Mathematicians, astronomers, teachers,
The Henri Poincaré Mathematics Museum in Paris is inaugurated this Saturday, September 30, 2023.
This is the opportunity for everyone to imagine the answer that the master of conventions would have given to the following question: does the Moon rotate on its axis?
Here is my contribution.
Argument for a non-rotating Moon
Gilbert Vidal, September 30, 2023
We will admit that the expression “to rotate on itself” is equivalent to “to rotate on its axis”, that this axis is unique and perpendicular to the orbital plane and that there is no libration.
The acronym EG (Euclidean Geometry) designates any geometry built on the five axioms of Euclid.
A1/ We have known since Henri Poincaré that the answer yes or no to the question “does the Moon rotate on its axis?” depends on the choice of a set of conventions. This set necessarily includes the axioms of a geometry in order to make space accessible to reasoning.
Given the preeminence of the EG in the solar system, no other geometry can contradict the yes or no answer that the EG will provide to the question asked.
A2/ In a galactic frame of reference the Moon moves in accordance with the following mathematical model: a sphere with center M (Moon) representing the Moon rotates around a point E (Earth) representing the Earth while maintaining the following three points aligned: the point E, the point N (Nearest) representing the crater of the Moon closest to the Earth and the point M.
According to the EG the line segment MN cannot rotate around the point M because its simple rotation around the point E is enough to keep the points M, N and E aligned. A second rotation around point M could only break the alignment. As the segment MN is an integral part of the sphere we deduce that it too simply rotates around point E without rotating on itself.
A3/ It follows from the previous arguments that the Moon does not rotate on its axis.
Comments
1.1/ Nothing prohibits a priori adding the following convention: “when we say that a planet rotates on itself, it is relative to a fixed direction provided by a star”. Unfortunately it is not compatible with the EG because it would contradict argument A2 which is part of the EG. We must therefore reject this convention if we want to maintain the coherence of the set of conventions that we have given ourselves.
1.2/ Riemannian geometry, although more precise, corrects the EG far too little to reverse the response of the latter.
3.1/ For reasons of consistency we cannot refute argument A3 as long as we claim EG, whatever the notoriety and/or the number of arguments (synchronous rotation, fixed direction, absence of absolute space , Mach principle…) or experiments invoked.
3.2/ Synchronous rotation does not exist since only one rotation is involved.
3.3/ The planet Mercury does not make 2 turns in 3 revolutions but 1 turn in 2 revolutions.