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This is very interesting. It could be argued that we really don't observe any of the moon's true motion. We don't observe the moon's axial rotation, even though we know that it happens. The swaying of the moon by libration is an apparent motion and not a true motion. This libration has to do with things like the moon's elliptical orbit around the earth, and the fact that its rotational velocity is just about constant. There is another libration that is related to the eccentricities of the moon's orbit relative to the earth's. The moon appears to rise in the east and set in the west, as does the sun, but this orbital motion is apparent and not true. The moon is orbiting the earth in the other direction. It appears to rise in the east and set in the west only because of the earth's very fast axial rotation. The earth rotates once each day, and the moon orbits the earth once in a lunar cycle. This means that the moon's true orbital motion around the earth can be seen only indirectly.

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