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 demonstration 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 a 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 demonstrated 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.

SUPPLEMENT

Although the demonstration is self-sufficient, these supplementary sections have been added to facilitate discussion on a highly controversial topic.

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, and 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 must rotate on its axis to keep the same face toward Earth. They overlook that such a claim requires changing conventions, and therefore changing geometry.

If we retain EG, we must also retain classical mechanics (see S1B). 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 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.

To save SM in EG, we would have to adopt the Moon as the galactic reference frame. We can assert that such a folly will never occur. Therefore SM does not exist in EG.

S2C — Relativity does not rescue SM

EG does not account for General Relativity. While a pseudo-Riemannian geometry does, its effects in the solar system are far too small to transform an NSM into an SM.

S2D — Conclusion

There is no geometry compatible with SM. We can conclude that SM has no reality.

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 follows from the correct interpretation of that model. This is why D4 follows directly from D3.

If the model disagrees with reality, reality prevails. One must then either find a new model consistent with both reality and our conventions, or revise the conventions themselves.

S3A1 — No valid SM model

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

S3B — The standard model

S3B1 — Unicity of the model

All known representations reduce to the standard model presented in 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 — “Justifications” of SM

We can identify in literature three “justifications” fo SM: the Fixed Direction Convention (FDC), synchronous rotation and stellar rotation. The quotation marks emphasize that all three, like SM, are incompatible with EG.

The most frequently invoked is, by far, synchronous rotation. However, we will see that the primary one is FDC, as it alone can claim to be a cause of SM. Moreover, it is the only one that does not betray logic. We will also see that it is the only one that would remain, at least implicitly, if NSM were to prevail.

S4A — The Fixed Direction Convention (FDC)

S4A1 — Definition

Let us define the following convention: “a planet rotates on its axis relative to a fixed direction provided by a distant star” as the Fixed Direction Convention (FDC).

S4A2 — Incompatibility with EG

FDC allows one to claim that the disk of the standard model is spinning. However, the opposite is demonstrated in D3. According to S1A, FDC is incompatible with EG. If FDC derives from Mach’s principle, then Mach’s principle cannot apply in the Solar System for the same reason.

S4A3 — Rotation periods

Sidereal rotation periods of celestial objects in the solar system are measured relative to a distant star, therefore using FDC, a non-Euclidean method.
Synodic rotation periods are measured relative to the Sun using an Euclidean method.
If we consider that the EG can represent reality while the FDC cannot, we can say that the former are fictitious and the latter real.

S4A4— Spin-orbit resonances

Spin-orbit resonances are traditionally identified by ns:no, where ns is the number of spins completed in no orbits. For consistency, the number of spins is counted as in the case of the Moon, by adding one false spin to each orbit. So the traditional spin-orbit catalog bases on FDC, it is not euclidean.
To convert it to an Euclidean catalog, one would simply subtract one spin per orbit, resulting in (ns-no):no. This is how Mercury would change from a 3:2 to a 1:2 resonance.

S4A5— The two traditional catalogs

Though they are not euclidean, the traditional catalogs of sidereal rotation periods (see S4A3) and of spin-orbit resonances (see S4A4) would probably survive in NSM, just as Celsius and Fahrenheit survived Kelvin.

S4B — Synchronous rotation

S4B1 — uselessness

Synchronous rotation is the most common argument for SM. However, NSM excludes it by definition, since it requires at least two rotations. The concept therefore becomes unnecessary within NSM.

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

S4B2 — Editorial consequences

If NSM is acknowledged, the eradication of synchronous rotation will require significant revisions, especially in school textbooks.

S4C — Stellar rotation

S4C1 — Misinterpretation

Some argue that stellar motion observed from the Moon proves axial rotation. In fact, the Moon’s revolution around Earth is sufficient to produce this effect.

This misconception appears in demonstrations such as the “two waltzers” or Hubert Reeves’ example (video). These interpretations conflict with classical mechanics, which forbids rotation around multiple parallel axes.

S5 — Mental experiments

Like the one we just saw, many common explanations are misinterpretations of valid models. They rely on intuition rather than geometry.

These misconceptions lead to persistent debates where intuitive arguments override rigorous reasoning.

S5A — A disturbing experiment

Bringing the Moon closer to Earth creates the illusion of increasing rotation. As long as the centers remain distinct, the effect is purely visual. When they merge, the orbit disappears, invalidating the interpretation.

S6 — Mechanics

S6A — Gyroscope test

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

S6B — Libration in NSM

In NSM, libration is explained by mechanics rather than kinematics. It may result from tidal locking (see reference) and a tumble effect due to mass asymmetry.

The Libration page presents a simulation of the longitudinal libration, allowing to confirm in addition NSM (using this time Newtonian mechanics instead of geometry).

S7 — What next?

Much remains to be done to address SM: to formally acknowledge its non-existence, along with the uselessness of synchronous rotation, to determine a policy for the EG spin-orbit catalog (see S4A4), to ask historians to trace its origin (Cassini?), to ask epistemologists to identify its primary “justification” (Mach’s principle, circular translation, FDC?) and the reasons for its remarkable longevity, etc.

FAQ

EG = Euclidean geometry
SM = Spinning Moon
NSM = Non-Spinning Moon
FDC = Fixed Direction Convention

FAQ8 — Why the absence of absolute space cannot rescue SM?
See S2A.

FAQ9 — Why Relativity cannot rescue SM?
See S2C.

FAQ10 — Can any argument rescue SM?
No. See S2D.

FAQ11 — Is there a valid model of a Moon rotating on itself?
Not within EG . See S3A1.

FAQ12 — Why FDC cannot rescue SM?
See S4A2.

FAQ13 — Is Mercury in a 3:2 spin-orbit resonance with the Sun ?
Yes in the traditional FDC catalog, no in an EG one, in which it would turn into 1:2. See S4A3.

FAQ14 — Could FDC survive in NSM?
Yes, due to its implication in two traditional catalogs. See S4A5.

FAQ15 — Why synchronous rotation cannot rescue SM?
Because it does not exist. See S4B1.

FAQ16 — Does an astronaut on the Moon see the stars rotating?
Yes, but this results from the Moon’s revolution around the Earth, not from any axial rotation. See S4C1.

FAQ17 — How can the Moon’s longitudinal libration be explained in NSM?
By tidal effect and tumbling effect, the latter being due to mass asymmetry. See S6B.

Gilbert Vidal — retired engineer (France)