I understand from Wikipedia that, "The length of the day, which has increased over the long term of Earth's history due to tidal effects, ...". If the angular velocity of the earth is decreasing then the stored rotational energy is decreasing. Where does the power/energy go?
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$\begingroup$ Is there also some energy lost as the earth "stretches" to become more round? $\endgroup$– IQAndreasSep 2, 2016 at 20:14
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2$\begingroup$ As a matter of vocabulary, "power" isn't a conserved quantity and one doesn't have to account for where it goes. Energy is conserved and has to be accounted. $\endgroup$– dmckee --- ex-moderator kittenSep 3, 2016 at 3:32
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2 Answers
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You're correct in assuming the net angular momentum of the system in question here will remain constant. The Moon's orbit around Earth is responsible for the slowing of Earth's rotation. This effect is extremely small.
The decrease in Earth's angular momentum is transferred to the moon, which resultantly sees it's orbit accelerate. This acceleration also causes the moon to move further and further from the Earth. This trend will continue until they reach a common speed.
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3$\begingroup$ And orbital dynamics mean that as the Moon is accelerated it moves to a higher orbit and so actually slows down. $\endgroup$– James KSep 2, 2016 at 18:12
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$\begingroup$ The answer by Brumder is correct, but forgets to mention that some of the orbital and rotational energy is transformed into heat via friction, which is called tidal heating. $\endgroup$– EbonairSep 2, 2016 at 22:31
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2$\begingroup$ +1, but strictly speaking this is an answer to "where does the angular momentum go" rather than "where does the power/energy go" as in the OP. This answer could be improved by mentioning that the kinetic energy in the system ultimately becomes heat, which happens because tidal forces flex the Earth and its oceans, which generate heat by moving against each other, and that's ultimately what causes the change in rotation speed. $\endgroup$– N. VirgoSep 3, 2016 at 1:29
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$\begingroup$ It might help to clarify that the acceleration mentioned herein is a nominal result assuming all else remained equal, but as the orbit of Luna enlarges the actual orbital speed (both linear and angular) is reduced. The energy goes into increased potential energy in the Earth-Moon system as well as into heating (the potential energy gain is twice the loss of orbital kinetic energy, after all). $\endgroup$ Sep 3, 2016 at 3:31
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Where does the power/energy go?
It goes into heating the Earth and the Moon. That heat in turn spreads out into the universe.
While the Earth-Moon system comes very close to conserving angular momentum, it does not conserve mechanical energy. In fact, that angular momentum transfers from the Earth's rotation to the Moon's orbit means that the total mechanical energy of the Earth-Moon system is necessarily reduced. Mechanical energy is only conserved in isolated, non-dissipative systems. The tides in the Earth's oceans, in the Earth as a whole, and in the Moon as a whole means that the Earth-Moon system is dissipative.
answered Sep 3, 2016 at 7:14