A band of solar cells all around the moon? Beaming energy in the form of microwaves at the earth? A Lunatic idea. And Murphy's law would seem to dictate that we'd want to design a system so that, even if the beam were deliberately pointed at Manhattan, no one would suffer much inconvenience or heating (let alone instant, smoking death).
But it's an idea that just might work, someday. At any rate, it's great that the modern world can fund and support NASA and academic (and even Japanese construction firm) scientists working on theoretically possible methods of achieving such a sustainable power source.
Why solar power in space and not on Earth?
Clouds.
Why the moon and not in closer, easier to get to, orbit?
1) Crowded space in the lowest orbits and in geosynchronous orbit.
2) Panels in space would considerably shade Earth (but that might be a good thing if global warming becomes a problem).
3) Cost. Cost. Cost.
Theoretically, at least, it could be cheaper to do it on the moon than closer to Earth.
That's because even low-earth orbit is very expensive to obtain (at least $2,000 per pound of payload to low orbit), and geosynchronous orbit costs about 5 times as much. And costs are not going to fall much until or unless we have a cabled space elevator (for geosynchronous).
It is, course, much more work to bring things and people to the moon. (We haven't done it recently, making cost estimates speculative.)
The moon is 250,000 miles away, versus ~200 miles for a rather low orbit and 22,000 miles for geosynchronous orbit; but bringing the material to the moon would not be proportionately more expensive, as we see with geosynchronous orbit being 100 times higher, but only 5 times more expensive, than low orbit. (That's because the cost of getting a mass to low orbit is more set by the need to obtain 18,000 MPH orbital velocity, than by the need to merely lift it 200 miles.)
More important, the Moon, unlike space, is filled with stuff. The trick is to design a system of mines and factories so that a modest amount of materials, robots and people sent to the moon can be be used to mine, smelt and manufacture that stuff into the materials needed to build a massive belt of solar cells all the way around the Moon's equator. (Half of the cells would be in the daylight at any given time; the power would be sent to the main Moon base, which position would always be facing the Earth.)
Consider one way to bootstrap materials: instead of shipping all the water that the base would need, ship hydrogen, which could be used to grab the oxygen from various moon rocks, producing water weighing 9 times as much as the brought hydrogen, and simultaneously producing metals and other elements (e.g., aluminum, titanium, silicon) of perhaps twice the weight of the hydrogen.
With silicon for solar cells, aluminum for electric transmission lines, and titanium for structural elements, you've got essentially everything you need to manufacture your enormous belt of solar cells.
Once the moon base was making more solar power than needed to maintain itself and keep its humans alive, this power could be used to separate minerals without much need for additional resources from Earth. Then a growing proportion of the growing power supply could be sent to Earth by some form of electromagnetic radiation, such as light (laser) or microwaves. Lasers sound rather dangerous to me, whereas there ought to be some radio or microwave frequency that could be picked up by giant antennas, but which would mostly bounce off the Earth if they missed the antenna.
While the Moon transmitter would need only one location (since the moon always keeps the same face to us), the Earth would have to have receivers in three locations, with each getting energy for about 1/3 of each 25-hour "day" when the moon was overhead. The energy received at each would in part be delivered as electricity for immediate use, and in part be stored, perhaps as synthesized fuels such as hydrogen or natural gas (used to generate electricity for the 2/3 of the time that no Moon energy would be arriving), or it could be delivered around the Earth by intercontinental electric transmission line.
So, there are a few problems yet to solve... But this concept is the first I've ever heard that justifies the manned space program as more than just bread and circuses, but without the bread.
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