Suppose you have a large rock, and a large source of gravity.
Suppose that rock is an asteroid, and that source of gravity is the Earth.
Suppose you gently push that asteroid to an Earth orbit, catch it with some kind of gigantic space-tower-like device, and use the force of the asteroid's descent to generate electrical energy.
Okay, several huge flaws with this plan. Moving the asteroid wouldn't be cheap, a space tower that big is grossly impractical, and if you missed you'd cause serious trouble on the ground. However the idea sticks with me and I think it will be a fun exercise in armchair physics. I am a physics newbie so bear with me as I fire my sawed-off physics shotgun from the hip.
Let's start with the rock. How about Cruithne? This rock might just be plausibly near to earth in a couple hundred years. It's sometimes called "Earth's second moon" as it is in a very similar orbit to the Earth, although it orbits the sun. Cruithne has a mass of 1.3e+14 kg and a size of about 5 kilometers.
Let's assume that the rock will start from a 36 kilometer geosynchronous orbit (which is ridiculous, really, with such mass).
Assuming the force of gravity at a constant 9.8m/s^2 (it's not!) then we have a potential energy of (1.3e+14)(9.8m/s^2)(36000m) = 4.5864e+19 joules. In 2005 the entire population of the earth consumed approximately 5e+20 joules. So even ignoring the difference in gravity at altitude (marginal although I've struggled with the equations), efficiency of the system, and so many other factors, you'd need ten of these every year.
As a side benefit, you could send down asteroids with materials you need. Unfortunately I doubt we humans could consume all these materials, so in a few years you'd have dozens of kilometer-sized boulders strewn around. You'd also have to find a way to unload the things or they wouldn't be strewn very far.
Perhaps the idea has more merit as a method for powering a space spire, and primarily for delivering materials which would be unloaded. But you'd need a ridiculously huge and strong tower. Completely at odds with current space elevator designs and introducing a whole new set of equations. Heck, you'd need so much material just to make something that tall you'd leave a pretty big hole. Suppose you can do the whole thing with four columns each 10 meters on a side - quite optimistic! That's 3.6 million cubic meters of material or at least 2.82999348e+13 grams - or the entire world steel output for 20 years.
Take it down a notch: what about just refining raw materials in orbit and then shunting them down the spire. Use them as one-time counterweights to lift other items into orbit. Take the residual energy - which could be considerable. Send lots of (relatively) smaller chunks down the elevator.
Really a crazy idea. But now it's out of my head.
A Look at the Shape of Temperature Change Over Time
35 minutes ago