Derivation of the Newtonian Gravitational Force from the Action of the AG Model
Year: 2026
Type: preprint
Abstract: Derivation of the Newtonian Gravitational Forcefrom the Action of the AG Model Valentin Ionescu This manuscript presents a step-by-step variational derivation of Newton’s attractive gravitational force as the weak-field, low-speed, test-body limit of the Alternative Model of Gravity (AG). Based on Part III of The Integral Corpus of AMC Theory, the calculation uses Euclidean reference space, without introducing a gravitational metric or the field equations of general relativity. For a fixed spherical source of mass M and a test body of reference mass m0, let r denote their Euclidean separation and G0 the reference gravitational constant. At Newtonian order, the force is directed towards the source and has magnitude FN: Expanding the adopted AG mechanical action produces the Newtonian kinetic and potential terms. The interaction term follows from the action’s rest-energy scaling; it is not appended afterwards to impose the desired force. Variation of the test-body trajectory yields the equation of motion, while the corresponding momentum, mechanical energy and dimensional relations provide consistency checks. The manuscript also examines the radial profile underlying the result. It separates the harmonic-exterior assumption, spherical symmetry and the reference boundary condition from the macroscopic source normalization that fixes the amplitude. The exponential exterior branch is sufficient, but not necessary, for the Newtonian limit: profiles sharing the same first-order expansion recover the same leading force law. A further contribution is the explicit distinction between canonical force and reference-coordinate acceleration beyond the Newtonian approximation. In the prescribed exponential exterior, their exact expressions at an instant of rest contain different scaling factors. Consequently, replacing the reference gravitational constant by a position-dependent coupling in Newton’s formula does not substitute for deriving the dynamics from the action. The scope of the result is stated explicitly. This is a variational recovery within the effective AG model, not an independent microscopic derivation of gravity from the Cold Big Bang Model (CBBM). The reference potential and source normalization are inherited inputs, and selection of the mechanical action already uses the Newtonian limit. The analysis treats a fixed source and neglects the test body’s self-field and backreaction; it does not claim a completed solution for two comparable, self-gravitating bodies. By presenting the derivation, its assumptions and its exact dynamical checks together, the study clarifies the connection between the AG action and Newtonian gravity. It provides a self-contained account of the established test-body result and identifies the additional source dynamics needed for a broader derivation. Keywords: Newtonian limit; Alternative Model of Gravity (AG); variational principle; Euclidean reference space; test-body dynamics; gravitational force; CBBM.
Author: Ionescu, Valentin
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225649017
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