The frame of fixed stars in Relational Mechanics

TL;DR

This paper discusses relational mechanics, a gauge theory of classical mechanics that emphasizes the evolution of distances between particles over absolute space, and explores how it compares to Newtonian mechanics especially in astronomical contexts.

Contribution

It introduces a relational mechanics framework that aligns with Newtonian mechanics for small systems but predicts deviations for systems with large angular momentum, offering a new perspective for astronomical tests.

Findings

Relational mechanics matches Newtonian mechanics for small subsystems.

Large angular momentum systems deviate from Newtonian predictions in relational mechanics.

Potential for astronomical observations to test relational mechanics theories.

Abstract

Relational mechanics is a gauge theory of classical mechanics whose laws do not govern the motion of individual particles but the evolution of the distances between particles. Its formulation gives a satisfactory answer to Leibniz's and Mach's criticisms of Newton's mechanics: relational mechanics does not rely on the idea of an absolute space. When describing the behavior of small subsystems with respect to the so called "fixed stars", relational mechanics basically agrees with Newtonian mechanics. However, those subsystems having huge angular momenta will deviate from the Newtonian behavior if they are described in the frame of fixed stars. Such subsystems naturally belong to the field of astronomy; they can be used to test the relational theory.