Generalized Milankovitch Cycles
The following movie is from climate model calculations by Dave Spiegel that came from a project he called Generalized Milankovitch Cycles (the paper that came from this study is Spiegel et al 2010).
The idea is that Milankovitch cycles, which are long term oscillations in the Earth's orbit (in particular its eccentricity and obliquity), have important and regular consequences for the Earth's climate. Dave and I (and collaborators) tried to generalize this idea, since the orbits of Earth-like exoplanets are not well known and there could certainly exist terrestrial exoplanets with much larger orbital oscillations than Earth; it really just depends on the planetary system architecture and how the planet got there (for example, there is an example simulation on my debris disk-terrestrial planet page that formed a planet with large oscillations in eccentricity and inclination).
A key thing to know about a planet whose orbital eccentricity oscillates is that the stellar flux received by the planet increases for higher orbital eccentricity. So, a circular orbit is colder than an eccentric orbit.
Now to the movie. On the top you see a view of the planet where the color corresponds to surface temperature: The green parts of the planet are at the right temperature for life (hotter than zero degrees Celsius), red is colder and blue is colder still (note that it's a 1-D code so longitude is meaningless). The bottom panel shows the eccentricity of the planet's orbit. The movie goes through a full secular cycle, as the eccentricity oscillates from zero to 0.83 on a 25 year timescale. This timescale is much shorter than the Earth's and in practice just makes it easier to visualize. The oscillation amplitude is also humongous but the same behavior as in the movie was seen in other cases with smaller oscillations.
What happens in the movie is that, as the eccentricity drops, the planets gets colder and ends up in a completely frozen, "Snowball Earth" state. As the orbital eccentricity increases the planet gets hotter and is eventually able to thaw and become habitable again (see Spiegel et al 2010 for more details).
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