Classical analysis of the rotational dynamic of spiral galaxies: Quo Vadis Dark Matter?

TL;DR

This paper uses classical mechanics to model spiral galaxy rotation curves, demonstrating that observed velocities can be explained without invoking dark matter by considering specific matter distributions and galaxy shapes.

Contribution

It provides a classical mechanics-based model for galaxy rotation, challenging the need for dark matter in explaining observed rotational velocities.

Findings

Velocity distribution matches astronomical observations

No dark matter needed to explain rotation curves

Different matter distributions produce similar velocity profiles

Abstract

In this paper we study a stellar dynamic model for the stars' rotational-dynamics, with a distribution of its own mass, rotating around its center with a higher density, like spiral galaxies happen, by means of a classical calculus of the rotation velocities of a particle around its rotational axis, inside a smoothed distribution of matter. The stars are supposed to be particles and their distribution in the galaxy is modelled as a matter distribution inversely proportional to its distance from its center. Two kinds of matter distribution are supposed: one with constant density, and other with radial distribution. Two types of galaxy symmetry are also considered: spherical and oblate ellipsoidal. Using only classical mechanics arguments it is shown that the calculated velocity distribution inside the galaxy is similar to that obtained from astronomical observations, without the necessity of suppose the existence of dark matter or other phenomena.