I'm still working on understanding some of the subtleties of the lunar orbit. We know that the lunar nodes ( where the lunar orbit crosses the plane of the ecliptic ( a cryptic term for the plane of the Earth's orbit.)) shift progressively and complete a cycle in 18.61 years: the period of lunar nodal precession. We also know that the lunar orbit, like most orbits, is not round but more like an ellipse, with a point of closest approach ( perigee ). Of course nothing is simple. The eccentricity varies and the alignment of the major axis also turns with time, taking about 8.85 years to return to the same position. Using Tony's amazing gravity sim to get some data, I have made the following plot of position of the lunar nodes and the argument ( angle ) of periapsis. We see the gradual drift ( precession ) of both of these obital "elements" and a small roughly six month oscillation in each one. The oscillation in the periapsis is modulated by the 8.85 year cycle. Now as far as I can tell, this modulation is due the change in eccentricity. When the lunar obit is more eccentric, there is a greater variability and when is less eccentric ( closest to being circular ) there is a lesser variation. Now I would have thought at first sight that the variation in eccentricty would be due to the pull of the sun. When the major ( long ) axis aligns with the direction of the sun at perihelion, the eccenticity would be greatest. When the minor axis aligns at perihelion, this would tend to make the orbit rounder : less eccentricity. However, the plane of the lunar orbit is inclined by about 5.3 degrees to the ecliptic orbital plane and this as we have seen rotates in 18.61y. So as far, as my mental gymnastics can conceive, the change in eccentricity is not due to the direction of pull of the sun. Now I've tried running the gravsim with the mass of the planets set to zero and the plot is almost identical, so while they may have contributed to pseudo-stable lunar orbit as it is at any point in real time, they do not seem to be a significant player in the 8.85 or 18.61y cycles. So what is changing the eccentricity of the lunar orbit?