A rotating object, especially something as large as a planet or a star, has kinetic energy. However, my question is how would you go about harvesting the energy the object has from rotation to go towards other purposes such as powering several thousand space stations? I'm making a hard science fiction short story, so if we could keep it as realistic as possible that would help. Thank you in advance.
The answer is the tides. Your space stations need to be numerous and large enough to cause tides on the planet below. Tidal forces slow the rotation of the planet, so if you set up some tidal stream generators, you are essentially taking the rotational energy of the planet and turning it into electricity.
This is not a great idea though, because not only do tidal forces slow a planet's rotation, they also push the moon further away. In real life, with our moon, this is only a few centimeters per year. We'll have our moon for billions of years. The rate the moon moves away is proportional to how strong the tides are. The stronger the tides, the faster the moon moves away. If you set something like this up to generate as much energy as possible, you would want the strongest tides possible. This would also mean your space stations would get pushed away quickly. To push the stations back to their original positions requires some other energy source; solar sails, chemical rockets, something. Which raises the question, "Why not cut out the middle-man and just use that other source for energy?"
If you're orbiting space stations around an Earth-like planet, tidal power plants beaming energy to the space stations would do the trick. Converting tidal power to electricity/radiant energy slows the planet's rotation.
If not, you're going to need a lot of space elevators. Transferring mass past the zero-g point to the counterweight (where it can then be given a gentle push and let go) will generate energy. A star would be trickier, but solar energy would work fine in that case.
An Alternative Space Elevator Solution
We're dealing with a future tech, so a hard-science solution is asking a bit much. But, let's assume we have access to...
- Can withstand impact on the surface of the earth from high orbit without damage to itself.
- Is remarkably magnetic.
Build your space elevator to a high enough orbit that the space-end can sit free.
Surround the elevator casing with coils of wire. Bazzillions of miles worth of windings.
At the base of the elevator, we want either (a) an indestructable piezzo-electric pad or (b) a mechanical pad that compresses on impact, spinning a flywheel in the process. (I'll explain this in a moment.)
Finally, we need a big-ole' hollow canister made of indestructonium.
This works great if you're mining in space and need to get materials down to Earth. Fill the canister with ore, give it a push, and let it drop straight down to Earth. Now, terminal velocity is estimated at 78 m/s, but let's say we're falling through 22,000 miles (35,406 km) of distance. The canister is highly magnetic and we're passing through a bazzillion miles worth of windings. Think "shake-it-up" flashlight.
When that sucker impacts, it's a bit (but only a bit) like the Tunguska event, except we want to capture the energy rather than letting it convert to felling trees. That's where the piezzo-electric pad or compressing pad with a flywheel come in. I'm not fond of the piezzo-electric pad as it would create a wire-frying burst of electricity that would require serious do-something-with-it-juju to use. The pad idea, where the impact pushed down the pad like a shock absorber, causing a flywheel to spin up to a bazzillion miles-per-hour... that lets the connected-to-a-turbine-generator flywheel run its course, providing a longer, more useful stream of power.
Empty the canister and power the windings to rail-gun the now much lighter canister back to the top. Uses less energy than it created via the drop.
How do I get the power to my space stations?
Run transmission lines along the elevator casing. Note, though, that getting energy off of a spinning object is a big deal. As fun as this thought experiment has been, it would be simpler and cheaper to power your stations with nuclear energy, shipping spent fuel rods off to the sun for disposal.
I recognize that this isn't what you had in mind. It uses gravity, not the kinetic energy of a spinning Earth, but it's whomping hard to get energy from a spinning sphere.
You could set up rigid poles to high orbit with fixed magnets on the end, and put a "disk" of windings in orbit that are stationary and kept so with some ion thrusters. As the earth spins, the rigid poles would move through the "disk" of windings, generating power. But this is so enormously complex and prone to accident that I don't see it happening.
But, with enough Clarkean Magic, you can do just about anything.
You could have a payload that undergoes a slingshot maneuver around a planet which allows it to convert some of the planets kinetic energy into its own via gravity. You then use that extra speed that you gained to generate power. If you could somehow get two planets, You could somehow slingshot the object around both planets to keep increasing its speed and have power stations between the planets that drain the gained speed so that you can keep this going to keep harvesting energy.
Assuming you have enough resources, you could expand this to literally have a line of iron/steel poles that fly between the planets passing through massive space station power planets that consist mainly of coils which will programmed to only drain a fixed about of kinetic energy so that the iron/steel poles can slingshot forever.
While it's maybe 'stretching' (soon-to-be pun intended) your definition of using rotation to generate energy, my method would certainly not be feasible without it.
Place a space elevator with magnetized tether in to orbit. Ride a platform from the planet's surface to the space station which contains a coil of wire around the tether. Place capacitors or other electricity storage devices on the platform. Balance out the weight so that the load will just barely get to the end of the tether.
This set-up could also be done in reverse, meaning the power would directly be transmitted to your space station, but this would require super conductors to overcome the motive resistance of power in the electrical lines.
Presumably you generate some sort of waste on your space stations. Place this on the space elevator and allow for gravity to pull the whole system back to the planet's surface.
Not only do you have free sources of power (presumably many of these space elevators would need to be built), but you also have an easy way to get rid of trash which doesn't involved launching and burning in the planet's atmosphere. Drone earth moving equipment will harness energy on the planet's surface and keep the area around the tethers clean of debris for centuries to come. Or have a big ol' incinerator down there to buy even more time.
Other systems may work whereas the device doesn't have the resistive, electricity generating force until the last several kilometers of the tether. Using this method, you could gather up a lot of speed with your elevator then generate power only over the last several kilometers with much stronger magnets. This helps because a situation could exist where the elevator is basically flung up and then 'caught' at the top, allowing it to then descended on its own due to its own mass. More green, less trash removal.
Oh, and the coil/magnet system is mechanically disengaged on the return journey to earth in whatever manner is necessary to ensure a slow descent. With the second option, you could in theory, generate electricity on the 'down stroke' as well.
EDIT: Forgot to mention, you will need motive force to bring the payload above GEO. You will also then need enough excess power generated to cover this in the power budget. The space tether is going to be quite long, but presumably, your ships are in deep orbit as well so as not to require as much power to stay there.