On May 26, 2011, at 2:29 PM, Clive D.W. Feather wrote:
> I took some numbers from the Williams paper that was cited and played with
> them in a spreadsheet. These suggest that about 90% of the terrestrial
> rotational angular momentum reappears as lunar orbital angular momentum. On
> the other hand, I can't see where the rest of it would go - apparently
> observations show no indication that the Earth's orbit is growing.
Impressive that you got the budget that close using simple modeling techniques.
>> 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,
>
> It's suggested in my reading that the present period has an abnormally high
> transfer rate because of the present arrangement of the continents and,
> therefore, the oceanic tides. Certainly the present rate cannot have happened
> for long periods - projecting back they make the moon collide with the earth
> about 1 to 2 Gyr ago.
Sounds plausible.
>> 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.
>
> That's not what the numbers appear to show.
Well, depends how you define "smoothed" and "long-term" :-)
There are several levels of issues here. For example:
1) Extrapolating from a single example. We only have one solar system. How
typical or atypical is it? This is currently being addressed via exoplanet
studies such as the Kepler mission:
http://kepler.nasa.gov/
In a few years we'll have a lot more examples to compare against.
2) Perhaps the Earth-Moon system is indeed rare. See, for example:
http://arxiv.org/abs/1105.4616
3) The need for physically appropriate modeling:
http://en.wikipedia.org/wiki/Nice_model
That is, back of the envelope (or spreadsheet) modeling can only get you so
far. However, applying reality checks is a very powerful technique in
astronomical reasoning (for example, light travel time constraints are often
applied). As you suggest there are boundary conditions appropriate to other
evidence about the age of the Moon. Or confidence in fundamental physics such
as the conservation of angular momentum.
4) But the science is in finding explanations for things that appear to diverge
from well established physical understanding, for example:
http://arxiv.org/abs/1105.4863
(Seems a lot of fuss for a 3 sigma result.)
5) Civil timekeeping is an exercise in engineering, however, not science per
se. The Earth's rotation rate is very steady, but our clocks are now more
steady. There are also longer term trends imposed on the short term wobbling.
The longest trend (I suppose) is the tidal deceleration due to our Moon, but
the Earth clock and Atomic clock have always differed in any event. The
engineering question is whether we seek to accommodate the Earth's natural
idiosyncrasies - or whether we attempt to ignore them.
Rob
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