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:
On a moon that was formed relatively recently, such that it was not yet tidally locked with its planet.
On a moon of Jupiter, using the gravitational pull of other moons.
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.