The Moon migrated to r _ { \leftmoon } \simeq 3.8 \times 10 ^ { 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 = hF / ( 2 Q _ { 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 \sim 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 .