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When something falls down, potential energy is transformed into kinetic one. Furthermore, you can attach a pulley and extract some energy (like in an aljibe), for example with a dynamo... If the object fall in a deep well, we can extract more energy, till the object reach downhole..

But what if we could have a "bottomless pit"... Endless energy?.. Well we would need an infinite earth... Or like a "black hole aljibe"... hmmm that doesn't seem an option..

Oh, wait a minute, we already have one! A satellite is like always "falling down"... Then is exchanging "potential energy"(who knows from what reference system) into kinetic energy..

What about tied it to a pulley (a long rope I see) to a dynamo, or an earth winding with a magnet satellite, or a satellite winding with the earth magnet, or whatever.. The idea is to USE the "bottomless pit" energy..

Where is the mistake? (just in case there be any =P)

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A satellite isn't falling down--for a circular orbit, it is maintaining a constant radius. Since the potential energy is a function of radius, the potential energy of the satellite remains unchanged. The energy of the orbit is constant--the speed, and thus, the kinetic energy is constant, and so is the position, and thus the potential energy, is also constant.

If you tied the satellite to a dynamo, then the dynamo would produce a drag on the satellite, which would slow it down, which would cause it to lose kinetic energy, which would then cause the central force to overcome the inertia of the satellite, which would cause the satellite to fall into the Earth.

Or, as Deepak says above, it is possible to have a particle convert the rotational kinetic energy a the black hole (or any rotating body) into energy taken out to infinity.

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You can, theoretically, extract energy from rotating black holes via the Penrose process.

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NASA has already experimented with something along the lines you describe, using earth as a sort of homopolar magnetic generator.

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