The earth's rotation rate is slowing down because of friction against the tidal bulges caused by the gravitation of the moon (major factor) and the sun (lesser factor). The earth's rotational energy is dissipated as heat, but where is the angular momentum going, and what physical mechanism brings that momentum there?
(In reply to
re(8): I disagree - me too, with you by Ken Haley)
I understand now why you used "dissipating". As for the problem's
assertion that the rotational energy is dissipated as heat, that's
probably not quite true.
Remember, that as a body is "raised" from the center of the earth (or a
body "raised" from the center of the moon), its gravitational potential
energy increases. Well, the same goes for the moon. I would
argue that the majority of the Earth's "lost" rotational energy is
bound up in the gravitational potential energy in the earth-moon
system, and perhaps in the kinetic energy of the earth and moon.
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That being said, the work, done to "pull" the moon into a higher orbit
by the oceans and the Earth, is associated with tidal forces (on the
oceans and the Earth itself) which cause friction and an increase in
temperature (heat).
Also (mostly as an aside), don't forget that energy can be (and is)
radiated away from the planet into outerspace. As you might
guess, over a long period of time, the Earth radiates as much energy as
the sun sends to Earth (or the Earth would either be a cincer or a
frozen wasteland).
re(9): I disagree - me too, with you
