On the Spin-axis Dynamics of a Moonless Earth

TL;DR

This paper analyzes the spin-axis dynamics of a Moonless Earth, showing that even without the Moon, Earth's obliquity changes slowly enough to maintain long-term habitability, using analytical estimates within a simplified model.

Contribution

It provides the first analytical estimates of chaos and diffusion rates for Earth's obliquity without the Moon, enhancing understanding of planetary climate stability.

Findings

Chaotic diffusion rate is slow enough to preserve habitability.

Analytical estimates align with numerical experiments.

Simplified model clarifies underlying dynamical structure.

Abstract

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.