Galaxies as Rotating Buckets - a Hypothesis on the Gravitational Constant Based on Mach's Principle

TL;DR

This paper proposes a novel hypothesis linking the gravitational constant to the rotation of galaxies, aiming to explain flat galaxy rotation curves without dark matter by modifying Newton's law based on Mach's principle.

Contribution

It introduces a functional dependence of G on galaxy properties, providing a quantitative framework inspired by Mach's critique of Newton and suggesting testable predictions.

Findings

Modified G explains flat galaxy rotation curves without dark matter

Spatial variation of G is proposed based on galaxy rotation parameters

Potential observational tests for the hypothesis are discussed

Abstract

According to Mach's principle inertia has its reason in the presence of all masses in the universe. Despite there is a lot of sympathy for this plausible idea, only a few quantitative frameworks have been proposed to test it. In this paper a tentative theory is given which is based on Mach's critisism on Newton's rotating bucket. Taking this criticism seriously, one is led to the hypothesis that the rotation of our galaxy is the reason for gravitation. Concretely, a functional dependence of the gravitational constant on the size, mass and angular momentum of the milky way is proposed that leads to a spatial, but not to a temporal variation of G. Since Newton's inverse-square law is modified, flat rotation curves of galaxies can be explained that usually need the postulate of dark matter. While the consequences for stellar evolution are discussed briefly, a couple of further observational coincidences are noted and possible experimental tests are proposed.