This document contains comments about the document "Modified Newtonian dynamics" in Wikipedia
• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.
Created in 1983 by Israeli physicist Mordehai Milgrom, the theory's original motivation was to explain the fact that the velocities of stars in galaxies were observed to be larger than expected based on Newtonian mechanics.
The primary reason IMO was that the calculated Galaxy Rotation curve (GRC) based on the observed mass in a Galaxy did not match the observed Galaxy Rotation curve (GRC).
MOND is an example of a class of theories known as modified gravity, and is an alternative to the hypothesis that the dynamics of galaxies are determined by massive, invisible dark matter halos.
The issue is not so much the dynamics of galaxies implying stability issues.
The solution of the discrepancy between calculated and observed GRC can be solved to assume that there is much more invisible mass in the disc of the galaxy. This invisible mass can be ordinary (baryonic matter)

### 1. Overview

While Newton's Laws predict that stellar rotation velocities should decrease with distance from the galactic centre, Rubin and collaborators found instead that they remain almost constant – the rotation curves are said to be "flat".
Newton's Law predicts correctly that stellar rotation velocities decreases with distance assuming that the masses of the stellar objects are point masses compared with the mass at the center. The best example is the solar system.
The stellar velocities that Newton's Law predict is a function of the amount of matter in the disc of a galaxy. Assuming the correct matter distribution it is each to calculate "flat" curves using Newton's Law.
This observation necessitates at least one of the following:
1) There exists in galaxies large quantities of unseen matter which boosts the stars' velocities beyond what would be expected on the basis of the visible mass alone, or 2) Newton's Laws do not apply to galaxies.
The former leads to the dark matter hypothesis; the latter leads to MOND.
The former should first of all lead to a much better investigation how much baryonic matter there before assuming non-baryonic matter which is also invisible.
This baryonic matter can be in the form of planet sized objects and smaller which can fill all outer space i.e the space in between the stars.
The basic premise of MOND is that while Newton's laws have been extensively tested in high-acceleration environments (in the Solar System and on Earth), they have not been verified for objects with extremely low acceleration, such as stars in the outer parts of galaxies.
First of all Newton's Law has been tested for the planets in our Solar system. It can be tested for all binary star systems assuming that the masses can be calculated based on visibility or other means. The same for the stars which circulate around the BH in the center of our galaxy.
To test MOND or Newton, based on stars in the outer parts of galaxies, encompasses the same problems.
This law, the keystone of MOND, is chosen to reduce to the Newtonian result at high acceleration but lead to different ("deep-MOND") behaviour at low acceleration:
FN = m * u(a/a0) * a
The issue is the function u(a/a0) with a0 being a constant.
Two common choices are:
u(a/a0) = a / (a + a0) ("Simple interpolating function")
and
u(a/a0) = sqrt( a^2 / (a^2 + a0^2) ("Standard interpolating function")
The reason why there are two choices is not clear. The differences are minimal.
• When a is large (a0 is small) u(a/a0) reduces to 1 and FN becomes: FN = m * a
This is the same for both functions. This is the standard Newton Force.
• When a is small u(a/a0) reduces to a/a0 and FN becomes: FN = m * (a/a0) * a
That means Newton force at large distances becomes smaller and and the objects at large distances are rejected. This is the same for both functions. The result is a flat curve.
• when a = a0 u(a/a0) becomes 0.5 and sqrt(0.5) = 0.7.
That means in the simple case you get FN = 0.5 * m * a.
In the standard case you get FN = 0.7 * m * a
In both cases Newton's Force FN becomes smaller.
Milgrom's law can be interpreted in two different ways. etc. In this case, the modified dynamics would apply not only to gravitational phenomena, but also those generated by other forces, for example electromagnetism.
When charged objects are included the extra forces should be handled separately for each object individually. They can not be used to modify a law in general.
By itself, Milgrom's law is not a complete and self-contained physical theory,
That is correct.
Its status within a coherent non-relativistic theory of MOND is akin to Kepler's Third Law within Newtonian mechanics;
It is not. Kepler's Third Law is a logical conclusion using Newton's Law. MOND as such is not.
Proponents of MOND emphasize predictions made on galaxy scales (where MOND enjoys its most notable successes) and believe that a cosmological model consistent with galaxy dynamics has yet to be discovered; proponents of ?CDM require high levels of cosmological accuracy (which concordance cosmology provides) and argue that a resolution of galaxy-scale issues will follow from a better understanding of the complicated baryonic astrophysics underlying galaxy formation.
The ending part of this sentence is the road to follow: baryonic matter

### 2 Observational evidence for MOND

Since MOND was specifically designed to produce flat rotation curves, these do not constitute evidence for the theory.
With MOND all rotation curves become flat. They never go to lower speeds at large distances. This is a major problem with MOND
Many of these came to light after the publication of Milgrom's original papers and are difficult to explain using the alternative dark matter hypothesis.
The dark matter hypothesis may be has its own problems.
The issue is that for each GRC it is possible to calculate the appropiate mass distribution that causes this. The problem is that all this mass may be is not observed. In these cases we speak of a missing matter problem which can either be baryonic, non baryonic or both. From a simulation point of view it does not matter because both follow Newton's Law. From a physical point of view it makes a large difference.

### 4. The external field effect

In Newtonian mechanics, an object's acceleration can be found as the vector sum of the acceleration due to each of the individual forces acting on it.
That is correct. This makes a simulation using Newton's Law simple. See also Reflection 1

### Reflection

• For a document to study the issues involved with MOND please study this:MOND - What is involved
• In order to simulate MOND I have written a Visual Basic Program, which demonstrates the issues involved. Please select. VB Gal MOND operation

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Created: 20 September 2016

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