[LEAPSECS] Far past and far future

Rob Seaman seaman at noao.edu
Wed May 25 10:56:20 EDT 2011

Hi Tony,

> Would the earth be slowing down so fast without the moon? There's some tidal coupling in the earth-sun system but isn't it much smaller?

Wonderful questions. I'll bet there are lurkers here who could speak authoritatively :-) Also, one of the "rare Earth" arguments is that we wouldn't have significant plate tectonics absent the Moon, and this would undoubtedly affect the geophysics of Earth orientation as well.

For the Earth's oceans the amplitude of the solar tides is down by a factor of just a few from the lunar tides. Hence a strong monthly variation in the high (and low) tide heights as the two contributions add and subtract depending on the Sun and Moon's relative positions in the sky.

The tides themselves are only a means to an end mediating the transfer of terrestrial rotational angular momentum to lunar orbital angular momentum. The efficiency of this is presumably an "interesting" (and perpetually varying) combination of many factors, but ultimately the Earth's angular momentum has to have somewhere to go (what "conserved" means). One suspects this is something like an impedance matching problem and that it is "more efficiently" coupled to the Moon (undoubtedly my naive discussion fails flamboyantly in several regards) than to either the solar rotation or the Earth's orbit (or other bodies?!?). Tides are an inverse-cube effect suggesting that the coupling was stronger in past aeons since the Moon was closer. The deceleration ought be decelerating in a smoothed long-term trend.

There are any number of solar system resonances, however, to suggest that tidal (or higher moment?!?) coupling is widely prevalent (although perhaps many of these are multi-body effects, e.g., the resonance in the inner Galilean satellites of Jupiter ?!?)

I'd be delighted to be corrected on any of this! Knowing that "the Earth goes wibble-wobble" is typically sufficient for civil timekeeping purposes :-)


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