  Using an energy balance model with ice sheets, we examine the climate
response of an Earth-like planet orbiting a G dwarf star and experiencing large
orbital and obliquity variations. We find that ice caps couple strongly to the
orbital forcing, leading to extreme ice ages. In contrast with previous
studies, we find that such exo-Milankovitch cycles tend to impair habitability
by inducing snowball states within the habitable zone. The large amplitude
changes in obliquity and eccentricity cause the ice edge, the lowest latitude
extent of the ice caps, to become unstable and grow to the equator. We apply an
analytical theory of the ice edge latitude to show that obliquity is the
primary driver of the instability. The thermal inertia of the ice sheets and
the spectral energy distribution of the G dwarf star increase the sensitivity
of the model to triggering runaway glaciation. Finally, we apply a machine
learning algorithm to demonstrate how this technique can be used to extend the
power of climate models. This work illustrates the importance of orbital
evolution for habitability in dynamically rich planetary systems. We emphasize
that as potentially habitable planets are discovered around G dwarfs, we need
to consider orbital dynamics.
