Scaling in global tidal dissipation of the Earth-Moon system
arXiv:1609.07474 · doi:10.1016/j.newast.2017.01.012
Abstract
The Moon migrated to $r_{\leftmoon}\simeq3.8\times10^{10}$ cm over a characteristic time Gyr by tidal interaction with the Earth's oceans at a present velocity of cm yr. 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 , where is the tidal wave amplitude, is the tidal frequency, and is the -factor at the present time. It satisfies 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 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.
8 pages, 5 figures