  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.
