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INTRODUCTION

The question of whether the Moon rotates on its own axis is usually answered within the framework of the Spinning Moon (SM). This article examines the opposite conception, the Non‑Spinning Moon (NSM), using only Euclidean Geometry (EG) and the conventions that make geometric reasoning possible.

The demonstration begins by establishing the axiomatic framework, then applies it to the standard geometric model of the Earth–Moon system. Once this model is interpreted strictly within EG, the conclusion follows directly: the Moon does not rotate on its axis.

The complementary sections clarify the logical, geometric, and physical implications of this result, and explain why several familiar explanations are incompatible with EG.

 

DEFINITIONS

We assume that the expressions “turns on itself”, “rotates around its axis”, and “spins” are equivalent. We also assume that the Moon’s axis is unique, passes through its center, is perpendicular to the orbital plane, and that alternating motions such as librations are not part of the definition of axial rotation.

The acronym SM (Spinning Moon) designates the conception in which the Moon rotates on its own axis.
The acronym NSM (Non‑Spinning Moon) designates the opposite conception, in which the Moon does not rotate on its axis.

In SM, the Moon undergoes two rotations: one around the Earth, and one around its axis.
In NSM, the Moon undergoes only one rotation: the orbital rotation around the Earth.

The acronym EG (Euclidean Geometry) designates all geometry built on Euclid’s five axioms.

 

COMPLEMENTS

C1 — CONSISTENCY

C1A — Internal consistency

As long as we remain within a consistent axiomatic set, any demonstrated property cannot be refuted elsewhere.

C1B — The Euclidean foundation

Euclidean Geometry (EG) underlies all classical spatial sciences that appeared after Euclid: analytic geometry, which links EG to algebra (17 centuries later), kinematics, which introduces time, classical mechanics, which introduces force. Euclid’s five axioms guarantee the internal consistency of this entire structure.

C1C — Consequence for NSM

From C1A and C1B, we deduce that since NSM is demonstrated within EG, no theory or experiment claiming to respect EG can legitimately refute NSM, however well‑known it may be.

C1D — Incompatibility of FDC with EG

We will see in C4A that the Fixed Direction Convention (FDC) is incompatible with EG.

C2 — ABSOLUTE SPACE

C2A — Symmetry of descriptions

The absence of absolute space allows us to say “the Earth revolves around the Moon” as legitimately as “the Moon revolves around the Earth.” Some use this symmetry to justify SM, arguing that, in the first case, the Moon has to rotate on its axis to keep the same face toward Earth. They forget that such a claim requires changing conventions, and therefore changing geometry. Indeed, if we retain EG we have to retain classical mechanics (see C1B). Now, an Earth launched at 980 m/s at 406,000 km from the Moon will not begin to revolve around it; given its mass, it will move in a straight line.

C2B — The non‑existent new geometry

The “new geometry” implicitly required by SM does not exist. Even if invented, it would be unusable for humans because, as Henri Poincaré pointed out, EG formalizes our perception of space in the simplest and most convenient way. Any alternative geometry would make calculations inextricably complex.

C2C — Relativity does not rescue SM

C3 — THE MODEL

C3A — THE MODEL IS THE JUDGE

The choice between NSM and SM can only be made by reasoning about a model.
The correct conception of the Moon is the one that results from the correct interpretation of the chosen model.
This is why, in the demonstration, D4 follows directly from D3.

Of course, If the model disagrees with reality, reality prevails; but then, one must either find another model consistent with both reality and our conventions, or change the conventions themselves.

C3A1 — NO VALID SM MODEL

There exists no model of SM that satisfies both observation (the three aligned points) and EG.

C3B — THE STANDARD MODEL

C3B1 — UNICITY OF THE MODEL

All known representations of the model addressing our subject reduce to the standard model presented in the article “Disk Rotation”.

C3B2 — JUSTIFICATION OF THE MODEL

The standard model represents the Moon as seen from celestial north in a geocentric reference frame.
Using heliocentric or galactic frames would complicate the model unnecessarily, since the Sun’s influence on Earth or the Galaxy’s influence on the Sun are too weak to change NSM into SM.

C4 — THE THREE OTHER DOGMAS

The main dogma, which is SM, relies on three other ones:
the Fixed Direction Convention (FDC),
synchronous rotation,
stellar rotation.

All three are incompatible with EG, just like SM.

C4A — THE FIXED DIRECTION CONVENTION (FDC)

C4A1 — DEFINITION

Let’s call the following convention FDC: “a planet rotates on its axis relative to a fixed direction provided by a star”.

