Can we convert the motion energy of bodies (such as satellites) moving around a high-gravity objects (like Earth or the Sun) to some kind of usable energy?
Consider the Earth and moon to start out with. Obviously we can extract energy through tidal power (which is a real thing, although the economic question is non-trivial). This is possible because the Earth is spinning faster than the moon orbits.
However, this tidal power is rate-limited. As long as we're using water as the working fluid, the theoretical maximum rate of power conversion is pretty close to what we'd get by damming up all the world's oceans.
What other kinds of systems can we get energy from? To answer this, I would suggest the following general checklist:
- Identify the initial system
- Identify a final system that is possible (angular momentum conserved), and is lower energy than the starting system
- Does the idea make any practical sense?
I can use this to answer for a number of configurations.
I will imagine a pair of binary asteroids in a highly elliptical orbit about each other. If you consider the burn necessary to circularize the orbit at perigee (the closest point), you are trying to throw away kinetic energy by burning your engines. Obviously you could, instead, convert that extra energy into useful energy.
I use asteroids as an example because the scales and forces can be handled by materials we can actually construct. You could literally connect the two bodies by some ropes designed for space. Then the energy conversion process consists of pulleys and generators.
To compensate for the change of angular momentum, you would simply speed up the rotation of the asteroids themselves. Even if this resulted in negative effective gravity on its equator, we know that some asteroids can still hold together. There are certainly some binary asteroid systems where this is possible within some bounds.
Circular, but rotating
This is the case of the Earth and the moon. If you're interested in a more directly mechanical (absurdist) process than tidal power, then you can imagine some. Just build space elevators all the way around Earth's equator. Then make the counter-weight station a full ring. Then build a space elevator from the moon's surface to the Earth-moon L1 point, with a fiber extending down to Earth's space elevator's counterweight ring.
Now you have a system with relative motion between the Earth's and moon's space elevators that can be essentially converted on contact to energy. The speeds would be too great for some kind of direct (space-train) mechanical connection, so we would have to postulate an electromagnetic connection, but this is not outrageous since we're already in space and (apparently) have the technology to build space elevators to begin with.
The initial system consists of 1 body tidally locked into the orbit with the other body rotating too fast. This is an interesting property of the Earth-moon system. The final state is that Earth throws the moon out into space. Our energy extraction system would hasten this process. Tidal power does too, but not as fast. The length of an Earth day would shorten faster the more power we produce. If we did it long enough the moon would fly away to play gravitational billiard balls with the rest of our solar system.
Completely tidally locked
This situation was the real challenge for me to think about. You can't get energy from the motion of the orbit or rotation of the bodies, unless you can grab hold of another reference frame. By the formulation of the problem, that's not allowed (it's also not very practical).
Turns out, we could get energy out of this system if one body is larger than the other, but only gravitational energy. Here's how:
Imagine the Earth-moon system. The moon's gravity-well is quite small compared to Earth's. So on the moon, lob rocks at the Earth with a railgun, aiming the orbit so they graze LEO. In LEO, have some catcher system that converts the energy. This could be a simple orbital ring (much easier than a space elevator), although the "catching" part will be difficult, it's still physically defensible. This system will work totally irrelevant of the rotation of Earth. You could throw rocks into East-West orbits or West-East orbits, and use this to balance the momentum changes from catching.
In the final state of this system, you're left with a major part of the moon's mass orbiting close to Earth's surface (safe? who cares). The low circular orbit is lower energy than what we started out with, and so we conclude that the energy gained by the catcher could be more than it took to launch rocks from the railgun on the moon. But importantly, this does not come from orbital motion. It comes from gravitational energy.
The final system will (again) be tossing the moon into space. In LEO, you'd have to dispel the extra momentum, which you would do by the East/West alternation, but to sustain the scheme as long as possible you'd prefer to park the caught mass in the West->East orbit because that contains the right direction of angular momentum. However, every payload you launch, regardless of its destination on Earth, will push the moon further out. The moon's gravity itself isn't a deal-breaker because the averaged gravitational binding energy of the moon is small compared to the energy from dropping something from infinity into a LEO orbit.
So at the end, one giant orbital ring of moon-rock is in LEO, a leftover moon is about to go rogue, and a bunch of politicians are asking "now what?"
The transition I'm describing is a sort of Ostwald ripening of planets, where energy is minimized by combining all small bodies into larger bodies, like corporate consolidation. Within orbiting systems, however, you still have to discharge a small part into space in order to preserve the angular momentum condition. After all, that's basically why we have a moon in the first place! It would be impossible to combine the Earth and moon into a single body because gravity is not strong enough to hold that body together with its present angular momentum value. At the end of the process, the larger planet may be left with some angular momentum (by design), and the smaller object may overshoot the escape velocity by some amount, dictated by the optimization of the problem.
Tidally locked, equal masses
This is the hardest system to get energy out of, because it can't be done differentially. You can throw some of the mass from one object into the other one, but even with 100% efficiency you'll exactly break even. For practical purposes, this makes the scheme impossible. You'll have to move planetary-scale masses before you could start getting a payoff, and that's nonsense... unless maybe we're talking about a binary asteroid system, which could transfer mass by using a (literal) conveyor belt.
As for large-scale systems, the only way you'd make energy from this is with another reference frame in the picture.