I got interested in plotting these because I have discovered that Milankovitch cycles are now being used to calibrate geological time. The Earth's spin and orbit do various sorts of precession, and these add up to make cyclic variations in the amount of sunlight that each place on Earth receives over the course of a year.

In particular, the Earth's eccentricity vector (eccentricity * (perihelion direction)) precesses forward quasi-periodically with periods of 70,000, 170,000, and 300,000 years, while the Earth's orbit north pole precesses backward quasi-periodically with a period of about 70,000 years.

These combined with the Earth's spin precession (period around 25700 years) to produce a vernal-equinox-relative perihelion precession with a period of about 20,000 years and an obliquity variation of about 2 degrees with a period of about 40,000 years. And the Earth's orbit's eccentricity various quasiperiodically from nearly circular to 0.06 with periods of about 100,000 and 400.000 years.

To date, these cycles have a good fit to the variations of the Pleistocene ice ages, but there is evidence of their effects in previous times, like Breakthrough Made in Dating of the Geological Record about correlating Miocene sediment variations with Milankovitch cycles.

The International Commission on Stratigraphy now endorses this effort, judging by its page on geological-time boundary points; one can find more details in Astronomical Time for Earth History and in Astronomical Time Scale, which links to a detailed paper on Cyclostratigraphy and the astronomical time scale.

The Neogene (Miocene to present; about 20.3 million years) is now dated with the help of these cycles, and they have been used to find relative dates in earlier geological periods. There are people working to extend Milankovitch dating further back in time, to cover the entire Cenozoic, and even some of the Mesozoic.


This led me to want to visualize how the planets' orbits precess, and for doing that, I found a paper with solutions extending back 10 million years: Secular evolution of the solar system over 10 million years.

I extracted the numbers from that paper and made animations from them for all the planets from Mercury to Neptune. I then uploaded them to YouTube and collected into these YouTube playlists:

The last million years
The last 10 million years

The axis labels are not rendered very clearly, so here they are:

Eccentricity videos:
e cos(omega)
e sin(omega)
e = eccentricity
omega = longitude of perihelion

Inclination videos:
sin(i/2) cos(Omega)
sin(i/2) sin(Omega)
i = inclination
Omega = longitude of ascending node