  The variation of a planet's obliquity is influenced by the existence of
satellites with a high mass ratio. For instance, the Earth's obliquity is
stabilized by the Moon, and would undergo chaotic variations in the Moon's
absence. In turn, such variations can lead to large-scale changes in the
atmospheric circulation, rendering spin-axis dynamics a central issue for
understanding climate. The relevant quantity for dynamically-forced climate
change is the rate of chaotic diffusion. Accordingly, here we reexamine the
spin-axis evolution of a Moonless Earth within the context of a simplified
perturbative framework. We present analytical estimates of the characteristic
Lyapunov coefficient as well as the chaotic diffusion rate and demonstrate that
even in absence of the Moon, the stochastic change in the Earth's obliquity is
sufficiently slow to not preclude long-term habitability. Our calculations are
consistent with published numerical experiments and illustrate the putative
system's underlying dynamical structure in a simple and intuitive manner.
