  The obliquity of the Earth, which controls our seasons, varies by only ~2.5
degrees over ~40,000 years, and its eccentricity varies by only ~0.05 over
100,000 years. Nonetheless, these small variations influence Earth's ice ages.
For exoplanets, however, variations can be significantly larger. Previous
studies of the habitability of moonless Earth-like exoplanets have found that
high obliquities, high eccentricities, and dynamical variations can extend the
outer edge of the habitable zone by preventing runaway glaciation (snowball
states). We expand upon these studies by exploring the orbital dynamics with a
semi-analytic model that allows us to map broad regions of parameter space. We
find that in general, the largest drivers of obliquity variations are secular
spin-orbit resonances. We show how the obliquity varies in several test cases,
including Kepler-62 f, across a wide range of orbital and spin parameters.
These obliquity variations, alongside orbital variations, will have a dramatic
impact on the climates of such planets.
