Undergrad Is the eccentricity of the lunar orbit constant?

[Orthoceras]

TL;DR

Confusion about a graph in wikipedia

The wikipedia article on Lunar distance contains a confusing graph. The graph seems to suggest that the eccentricity of the lunar orbit is maximal in january and ~july, and minimal in april and ~october. I think the eccentricity should be constant. Is wikipedia right or wrong, or is there some trivial confusion?

Wikipedia legends: The Moon's distance from the Earth in 2014 ...

 

[WernerQH]

I think the eccentricity should be constant.

No, the eccentricity varies between 0.044 and 0.067 during the course of half a year; the value e = 0.0549 is just an average. The cause is the tidal force of the sun on the earth-moon system. When the direction to the sun is aligned with the major axis, the eccentricity is biggest, and smallest when aligned with the minor axis. Since the ellipse is not fixed in space, but rotates once every 8.8479 years, the confusing graph will look different from year to year.

 

[Orodruin]

To build upon that: The elliptical orbit of the Kepler potential is only an exact solution for the Kepler potential. Add any lower order effects (such as the tidal forces from the Sun mentioned above) and you will break that. The only question is by how much.