# Moon rotation

## Main Question or Discussion Point

Moon "rotation"

The experiment below is to demonstrate that the moon does not rotate on its "internal" axis as it orbits earth.

Hold an orange (the moon) with an X marked on it straight out from you in the palm of your hand with the X pointing toward you. Then, while standing in the same spot, rotate your body (earth) in a complete circle to simulate the moon making one orbit of earth.

From the perspective of earth, the moon will have made one complete orbit of earth and the same side of the moon will always face earth. And from the perspective of a distant observer, they would see all sides of the moon.

Since the observations of the orange from earth, and from a distant point, match what would be observed of our actual moon without having to rotate the orange on its internal axis during its orbit, then the moon does not rotate on its internal axis either. If it did, from the perspective of earth, all sides of the moon would be seen from earth, just as all sides of the orange would be seen if it had been rotated one time on its internal axis during its orbit of earth.

Is there anything wrong with this demonstration or the conclusion?

## Answers and Replies

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D H
Staff Emeritus
Science Advisor
Is there anything wrong with this demonstration or the conclusion?
You disproved your own conjecture right here:

From the perspective of earth, the moon will have made one complete orbit of earth and the same side of the moon will always face earth. And from the perspective of a distant observer, they would see all sides of the moon.
You have implicitly defined a reference frame, the Earth-Moon frame. This is a rotating reference frame. You are correct that, in this frame, the Moon does not rotate. The "distant observer" has a different point of view. It is called an inertial reference frame. From the perspective of an inertial reference frame, the Moon is rotating.

russ_watters
Mentor
And from the perspective of a distant observer, they would see all sides of the moon.

Since the observations of the orange from earth, and from a distant point, match what would be observed of our actual moon without having to rotate the orange on its internal axis during its orbit, then the moon does not rotate on its internal axis either.

Is there anything wrong with this demonstration or the conclusion?
Yes: how can a distant observer see all sides of the moon if it isn't rotating wrt the distant observer?

It is true, though (and kinda pointless) to say that a rotating observer would see the moon as not rotating.

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The 'moon does not rotate on its "internal" axis' because the rotation defines the axis. The axis does not define the rotation as you imply here. Aside from this point you weigh more at the moons poles than you do at its equator due to centrifugal force.

You are mistaking an issue of Galilean relativity with proof.
http://en.wikipedia.org/wiki/Galilean_relativity

You disproved your own conjecture right here:

You have implicitly defined a reference frame, the Earth-Moon frame. This is a rotating reference frame. You are correct that, in this frame, the Moon does not rotate. The "distant observer" has a different point of view. It is called an inertial reference frame. From the perspective of an inertial reference frame, the Moon is rotating.

So which observer, the one on earth, or the distant observer, is actually correct about whether the moon is rotating on its internal axis or not as it orbits earth?

Yes: how can a distant observer see all sides of the moon if it isn't rotating wrt the distant observer?

Since the distant observer did see all sides of the orange, are you saying the orange did rotate on its internal axis during its orbit in my example?

The 'moon does not rotate on its "internal" axis' because the rotation defines the axis. The axis does not define the rotation as you imply here. Aside from this point you weigh more at the moons poles than you do at its equator due to centrifugal force.

You are mistaking an issue of Galilean relativity with proof.
http://en.wikipedia.org/wiki/Galilean_relativity

Just to be clear, are you saying the moon does not rotate on its internal axis?

D H
Staff Emeritus
Science Advisor
With respect to any inertial frame, the moon does rotate about its own axis. Motion, including rotational motion, is relative to a reference frame in which an observer is fixed. However, it is motion relative to some inertial frame that makes the most sense.

Look at it this way: From the perspective of a geosynchronous satellite, the Earth is not rotating. Does that prove the Earth is not rotating?

russ_watters
Mentor
Since the distant observer did see all sides of the orange, are you saying the orange did rotate on its internal axis during its orbit in my example?
Yes.
Just to be clear, are you saying the moon does not rotate on its internal axis?
No, what he's saying is that if you define the reference frame to be one that rotates with the moon, then the moon is not rotating with respect to it.

Think of it this way: stand up and spin around a few times. Did you spin or did the room spin? If you really want the trouble, you can say the room spun, but then doing physics calculations on it might be difficult (at best). But to anyone in the room watching you, the answer is unequivocable: you spun.

Just to be clear, are you saying the moon does not rotate on its internal axis?
No. The moon does in fact rotate. The variation of test mass weights at different points on the surface proves it without even considering other bodies. Russ's explaination was as good as any.

D H
Staff Emeritus
Science Advisor
Since the distant observer did see all sides of the orange, are you saying the orange did rotate on its internal axis during its orbit in my example?
Just as Russ said, yes.

Timoothy, you are a bit too hung up on this "external axis of rotation" thing. Suppose you have an object that is translating and rotating about some axis. Now consider another axis of rotation parallel to but displaced from the first. From a mathematical perspective, the object can be equally viewed as translating and rotating about this displaced axis as well. Where you choose to place the axis of rotation doesn't really matter. From a mathematical perspective, this is just an argument over semantics.

From a physics perspective, the choice of axis of rotation does matter. One choice will lead to a much simpler description of the behavior than any other. In the case of the Moon, the simplest description arises from describing rotation as about an axis passing through the Moon's center of mass. This viewpoint effectively decouples the translational and rotational aspects of the Moon's motion. The linear acceleration of the Moon's center of mass is exactly the same as if all of the external forces were acting on a point mass located at the Moon's center of mass, and the angular acceleration is described by Euler's equations.