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On Earth, we generate electricity from the Moon's orbit using tidal turbines. Would it be possible for denizens of the Moon to generate electricity using the Earth's gravity, using a windmill-sized machine that converts the gravitational gradient between the two bodies into rotational mechanical energy?

I suspect the answer for our Moon would be "no", because it is tidally locked with Earth so there is perhaps not enough variation in Earth's gravitational effect to generate energy. But maybe a "gravity windmill" would be possible on a different pair of celestial bodies.

Question: would it be possible to generate a useful amount of energy using a turbine that is pushed by the gravity of a nearby celestial body?

The size and arrangement of the two celestial bodies in question (the one where the generator is constructed and the one that powers the generator) are flexible - whatever makes this possible, so long as the celestial bodies in question can be in stable orbit.

Some suggested bodies on which this machine might work:

  1. On a moon that was formed relatively recently, such that it was not yet tidally locked with its planet.

  2. On a moon of Jupiter, using the gravitational pull of other moons.

  3. On a hunk of rock in Saturn's B ring, where vast mountains of debris are stirred up at the outermost edge by tidal disturbances (perhaps suggesting a source of energy to tap?).

Not looking for a large amount of energy here. Basically trying to envision a space windmill for a very tech-primitive setting. I'm asking about generating electricity because the answer will serve my own purpose and is also more likely to be useful to other people, but for my project I really just need rotational mechanical energy.

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    $\begingroup$ You are asking 4 different questions here, one per scenario you have listed. $\endgroup$
    – L.Dutch
    May 16, 2022 at 4:52
  • $\begingroup$ The cost-benefit vs solar on our Moon most likely says 'no' for the Moon, but further out in the solar system? Maybe. Focus your question. $\endgroup$ May 16, 2022 at 13:27
  • $\begingroup$ @L.Dutch the celestial bodies in question can be whatever makes this technology possible. I was just trying to provide some scenarios to explain my own progress on the question. I can see that I wasn't clear enough about this though, so I've edited my question. $\endgroup$ May 16, 2022 at 16:15

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Energy conversion

Electricity is produced by conversion of some other form of energy (mechanical, chemical, solar, thermal etc.) into it. Tidal waves have mechanical energy.

Tides

Tides are produced by

  • Earth's rotation
  • Gravitational gradient from moon (stronger)
  • Gravitational gradient from sun (weaker)

As told here

As detailed in "The Moon Book" by Kim Long, the ocean tides we experience on earth are caused by the sum of the moon's gravitational gradient and the sun's gravitational gradient. When the sun and the moon are aligned, or nearly aligned, their gravitational gradient fields add together constructively, leading to extra strong tides (high tide is extra high and low tide is extra low). This alignment happens when the moon is a new moon or a full moon, which occurs about every two weeks. The moon takes about a month to orbit the earth, hence strong tides occur about twice a month. In contrast, when the sun and the moon are unaligned, their gravitational gradients tend to cancel out, leading to weak tides (high tide is not very high and low tide is not very low). But even when the sun and moon are perfectly unaligned (they form a 90 degree angle relative to the earth), there are still tides because the moon's gravitational gradient is stronger than the sun's. The sun's gravitational gradient never completely cancels out the moon's. The biweekly strong tides are called "spring tides" even though they occur all year long. The name does not refer to the season "Spring", but to the verb "spring" which means to leap forth, because the strong high tides leap higher up the shore. The biweekly weak tides are called "neap tides".

Energy Medium

Solids are fixed and gases are thin or rare (less dense) so solids and gases are not much affected by gravity. A huge amount of liquid is needed to be affected by gravity and rotation.

To get electricity from gravity:

  • A huge amount of liquid to cause tides.
  • A large enough gravitational gradient.
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  • $\begingroup$ Lovely and well written explanation of tidal energy! Do you think a gravitational gradient could be high enough to enable a "gravitational windmill" to function, or would such a high gradient not be possible on a stable satellite? The moon and earth are relatively close in mass compared to other moon/planets. $\endgroup$ May 16, 2022 at 15:40
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A mining colony on Io might draw energy from a core tap (with a large radiator farm, as there is little atmosphere). The interior of Io is quite hot.

The internal heat of Io is almost entirely due to tides. These are different from the flow and ebb tides of Earth's hydrosphere, as they are not caused by Io's rotation. Rather, the tides of Io result from differences in Jupiter's gravity well gradient throughout Io's eccentric orbit.

So instead of constructing a "gravity windmill" on Io, the colonists would be taking advantage of one that already exists -- Io herself.

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You can extract energy, but not in useful quantities.

  1. Libration. While the moon has tidally locked to Earth the process is not complete, the moon wobbles. Thus the local vertical will change.

  2. The Moon's orbit is not circular. At the center of nearside and farside you will find the gravity going up and down slightly on a monthly cycle. As you move away from the axis pointing towards Earth this converts to a shift in the local vertical.

On Earth tidal energy is far too diffuse to be worth bothering with other than when collected by a world-spanning ocean and both of these sources are even lesser.

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