A drifting moon

The other day someone wrote to a local radio program he wanted to know whether the Moon rotates (spins) around it's own axis. The Astronomer said yes of course because the Moon has a day and night cycle.

I wasn't quite sure perhaps it was a cop-out I mean the idea is plausible and tempting. Thinking around the whole thing of our orbital moon and stellar moon rotations it could be that they cancel out and the moon spin-rotation was zero with the moon thus just drifting in space like an asteroid for example.

Note that we need work only with rotational (angular) velocities.

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As workable approximations one can make a simple sketch I have such sketches for my other essays on the moon but I have in mind just a very simple basic free-hand diagram. As simple geometry of the motion just two circles representing the Earth and Moon and then rotations and their direction.

There are two different rotations of the moon- the stellar day or celestial spin and the orbital revolution. Our intuition led us to believe that perhaps they “cancel” thus since the moon stellar day equals its earth-orbit period. This is in fact just wishful thinking because the moon spin and orbital revolution is given as the same, as physically observed and well known. So that the orbital velocity has to be zero if the spin is zero.

From the geometry the moon orbital time equals its stellar day which would mean the resultant rotation has to be zero and the moon would stand still. You can see it from your sketch. Just hangs in the air, since from a geometric viewpoint we see a stationary free-floating moon is impossible.

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I found the result rather surprising and contrary to intuition. As is well known the rotation of the Moon and its Earth orbit revolution are in the same direction and equal.

The solution and answer to the question then simply: No, the Moon does rotate and indeed it is as a lunar stellar day, that is a revolution period of slightly more than 29 Earth days.

Note this reasoning would apply specifically to the Moon although other instances are possible and here it all depends on rotational synchronisation.

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Solar bodies move in elliptical orbits in approximately the same ecliptic plane in space. According to observation they almost all rotate in the same direction. Both around their own axis, normal to the plane, and around the sun. In orbits around the sun and planets and their moons now the ideas should be the same.

But then we wonder about Venus? The odd one out. Venus rotates in the opposite direction around it's axis than all the planets. Perhaps this has to do with the ideas of this essay? And Uranus that is altogether a different story since the axis of the rotation of Uranus is in the ecliptic plane itself, instead of  ninety degrees the axis is parallel to the orbital plane and close to zero.

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There is a place for everyone in mathematics. It is amazing what one can do with only very basic mathematics such as the ancient civilisations had and the first philosophers and mathematicians.