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If we could utilize gravitational force to create energy, could gravity, being unlimited, generate unlimited energy?

Consider electricity generation from tides. Since tides are due to gravity, aren't we creating energy from an unlimited source and thus generating unlimited energy?

This seems highly contradictory to conservation of energy. What am I missing?

Qmechanic
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kousik
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2 Answers2

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Tides gradually reduce the internal kinetic energy and gravitational potential energy of the Earth-Moon system, that is, the speed and height of the Moon's orbit.

Whether or not humans extract some electricity from it along the way, the same amount of energy per tide ends up as random thermal internal energy in the materials that make up the Earth and the Moon. The Earth and Moon are doing work on each other; harvesting tidal energy lets us redirect a tiny fraction of this work to our own purposes before it ends up dissipated as heat.

The energies available are exceedingly large relative to the energies dissipated.

Our Moon is actually on a (very, very slow) outward spiral. The energy dissipated by tides on Earth and on the Moon (which lacks water, of course, but rock still deforms a little bit) acts to counteract this. If the Earth-Moon system were left alone forever, tidal energy dissipation would eventually stop the outward spiral and begin an inward spiral, eventually ending either with the Moon crashing into the Earth or perhaps developing an orbital eccentricity that eventually would result in the moon being captured by another body's gravity and leaving Earth forever. I haven't seen the calculation, but the estimate I've seen projected for time at which the outward spiral would stop and the inward spiral would begin is about fifty billion years from now, with collision or ejection at about 65 billion years. https://en.wikipedia.org/wiki/Timeline_of_the_far_future

g s
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  • This is the scenario I'd been groping for, in my comment on the question. The notion that extremely tiny and primitive terrestrial life-forms (virions, prions, etc.) might survive such effects, and subsequently evolve into life-forms as intelligent as ourselves (through their evolution on a moon ejected into an orbit more favorable to life than most extra-terrestrial orbits, for instance) does exist, but would be a phenomenally slim chance. A probability strongly favoring the use of tidal energy is the probability that we'd be able to leave, en masse, "when the time comes". – Edouard Mar 13 '22 at 17:24
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    @Edouard To be clear: 100% of the energy of each tide will end up dissipated, no matter what humans do with it. Nothing we do with tidal energy will influence the orbit of the moon. Also, by the time any prions have to worry about losing the moon, all life on Earth will probably have been extinct for tens of billions of years, assuming there's anything left of Earth at all, because of the expansion and subsequent collapse and dimming of the dying Sun. – g s Mar 13 '22 at 17:31
  • Yes; the net advantage you've found is clearly stated in your good answer's 3rd paragraph. The life expectancies (if any), travel modes, & future interests of any evolved prions are, indeed, EXTREMELY hypothetical. We know much more about physics than we know about biology, and the time scales involved are multiples of the time since the Universe's Big Bang. – Edouard Mar 13 '22 at 17:46
  • Would it be correct to say that if we were able to capture a huge proportion of tidal energy - say 90%, then the effect would be to slow the spinning of the earth so tides would be slower. There is no free lunch? – foolishmuse Mar 14 '22 at 15:27
  • @foolishmuse I have no idea what capturing that energy could possibly entail, but supposing we use magic to capture the energy, it still wouldn't matter. Earth and the moon capture the tidal energy already - as internal thermal energy. Angular momentum doesn't care about entropy, just energy, and 100% of tidal energy is captured already. It doesn't matter if it ends up in the internal chemical energy of a battery, or dissipated as heat in electric cables, or dissipated as heat in rocks and oceans. – g s Mar 14 '22 at 17:16
  • If you want to slow the spinning of the Earth by extracting kinetic energy from the system, you have to tie an 800,000 km drive chain around the moon and physically strap it to a generator around the equator. – g s Mar 14 '22 at 17:19
  • Tidal power generation is already in testing. Giant propellors under the water turn with the tide moving in and out of a narrow bay. I'm wondering if you are correct on your answer to my posting. Right now the tidal power is just dissipated up on the beach. But we we were to literally slow down the movement of the waves by generating electricity, then wouldn't that slow the spin of the earth? A good thought experiment. – foolishmuse Mar 14 '22 at 18:06
  • @foolishmuse Angular momentum is conserved. If you want to take it away from the Earth, you have to give it to something else, so you either need to launch those propellers into a west-to-east orbit or strap a drive chain to the moon. – g s Mar 14 '22 at 18:27
  • I guess we would just be converting the energy used for beach erosion into electrical energy. – foolishmuse Mar 14 '22 at 18:43
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You are missing the fact that the tidal energy you convert into electricity comes from the relative motion of the Moon and the Earth. Very gradually, that motion is slowing down as energy is lost through tidal effects. So energy is conserved, as the gain in tidal energy is offset by the loss of kinetic energy of the Earth and the Moon.

Marco Ocram
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