This is the 4th of June 2022 edition

Introduction

In this page entitled “The Yellow Scale” it is proved that the Moon does not turn on itself. The demonstration is based on Euclidean geometry on the one hand and observation on the other hand. It fits entirely in chapter 1 “Demonstration”.

Astronomers and mathematicians affirm on the contrary that the Moon turns on itself. They rely on the following convention: “when we say that a star turns on itself, it is relative to a sufficiently fixed direction”.
The application of this convention leads to a conflict with Euclidean geometry.

Henri Poincaré teaches us that no convention is better than another because absolute space does not exist. The choice must be guided by practical considerations, taking into account what has been learned and leading to the simplest possible application results. He argued that one could very well consider that the sun revolves around the Earth at the cost of inextricable complications. He then had to fight against cumbersome supporters: the Calotins who found there a strong argument in favor of the Church against Galileo.

In our case, it is clear that it is impossible to adopt a convention that conflicts with Euclidean geometry. It is indeed on this last that we have based our conception of space around us for thousands of years. It is the basis of all classical mechanics. Moreover, astronomers have never proposed another geometry to deal with the case that interests us.
In the end we have to admit that the Moon does not turn on itself.
Let us note moreover that the change brings a simplification due to the fact that the synchronous rotation disappears, which concerns not only the Moon but also many other stars of the solar system (see chapter 3).

Why has an error that is so easily demonstrated formally been able to persist for more than a century?
I try to bring in chapter 4 “Epistemology” some elements of answer which hardly begin the vast field of this question.

The page “A yellow libration” confirms by classical mechanics what we have obtained by geometry.
It is a simulation in Python 3 of the motions of the Moon during a revolution around the Earth in a frame of reference having for origin the center of the Earth. It is then assumed that the reference frame remains motionless or moves in uniform translation in the Galaxy (and not in rotation around the Sun) during a revolution around the Earth. The Earth/Moon system is supposed to be isolated in space but the results of the simulation are not very far from reality. For example, for the characteristics of the orbit they give a revolution of 27.9 days instead of 27.3. Regarding the rotation we can find an acceptable result only in the case where the rotation speed omega is equal to zero. If we assign to omega the value that astronomers give it, we obtain a full face-down object turned towards the Earth after half an orbit! It is difficult to see how taking into account the influence of the rest of the galaxy could provide an acceptable result in this last case.

We can therefore safely make the following prediction: if an accelerometer of sufficient resolution is installed one day on the Moon’s equator, it will not detect any radial acceleration due to a continuous rotation of the Moon on itself. Why wait for such a predictable event to react?

There are dozens of sites on the Internet that aim to prove that the Moon rotates on itself. Their false demonstration is most often presented in the form of an “empirical” mental experiment (I mean that it does not require any scientific tool such as geometry or mechanics; the quotation marks are there to warn that philosophers could contest this definition). The axes or centers of rotation are rarely defined. I will try to refute the ones you will submit to me in the “Empiricism” blog. I’ll start the pump by treating the classic example of the two waltzers.

A SOC (Statement Of Commitment) is a particularly important statement that summarizes a given point.
Refuting a SOC would result in the site being closed.

1 Demonstration

1.1 Geometry

The notations are those of figure ys1.
Let there be a line segment EM in the plane and a point B located between E and M.

A/ Let us rotate the segment EM in the plane by an angle a around the point E.
Let us dedicate the index “₀” to the initial position of the elements of the figure and “₁” to their final position.
This is how we go from E, M₀ and B₀ to E, M₁ and B₁.

B/ In a rotation a line segment turns into a line segment. If the point B₀ is on the segment EM₀ then its counterpart B₁ will be on the segment EM₁.
C/ Conversely, if the points E, M and B remain aligned then the segment B₁M₁ is deduced from the segment B₀M₀ by a rotation of center E and angle a.
D/ Any further rotation would change the position of point B₁ or point M₁.
E/ So let us remember in particular that the segment MB does not rotate around the point M. One might add that it has no more reason to rotate around the point M than it has to rotate around the point B.

