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Newton’s Law of Umversal Gravitation and the Scalę Principle

Rodolfo A. Frino - July 2014

Electronics Engineer - Degree from the National University ofMar del Plata - Argentina ([e-mail])

Earlier thisyear I w role a paper entitled Scalę Facłors and the Scalę Principle. In that paper 1 formulated a new law which describes a number of fundamenlal ąuantum mechanical laws and part of Einstein ’s theory of relatmty. The purpose of this article is to show that this theory also predicts Newton ’s law of uniwersał gravitation. Thus this new formulation can be extended to classical mechanics.

Keywords: Newton ’.v law of universal gravitation, Coulomb ’s law, Planck charge, Planck length, Planck time, Planck mass, Planck acce/eration, Planck force.

1. Introduction

In a previous article [1] I introduced the scalę principle or scalę law through the following mathematical relationship

(o

Scalę principle or scalę law
	e, a	[<|=p]^	a)' aj

Where

a) Qi, Qi, (?3 and Q₄ are physical ąuantities of identical dimension (such as Length, Time, Mass, Temperaturę, etc), or

b)    Qi and Q₂ are physical ąuantities of dimension 1 or dimensionless constants while Q₃ and Q_A are physical ąuantities of dimension 2 or dimensionless constants. However, if Q_x and Q₂ are dimensionless constants then Q₂ and Q₄ must have dimensions and viceversa.

The physical ąuantities can be variables, constants, dimensionless constants, differentials, derivatives (including Laplacians), integrals, vectors, any mathematical operation between the previous ąuantities, etc.

Ne\vton's Law of Universal Gravitation and the Scalę Principle vl. Copyright 2014 © Rodolfo A. Frino.

Ali rights reserved.

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