I had hoped to calculate from the JPL ephemeris how the regular 100,000 and 400,000 cycle in the eccentricity of the earth-moon orbit around the sun would also effect the moon-earth orbital eccentricity. Such variations could dramatically change the tidal forces acting on earth and play a leading role in triggering interglacials.
The seminal work on solar system dynamics has been done over decades by the French group at Observatoire de Paris. The latest paper La2010: A new orbital solution for the long term motion of the Earth gives the most accurate orbital parameters for the earth over the last 20 million years. However it also shows just how difficult it is to disentangle the moon’s orbit around the earth from their barycentre orbit around the sun, making it almost impossible to predict any long term changes in tides. Their quoted error in calculating the moon’s eccentricity the last 1 Mya is ±0.03 compared to ±0.00000005 for the earth eccentricity around the sun!
So it is indeed quite possible that major changes in the moon’s orbital parameters will occur as the eccentricity of the Earth-Moon barycentre increases every 100,000 years. However it is almost impossible to calculate how large is the effect.
LA2010 also published some very accurate eccentricity values for the earth over the last 20 million years and into the future. I plotted these out and could not help but notice that the earth’s next 400 y cycle looks almost exactly the same as that which occurred roughly 3 million years ago. That was during an when glaciations followed the 41,000 year obliquity cycle. Exactly the same eccentricity cycle is observed nearly 5 million years ago. There is therefore a larger 2.8 million year super-cycle in the earth’s eccentricity .
The graph below shows the L04 stack sediment data from 3 million years ago (colder is larger dO18). The larger the obliquity the larger are the extremes between the seasons. For large eccentricity the precession term then introduces a significant north-south asymmetry which depends on which particular northern/southern hemispheric season aligns with perihelion.
I am proposing that it was only when the obliquity cycle became insufficient to trigger an interglacial 800,000 years ago that the moon’s resonant tidal effect was needed to complete the job. This was the cause of the switch in phase to a 100,000 year glacial cycle.