Modified inertia as nonconservative Newtonian dynamics

Abstract

Modified Newtonian dynamics by Milgrom is a paradigm for explaining the rotation curves of spiral galaxies and various other large scale structures. This paradigm includes several different theories. Here we present Milgrom's modifed inertia (MI) theory in terms of a simple and tractable nonconservative Newtonian dynamics, which is useful in obtaining observable predictions of MI. It is found that: 1) Modified inertia theory is equivalent to a Newtonian theory, with a nonconservative gravitational field, and dark matter density; 2) The tidal force in the equivalent Newtonian dynamics is nonconservative, and its effect on a binary system in free fall in the gravitational field of a spheroid is addressed. We also discuss attempts to restore conservations in MI.