Quick rotational motion question

[Sarda112]

We all know that the Moon rotates around the Earth, and the Earth also rotates to a lesser extent around the Moon. It is also true that the center of this rotation is the center of the Earth. If this is true, however, what does the Moon's path look like to someone looking from the North Pole?

Just imagining it in my head, I would think that the Moon would not appear to be moving but I'm not 100% sure. Anyone have any ideas?

 

[pixel01]

Because the orbiting plane of the moon is not the same with the equatorial plane of the Earth but about 5 degrees inclined, so you may see it moving along the horizon for some time and other times, it disappears below the horizon.

 

[belliott4488]

Okay, one thing at a time ...

First, and this is a very small point, "rotation" is usually used to describe motion about an axis running through a body, so the Moon rotates about its own center of mass. On the other hand it revolves around the Earth.

Next, it is only an approximation to say that the Moon revolves about the Earth, especially if you say that the center of revolution is the center of the Earth. This would be true only if the mass of the Moon were negligible compared to the mass of the Earth, which is only very approximately true.

What is correct to say is that both the Moon and the Earth revolve about their common center of mass. This point is located on the line running between their respective centers of mass. The distance from the Earth's COM to this point has the same ratio as the distance from the Moon's COM, as the ratio of the Moon's mass to the Earth's mass. IOW, it's pretty close to the center of the Earth but is not exactly there.

As for what all this would look like to an observer at the North Pole ... well, do you mean "at some distance X above the North Pole", or literally on the North Pole? (It sounds as if you meant the latter, which is what I'll assume.) Also, are you considering your observer to be fixed on the Earth, i.e. so that he rotates with the Earth in its daily rotation? In that case, I'd say he sees the Moon move East to West close to the horizon (close, since the plane of the Moon's orbit does not coincide with the Earth's equatorial plane), completing almost one complete orbit per day. "Almost", because he'd also observe the Moon's monthly motion as it orbits the Earth, so that each day he sees it a few degrees East of where it was 24 hrs. earlier.

 

[pixel01]

How'd you define the East or West standing at the North Pole?

 

[belliott4488]

Looking at the horizon, East is to the left, and West is to the right - pretty much the way it works any time you look to the South.