Scaling in global tidal dissipation of the Earth-Moon system

TL;DR

This paper develops a scaling model for Earth's tidal dissipation over 4.52 billion years, explaining the Moon's orbital evolution and implications for planetary habitability.

Contribution

It introduces a new scaling approach for global tidal dissipation that accounts for complex ocean dynamics and matches observed lunar migration.

Findings

Q-factor at present time is approximately 14.

The Moon was rapidly evicted from near-synchronous orbit.

Early Earth experienced rapid spin-down, influencing climate development.

Abstract

The Moon migrated to $r_{\leftmoon}\simeq3.8\times10^{10}$ cm over a characteristic time $r/v=10^{10}$ Gyr by tidal interaction with the Earth's oceans at a present velocity of $v=3.8$ cm yr$^{-1}$. We derive scaling of global dissipation that covers the entire history over the past 4.52 Gyr. Off-resonance tidal interactions at relatively short tidal periods in the past reveal the need for scaling {with amplitude}. The global properties of the complex spatio-temporal dynamics and dissipation in broad spectrum ocean waves is modeled by damping $\epsilon = h F/(2Q_0)$, where $h$ is the tidal wave amplitude, $F$ is the tidal frequency, and $Q_0$ is the $Q$-factor at the present time. It satisfies $Q_0\simeq 14$ for consistency of migration time and age of the Moon consistent with observations for a near-resonance state today. It shows a startingly fast eviction of the Moon from an unstable near-synchronous orbit close to the Roche limit, probably in a protolunar disk. Rapid spin down of the Earth from an intial $\sim30\%$ of break-up by the Moon favored early formation of a clement global climate. Our theory suggests moons may be similarly advantageous to potentially habitable exoplanets.