As far as I can tell no long term study of lunar eccentricity has been done, so I decided to begin investigating this myself, even though I am a complete novice in astronomical calculations. The key resource for all planetary motions in the solar system is the JPL ephemeris, and the easiest way to access it is through their Horizon web interface. Initially I ran a simulation of the lunar orbit relative to the earth-moon barycentre over a 10 year period beginning in december 2000.
I was amazed to discover that the moon’s orbit around the earth is anything but simple and the quoted parameters are just approximations. The eccentricity of the orbit is changing almost on a daily basis due to complex variations in gravitational effects depending on the relative positions of the sun and the earth, and also Jupiter and Venus. Figure 1 plots the eccentricity from Dec 12 2000 until October 12 2010 on a daily basis. The eccentricity varies in total between the extreme values of 0.026 and 0.077. This is a huge range which can alone change the strength of lunar tides up to a maximum of 20%.
There are at least 2 regular resonances which at first sight seems odd because neither coincide with the orbital period of the moon (27.32days) nor that of the earth (365.25 days). There are also beats in the amplitude. Following this german article, I made a least squares fit shown as the blue curve which reproduces almost perfectly the signal .
eccentricity(d) = 0.55 + 0.014cos(0.198*d + 2.148) + 0.0085cos(0.0305*d +10.565)
This variation in eccentricity changes the perihelion distance from the earth significantly causing large variations in the strength of spring tides on a yearly basis. The eccentricity becomes a maximum when the semi-major axis of the orbit lines up with the sun. This happens every 205.9 days – more than half a year due to the precession of the orbit every 18.6 years. The 31.8 day variation is I think the regular orbital change in distance from the sun.
Horizons only goes back as far as 8000 BC, so in order to investigate paleoclimate effects of eccentricity of lunar orbit around the time of the last interglacial we now need to find another tool.