C4A2 — INCOMPATIBILITY WITH EG

FDC allows to justify that the disk of the standard model is spinning. It is demonstrated the opposite in D3. According to C1A, FDC is incompatible with EG for reason of inconcistancy.
If FDC derives from Mach’s principle, then Mach’s principle cannot apply in the Solar System for the same reason.

C4A3 — CONSEQUENCES OF ABANDONING FDC

In SM, determining the rotation of celestial bodies in the Solar System relies primarily on adherence to the FDC. This justifies the link SM/FDC. By symmetry, we can introduce the link NSM/EG.

In theory:
In NSM/EG, since the FDC is rejected, sidereal rotations would be ignored and only synodic rotations would be retained (possibly corrected for the Sun’s galactic rotation).
Orbital‑resonance notation would also change.
In SM/FDC, ns:no denotes the number of spins per orbit.
In NSM/EG, one spin must be subtracted per orbit, giving (ns–no):no.
For example, Mercury would go from 3:2 to 1:2.

In practice:
Just as the Kelvin scale has not replaced Celsius or Fahrenheit, it is unlikely that NSM/EG will replace SM/FDC.

C4B — SYNCHRONOUS ROTATION

C4B1 — LOGICAL IMPOSSIBILITY

Synchronous rotation is the most frequently used argument for SM.
However, NSM immediately excludes synchronous rotation because its very definition requires at least two rotations. Synchronous rotation must therefore be eradicated.

Moreover, synchronous rotation could only ever be a consequence, not a cause, of SM.
Using it to justify SM is a logical fallacy (circular reasoning) to be seen very often.

C4B2 — EDITORIAL CONSEQUENCES

Eradicating synchronous rotation will require countless editorial changes.
It must be replaced by NSM in all cases (especially in textbooks) where it is used to justify the far side of the Moon.

C4C — STELLAR ROTATION

C4C1 — MISINTERPRETATION

Some justify SM by noting that an astronaut on the Moon sees the stars rotate.
But the Moon does not need to rotate on its axis for this effect: its revolution around Earth is sufficient.
Stellar rotation is not evidence of SM.

C4C2 — THE TWO WALTZERS

This error appears in many mental experiments such as the “two waltzers” or Hubert Reeves’ demonstration (https://www.youtube.com/watch?v=RODh1gte1lU). In this video, two figures spin with arms outstretched, holding hands.
From the fact that they see their surroundings rotate, the conclusion is drawn that they rotate on their axis.
This is easily contradicted: classical mechanics forbids a rigid body from rotating around three parallel axes.

C5 — MENTAL EXPERIMENTS

C5A — THE LIMITS OF MENTAL EXPERIMENTS

Aside from the three dogmas mentioned above, the “demonstrations” of astronomy commonly found on the Internet, are false interpretations of most often correct models or mental experiments. The one mentionned in C4C2 is only one of them.

These lead to endless debates in which professionals prevail over amateurs only because they rely on the three dogmas, most often the synchronous rotation.
They systematically ignore scientific tools; these arguments take us back to the millennia before Euclid.

C5B — A DISTURBING EXPERIMENT

The most troubling mental experiment consists in bringing the Moon closer to Earth.
As the distance decreases, the Moon appears to rotate more and more.
In a first phase, as long as the centers remain distinct, the experiment is valid (but its interpretation remains false). The effect is simply a reinforcement of the optical illusion.
In a second phase a subtle limiting transition occurs. When the centers merge, one could indeed say that the Moon rotates on its axis.
But at that very moment the orbit disappears — and with it the validity of the experiment.

C6 — MECHANICS

C6A — GYROSCOPE TEST

If a sufficiently sensitive gyroscope is ever installed on the Moon’s equator, it will detect no radial acceleration due to any continuous rotation of the Moon on its axis.
It will detect only the acceleration due to the Moon’s revolution around Earth.
Such an experiment would force us to abandon SM.
Why wait for such a predictable result before reacting?

C6B — LIBRATION IN NSM

In NSM, longitudinal libration is not explained by kinematics but by mechanics.
It results from two effects:
1/ The tidal effect, perfectly explained on
https://en.wikipedia.org/wiki/Tidal_locking
2/ A tumbling effect, due to a slight mass imbalance favoring the visible hemisphere of the Moon.

The Libration page on this site presents a simulation of libration in the textbook case where the first effect is assumed to be zero and the second is caused by a high density litle spot located at point N. In the specific case where the high density litle spot is zero, the program also allows us to prove NSM again, this time using Newtonian mechanics instead of geometry.