Lunar Librations II

After my last post on lunar librations, my dissatisfied friend was still dissatisfied. He said:

Okay so my intuition failed me wrt to the major component of lunar librations, but the pictures should still be different since the close one is below the equator and the far one is above it...

My friend is assuming that apogee and perigee correspond with the points at which the moon is furthest from the ecliptic. I had a vague memory that such was not the case, but I couldn't remember the details. A little Googling research today got the answers.

It turns out that the moon's apogee and perigee are not always the place where the moon is the furthest from the ecliptic. There are two phenomena that determine this. One is called "nutation", which is the rotation of the moon's "node line" around the Earth (the node line is an imaginary line drawn between the two points in the moon's orbit where it crosses the ecliptic). The moon's nutation period is 18.60 years, direction to the west. The other phenomenon is the rotation of the "line of Apsides" (the line between the moon's perigee and apogee); it rotates in the opposite direction, once every 8.85 years (reference, more info).

If (big if!) I'm juggling all these phenomena correctly, then the apogee and perigee move with respect to the points at which the moon is the furthest from the ecliptic on a cycle of 18.60 - 8.85 years; in other words, every 9.75 years. So ... once each 9.75 years, my friend's assumption would be correct; in between he'd be wrong to some degree. One interesting consequence of this is that every 9.75 years the maximum longitudinal libration would be coincident with the maximum latitudinal libration. I was unable to confirm this on the web (when the line of Apsides was coincident with the node line).

In the course of researching this, I came across an article that talks about another consequence of lunar librations; one that I had not considered.

Imagine you're an astronaut, and you're standing on the lunar surface. If you ignore librations, the earth is always at the same place in the sky, as a consequence of the moon always "turning the same face" toward the earth. But ... factor in librations, and you get an odd result: the earth, seen from the moon's surface, moves about in a little "box" in the sky. Seen from the lunar surface, the earth appears to be about 2 degrees wide. The box it moves around in is about 15 degrees wide in longitude, and 13 degrees wide in latitude. That's a fairly large motion, one that would be quite evident to a naked-eye observer. From what I know (now!) about the librations, that must be a very complex motion in that box. And to my surprise, I was able to find (on the web) a computed path, illustrated, and that's the picture you see above right.

As usual, click on the picture for a larger view.