild of our universe.

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Item Type: Preprint
Creators:
CreatorsEmailORCID
Heinrich, Werner F.newtonsconst@gmail.com
Keywords: Cavendish experiment, Newton's gravitational constant, Planck's natural units.
Subjects: General Issues > History of Philosophy of Science
General Issues > Philosophers of Science
General Issues > Theory/Observation
Depositing User: Mr. Werner Heinrich
Date Deposited: 06 Feb 2021 21:19
Item ID: 18688
Subjects: General Issues > History of Philosophy of Science
General Issues > Philosophers of Science
General Issues > Theory/Observation
Date: 5 February 2021
URI: https://philsci-archive.pitt.edu/id/eprint/18688