Scaling in global tidal dissipation of the Earth-Moon system

The Moon migrated to cm over a characteristic time r/v=10 Gyr by tidal interaction with Earth's oceans at a present velocity of v=3.8 cm yr−1. We model global dissipation to cover the entire history over the past 4.52  Gyr. We use scaling and numerical integration to model the off-resonance tidal interactions at relatively short tidal periods in the past to a near-resonance state at present. The global properties of the complex spatio-temporal dynamics and dissipation in broad spectrum ocean waves is modeled by damping ϵ=hF/(2Q0), where h is the tidal wave amplitude, F is the tidal frequency, and Q0 is the Q-factor at the present time. It satisfies Q0 ≃ 14 for consistency of migration time and age of the Moon consistent with observations for a near-resonance state today. Numerical results reveal the need for scaling with amplitude. It shows a startlingly 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 Earth from an initial ∼ 30% 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.