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Kind of an odd, random question that popped into my head. Tidal energy - earth's ocean movement, volcanism on some of Jupiter's moons, etc. - obviously comes from the gravitational interaction between large bodies. On earth the interactions with the moon are pulling water around the surface, creating some amount of heat due to friction, etc.

My question is, where does that energy come from exactly? More specifically, what potential energy source is getting depleted to do that work? Is the earth minutely slowing down in its spin - or are the orbits of earth and the moon subtly altered over time by the counteractive movement and friction of liquids and gasses?

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My question is, where does that energy come from exactly? More specifically, what potential energy source is getting depleted to do that work? Is the earth minutely slowing down in its spin - or are the orbits of earth and the moon subtly altered over time by the counteractive movement and friction of liquids and gasses?

In the case of the Earth's oceans and of the volcanoes of Io and Enceladus, the source of the energy is the planet's rotational kinetic energy rather than orbital energy. I wrote extensively about Io in this answer to the question When a planet is heated through gravitational pull, where is the energy taken from at this site. Unless there are objections, I'll let that answer stand with regard to explaining the source of the sulfur volcanoes on Io and the cryovolcanoes on Enceladus.

In the case of the Earth's oceans, the Earth's rotation rate (one revolution per day) is much faster than the Moon's orbital rate (once revolution per month). Friction, viscosity, the Coriolis effect, and the sizes and shapes of the ocean basins means that the tides raised by the Moon are simultaneously slowly slowing down the Earth's rotation rate and are slowly making the Moon recede from the Earth.

The slowing of the Earth's rotation rate and the Moon's orbital rate are written in rock (hardened clay, actually) in eclipses of the Moon and the Sun recorded by ancient Babylonian astronomers. For example, the path of totality of the total solar eclipse observed in Babylon on 15 April 136 BC would have passed over Algiers rather than Babylon if the Earth's rotation rate and the Moon's orbital rate were constant (stephenson).

The slowing of the Earth's rotation rate and of the Moon's orbital rate are even more clearly written in rock (quite literally) in the form of some fossils and tidal rythmites, sedimentary rock formations that have extremely ancient records of daily/monthly/yearly variations in the tides. The day was a couple of hours shorter than it is now 450 million years ago, shorter yet 900 million years ago (williams).


References:

R. Stephenson, "Historical eclipses and Earth's rotation", Astronomy & Geophysics 44:2 (2008): 22-27.

G. Williams, "Geological constraints on the Precambrian history of Earth's rotation and the Moon's orbit," Reviews of Geophysics 38.1 (2000): 37-59.

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Though total potential energy of the system of solid earth + oceans + moon + sun would remain approximately constant the energy of one of these can increase at the expense of the other three. Thats how the tidal energy comes up. Tidal friction does contribute to the reduction of the total gravitational potential energy of the entire system. It also causes reduction in the rotation speed of the earth.

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    $\begingroup$ It's worth mentioning that the end result of this is that the moon moves further away from the Earth, an effect that has been measured using equipment left by the Apollo missions. The moon used to be much closer than it is now. $\endgroup$ – Nathaniel Sep 17 '13 at 11:39
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    $\begingroup$ Another thing worth mentioning is that the earth will eventually also be tidally locked to the moon, however this processes takes a very long time. "Atomic clocks show that a modern day is longer by about 1.7 milliseconds than a century ago." - Wikipedia But this rate of change in angular rotation of the earth will slow down when earth's rotation gets closer to that of the angular motion of the moon. $\endgroup$ – fibonatic Sep 17 '13 at 14:55
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    $\begingroup$ This answer seems to be wrong. Why would total potential energy of the system of solid earth + oceans + moon + sun remain constant? It is the total energy which should be constant, including gravitational, kinetic and internal energy of the bodies (in an inertial frame). And the tidal friction leads to $increase$ of the gravitational potential energy - Moon is getting farther from Earth by 3.8cm/year, while maintaining roughly circular orbit. The only thing that seems right is that the angular velocity of Earth should decrease due to Moon. $\endgroup$ – Ján Lalinský Jan 6 '14 at 20:36
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    $\begingroup$ @JánLalinský - You are correct; this answer is not correct. There is no such thing as a law of conservation of mechanical energy, let alone potential energy. $\endgroup$ – David Hammen Jul 31 '16 at 6:14
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My question is, where does that energy come from exactly? More specifically, what potential energy source is getting depleted to do that work?

This in general depends on the frame of reference to which the definition of energy refers. The frame co-moving with the Earth-Moon center but free of rotation can be regarded as inertial. In this frame, the kinetic energy of the solid Earth decreases, as well as kinetic energy of the Moon. The gravitational potential energy of the system increases, as well as the internal energy of the Earth (swirling ocean and atmosphere). So in this view, the energy for the tides, waves and heating comes from the kinetic energies of both solid bodies.

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protected by Qmechanic Jan 6 '14 at 15:00

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