Scale dynamical origin of modification or addition of potential in mechanics. A possible framework for the MOND theory and the dark matter

TL;DR

This paper introduces a scale dynamics framework to reinterpret potential modifications in mechanics, providing a possible explanation for galactic rotation curves without dark matter or altering Newtonian laws.

Contribution

It presents a novel mathematical approach to potential modifications in mechanics, offering insights into galactic dynamics and the MOND theory.

Findings

Velocity of orbiting body remains constant in the two-body problem

Potential modifications can explain flat galaxy rotation curves

No need for dark matter or law modifications in this framework

Abstract

Using our mathematical framework developed in \cite{cresson-pierret_scale} called \emph{scale dynamics}, we propose in this paper a new way of interpreting the problem of adding or modifying potentials in mechanics and specifically in galactic dynamics. An application is done for the two-body problem with a Keplerian potential showing that the velocity of the orbiting body is constant. This would explain the observed phenomenon in the flat rotation curves of galaxies without adding \emph{dark matter} or modifying Newton's law of dynamics.