Scaling in global tidal dissipation of the Earth-Moon system
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.
- Publication:
-
New Astronomy
- Pub Date:
- July 2017
- DOI:
- 10.1016/j.newast.2017.01.012
- arXiv:
- arXiv:1609.07474
- Bibcode:
- 2017NewA...54..115V
- Keywords:
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- Astrophysics - Earth and Planetary Astrophysics
- E-Print:
- 8 pages, 5 figures