F/ Now let us consider a disk (D) with center M and radius MB, and a point C on its periphery. Suppose that the point C of the disk remains permanently confused with the point B of the segment (this is why C does not appear on the figure ys1).
G/ It follows that the disk remains connected to the segment MB.
H/ In this case, since the segment MB does not rotate around the point M, the disk cannot either. Hence SOC 1.1 (which incidentally is valid for any point on the disk other than point M):

SOC 1.1:
During a rotation in the plane of a disk (D) of center M around a point E, if one of the points of the periphery of the disk (D) remains aligned with the points E and M, then the disk (D) does not rotate on itself.

1.2 Application to the Moon

We recognize in figure ys1 a classical representation of the Moon that we find in all articles dealing with its rotation.
E represents the Earth, M the center of the Moon, B its crater closest to the Earth and (D) the section of the Moon in its orbital plane.

We have known for centuries that the Moon always presents us with the same face, or, to put it differently, the same crater B. We can therefore say that the Earth E, the crater B and the center of the Moon M remain aligned. We deduce that SOC 1.1 applies to the Moon, hence SOC 1.2:

SOC 1.2:
The Moon does not rotate on itself.

2 Refutations

2.1 Emblematic site

Among the many Internet sites dealing with the rotation of the Moon, the site https://en.wikipedia.org/wiki/Tidal_locking will hold our attention particularly.
We can see that the animated figure on the left is a perfect animated replica of the figure ys1 of chapter 1. The center of the fixed disk becomes point E (the Earth); the black part of the Moon becomes point B; the center of the Moon becomes point M. We can see that these three points remain permanently aligned. According to SOC 1.1 this Moon does not rotate on itself.

SOC 2.1
The left moon of the site https://en.wikipedia.org/wiki/Tidal_locking does not rotate on itself.

Note: It would also be shown that the animated figure on the right shows a disk turning on itself in reverse.

2.2 Blog “Empiricism”

See the “Introduction” chapter.

3 Consequences

3.1 Introduction of the PS (phantom spin)

So the Moon does not rotate on itself.
A lunar meridian will look like it rotates around the center of the Moon when in fact it has only one center of rotation: the Earth.
This false rotation of the Moon which seems to be around its center M will be called PS (phantom spin).
The spin of the Moon is of the PS type, it has no reality: an accelerometer of sufficient sensitivity placed on its equator would show only one component, that due to its orbit, and none due to any spin.

A real spin (continuous rotation on itself) will be called RS (real spin).
When the Earth makes 1 orbit around the Sun it makes 365.25 RS and 1 PS. An ultra precise accelerometer placed on its equator would show 2 components due to its orbit and to its RS, and none due to its PS.

3.2 Synchronous rotation

How could a rotation be called synchronous if only one rotation is involved?
It is true that the vector that joins the center of the Moon to the Bright crater makes in galactic space 1 turn in each orbit. But this rotation is not around the center of the satellite. It takes place around the Earth. Its only cause is the orbital rotation, it is a PS.

A false interpretation of an observation is by definition a mirage.

SOC 3.2:
The concept of synchronous rotation must be abandoned.

3.3 Orbital Resonance

Traditionally the orbital resonance of a body orbiting another is noted no:ns, no being the number of orbits and ns the number of spins it performs during the orbital resonance.

Unfortunately it includes wrongly in the number ns not only the real spins RS but also the phantom spins PS. The following SOC should be adopted:

SOC 3.3.1:
The traditional notation no:ns of an orbital resonance should be replaced by no:(ns-no).

In particular, it would result in:

SOC 3.3.2:
The Mercury planet does not perform 3 spins in 2 orbits, it performs 1 spin in 2 orbits.

3.4 Textbooks…

As wrong as it is, the white approach does not question any scientific result, Huygens did not miss Titan. But it is still a scientific error which will take time to eradicate. Many changes are to be expected in many areas. In addition to those already mentioned, let us note two of them that it would be good to carry out in the school textbooks:

SOC 3.4.1:
On the Moon an astronaut sees the constellations spinning in the sky. A sentence adding “This proves that the Moon revolves around itself”, or equivalent, should be replaced by “This is because the Moon revolves around the Earth”, or equivalent.

SOC 3.4.2:
The sentence “The hidden side of the Moon is due to synchronous rotation”, or equivalent, should be replaced by “The hidden side of the Moon is due to the fact that the Moon does not rotate around itself”, or equivalent.