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

2016/01/06 by Frédéric Pierret, Pierret, Frédéric
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Astrophysics of Galaxies (astro-ph.GA) #Dynamical Systems (math.DS) #Earth and Planetary Astrophysics (astro-ph.EP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Relativity and Gravitational Theory #Scientific Research and Discoveries #astro-ph.EP #astro-ph.GA #math-ph #math.DS #math.MP

paper · pdf · doi:10.48550/arxiv.1601.01130

arxiv created 2016/01/06 · openalex publication_date 2016/01/06 · arxiv updated 2016/01/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Using our mathematical framework developed in \citecresson-pierret_scale called 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 dark matter or modifying Newton's law of dynamics.

Citations

• A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis

Related

• Cosmological Difficulties with Modified Newtonian Dynamics (or: La Fin du MOND?)
• Revised dynamics or dark matter in galactic and extra galactic scales?
• Scale Symmetry and Friction
• Modified Newtonian Dynamics (MOND)
• MOND theory