How does the three-body system (Earth, moon, Sun) work?

[spare ohs]

I have only taken my high school Physics course so excuse me if I don't understand some things right away. I looked at the two stickies and neither seemed to explain my question.

I have been trying to understand why the moon's orbit's apogee moves around Earth over a period of time. The moon's orbit isn't quite an ellipse because of the Sun's gravitational pull. I want to understand how the three bodies (the Sun, moon and Earth) influence each other. I have been told by one person that astro-physicists have yet to understand this and I have been told by someone else that they understand it but are just having a hard time making accurate calculations partly because they have to take into account Einstein's theory of relativity. However, I can't find any articles on the internet that attempt to explain the orbit of the moon in detail and the reasons for the peculiarity in it's orbit.

 

[D H]

I have been told by one person that astro-physicists have yet to understand this

Not true. That person probably read somewhere that three body problem is not soluble. That isn't true. What is true is that the three body does not have a general solution in the elementary functions. So what. Numerical techniques can (and are) employed, and for that matter, numerical techniques would have to be employed even if a solution did exist in the elementary functions.

and I have been told by someone else that they understand it but are just having a hard time making accurate calculations partly because they have to take into account Einstein's theory of relativity.

Also not true. The effects of general relativity are known, and in the case of the Moon, they are exceedingly small. The geodetic precession of the Moon is 19.2 milliarcseconds per year. Written another way, that is 360 degrees per 67.5 million years.

However, I can't find any articles on the internet that attempt to explain the orbit of the moon in detail and the reasons for the peculiarity in it's orbit.

You aren't using the right search terms. Here is one that yields a wealth of information. I won't even be mean and use "let me google that for you".com.

http://www.google.com/search?q=lunar+theory+site:adsabs.harvard.edu

A large number of those entries are in the late 18th century / early 19th century. The key people in the development of this description include E.W. Brown, C.E. Delaunay, G.H. Hill, A.E.H. Love, and G.B. Airy. The description of the Moon's orbit was pretty much complete about 100 years ago. Everything since then is more or less tweaking of an already solid theory.