**69**, 4, pp. 457–488, 2021

**10.24423/EngTrans.1415.20211210**

### The Origins of Newton’s Mechanics. Mass, Force, and Gravity

In this work, the axiomatic model of dynamics is developed corresponding to the classical model of Newton’s dynamics. The key elements of the model are the ability to distinguish isolated systems, and their subsequent division into a selected body (*material particle*) and its surroundings (*attractor*). The material particle (usually assumed to be small relative to surroundings), and the attractor are the axiomatic model’s primary concepts. The only fundamental *state parameter *of the model is *acceleration *(kinematic quantity), which is accepted as the starting point of dynamics. The concepts of *mass *(dynamic characteristic of the material particle) and *force *(dynamic characteristic of the surroundings impact on the material particle) are derivative quantities in the model. Two types of (acceleration) measurement procedures deliver precise *operational definitions *of inertial mass and force. Thus, difficulties with the ideas of mass and force present in original formulation of Newton’s laws of dynamics are removed. The present model shows that for formulation and interpretations of the laws of dynamics, the general ideas about the particle and the environment affecting its motion, and the concept of *acceleration, are sufficient*. Neither masses nor forces are necessary to formulate the *essence of dynamics*. However, the elegance and power of the concepts of force and mass prompt for their introduction in any isolated system with a separated body as very convenient and useful quantities. Following the developed methodology, an axiomatic model of Newton’s *universal gravitation *is formulated, and it is shown that neither inertial mass nor force is actually needed for that purpose. Moreover, in the closed world of gravity, the force concept *cannot be introduced *as a dynamic feature of an attractor only – it must be a feature characterizing a pair of the specific particle and attractor. Reconciliation of the axiomatic model of universal gravity with the axiomatic model of dynamics leads to the equivalence of *gravitational mass *and *inertial mass *concepts.

In Translator opinion, the work contains a very original and elucidating approach towards classical dynamics and due to that deserves worldwide dissemination and knowledge. Nowadays, this can only be achieved, to the extent that the study deserves, by its publication in English language.

*Editorial note: *The present document is an English translation of Appendix C of Jan Rychlewski’s book titled *Dimensions and Similarity *(original Polish title *Wymiary i podobienstwo*), Wydawnictwo Naukowe PWN, Warszawa, 1991, pp. 185–208, ISBN 83-01-10557-7.

*Editorial note: *Abstract by Andrzej Ziółkowski.

**Keywords**: axiomatic model of dynamics; operational definition of inertial mass; operational definition of force; axiomatic model of universal gravity; Newton’s dynamics; concept of attractor; concept of material particle; equivalence of inertial mass and gravitatio

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DOI: 10.24423/EngTrans.1415.20211210