  :It may be true that the Moon's annual path isn't precisely periodic, and isn't precisely a closed curve, and that its center of survature isn't precisely in the Sun-Earth-Moon plane.  But it's close enough.  So let's not get distracted by things that aren't important to the broader discussion.  :I acknowledge, again, that the Godfray and Turner references say the Moon's annual path is concave.  But there are other references that describe it as convex.  I see no reason to believe that the Godfray and Turner references are any more reliable on this point than the other references.  :Terry0051, I'm going to ask you the same questions that I asked Marc Kupper about what your source is for the distinction between convex/concave when looking outward from the inside, and convex/concave when looking inward at the entire system.  But before I ask you all those questions, I'll let Marc respond to the questions I asked him, since he might resolve some of them. -   