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Moon Rotation — Does the Moon Rotate on Its Axis?

Does the Moon rotate on its axis? In standard astronomy, the answer is yes: the Moon is said to rotate once per orbit (Spinning Moon, SM).

This article examines the opposite conception, the Non-Spinning Moon (NSM).

After establishing the necessity of adopting the axiomatic framework of Euclidean geometry (EG), the argument builds on the result obtained in Disk Rotation.

The reasoning is purely geometrical: no forces or dynamics are introduced at this stage. The reference frame is the one implicitly defined by the standard model.

The question can therefore be reformulated as follows: what follows necessarily from the standard model when it is interpreted strictly within Euclidean geometry?

The answer is: the Moon does not rotate on its axis.

DEFINITIONS

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

Recall: 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.

DEMONSTRATION OF THE NSM

D1 — Henri Poincaré might tell us that the choice between NSM and SM depends on the set of conventions we have established. This set necessarily includes the axioms of geometry, in order to make space accessible to mathematical reasoning.

D2 — Given its preeminence in the solar system, the EG is essential for choosing between NSM and SM. Our set of conventions therefore includes (at least) Euclid’s five axioms. We will therefore refer exclusively to the EG.

D3 — As shown in the article Disk Rotation, the disk representing the Moon in the standard model does not rotate on its axis.

D4 — The Moon therefore does not rotate on its axis.

FAQ

Does the Moon rotate?
The standard interpretation says yes, it rotates on itself. This article shows that this interpretation contradicts Euclidean geometry.

Why do we always see the same face?
This is usually explained by synchronous rotation. This explanation is re-examined here (see S4B).

Why does an astronaut on the Moon see the stars rotate?
This is usually explained by Moon rotation on itself. This explanation is re-examined here (see S4C).

Supplements summary

S1 — Consistency

A result established within a consistent axiomatic system cannot be contradicted elsewhere within the same system.

Since NSM is demonstrated within EG, no theory or experiment consistent with EG can refute it.

S2 — Absolute Space

The absence of absolute space allows symmetric descriptions (Earth around Moon / Moon around Earth), but changing interpretation requires changing geometry.

No alternative geometry compatible with human reasoning replaces Euclidean geometry in this context.

S3 — The Model

The correct conception of the Moon follows from the correct interpretation of the model.

There exists no geometrical model of SM that satisfies both observation (alignment of E, M, N) and Euclidean geometry.

S4 — Related Assumptions

SM relies on additional assumptions such as fixed direction, synchronous rotation, and stellar rotation. These are incompatible with EG.

S5 — Mental Experiments

Many common explanations are misinterpretations of correct models. They rely on intuition rather than geometry.

S6 — Mechanics

A sufficiently sensitive gyroscope on the Moon would detect only orbital acceleration, not axial rotation.

SUPPLEMENTS

S1 — CONSISTENCY ************************

S1A — Internal consistency

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

S1B — 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.

S1C — Consequence for NSM

From S1A and S1B, 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.

S1D — Incompatibility of FDC with EG

We will see in S4A that the Fixed Direction Convention (FDC) is incompatible with EG.

S2 — ABSOLUTE SPACE ************************

S2A — 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 S1B). Now, in classical mechanics, 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.

S2B — The non‑existent new geometry

The“new geometry” implicitly required in S2A 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.

S2C — Relativity does not rescue SM

EG does not account for General Relativity. We know of a pseudo-Riemannian geometry that does. But in the solar system, thousands of light-years from the first black hole, its application would lead to corrections to EG that are far too small to change an NSM into an SM.

S3 — THE MODEL ************************

S3A — 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.

S3A1 — No valid sm model

There exists no geometrical model of SM that satisfies both observation (the alignment of E, M, and N) and Euclidean geometry.

S3B — The standard model

S3B1 — Unicity of the model

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

S3B2 — 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.

S4 — Related Assumptions ************************

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.

S4A — The fixed direct convention (FDC)

S4A1 — DEFINITION

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

S4A2 — 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 S1A, FDC is incompatible with EG for reason of inconsistency.
If FDC derives from Mach’s principle, then Mach’s principle cannot apply in the Solar System for the same reason.

S4A3 — 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 instead of ns: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.

S4B — Synchronous rotation

S4B1 — 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. The concept of synchronous rotation therefore becomes unnecessary within NSM.

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) very often seen in Internet and literature.

S4B2 — 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.

S4C — Stellar rotation

S4C1 — 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.

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.

S5 — 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 mentioned in S4C2 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 (though not to be despised but venerated).

S5A — 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.

S6 — Mechanics ************************

S6A — 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?

S6B — Libration in NSM

In NSM, longitudinal libration is not explained as in SM by kinematics but by mechanics.
It could result from two effects:
1/ The tidal effect, perfectly explained on https://en.wikipedia.org/wiki/Tidal_locking
2/ A pendulum 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 little spot located at point N (Nearest). In the specific case where the high density little spot is zero, the program also allows us to prove NSM again, this time using Newtonian mechanics instead of geometry.