Re: [Phys-l] day -> month -> year

[John Denker <jsd@av8n.com>]

On 12/05/2011 12:20 AM, Bob Sciamanda wrote:

> Is there any reason to doubt that 
> the same effect will eventually occur with the earth’s motion – eventually 
> making the day equal to a year?  If so, is there any way to estimate the 
> time rate of advance of this effect?  Just curious.

Long before the day becomes equal to the year, it would
become equal to the lunar month.  That is, the earth 
would always turn one fact to the moon, just as the moon 
always turns one face to the earth.

  I say "would" rather than "will" because the process
  is very slow;  the sun is expected to turn into a red
  giant and engulf the earth and moon before the process
  runs to completion.
  http://www.astro.uu.nl/~strous/AA/en/antwoorden/getijden.html

       The day becoming equal to the year would take
       even longer;  far, far longer.

There is no doubt that the day -> month process is under
way.  The day is getting longer, as angular momentum is 
transferred from the spin of the earth to its orbital motion 
around the earth-moon center of mass.  As part of the 
same process, the earth-moon separation is getting larger,
in accordance with conservation of angular momentum.
Among other things, this means that "soon" there will
be no more total eclipses of the sun;  the moon will
not subtend a large enough angle.

The mechanism for this process is that the moon sets
up tides in the earth, and that allows friction to take
energy out of the system.  The principle of virtual 
work says the system tends toward the lowest energy 
configuration.  That is the one with the largest moment 
of inertia.