Electricity from L-5

I'm a bit surprised that no denizen of these newsgroups remembers precisely what the proposal was and what claims were made for it. I have no literature on hand about it, so this is from memory.

The sunlight was to be collected by photovoltaic arrays and the electricity generated microwaves of a carefully chosen wavelength. I don't remember what it was. An antenna of sufficient size compared to this wavelength focussed a microwave beam at *rectenna* on the earth some kilometers square. I suppose there must have been several rectennas, because of the earth's rotation. I am sure that O'Neill and others got the ratio of antenna size to wavelength right so that the beam was properly focussed on a rectenna on earth.

(I'm informed that the solar collectors were to be in geostationary orbit rather than at L-5. This permits each collector to be serviced by one rectenna. This seems right to me.)

A rectenna both received the microwaves and rectified the resulting current giving a DC output. I believe the power density at the rectenna was said to be such that cows and sheep could graze on the same land. Let's do the calculation.

Supposing the rectenna to be 10 km square, that's 10^8 m^2. Suppose the beam to carry 100 gigawatts, i.e. the equivalent of 100 current nuclear power stations. We then have a power density of 1 kw per square meter, i.e. slightly less than the much touted solar constant. So the sheep underneath the rectenna is as though in the sun, but the sunlight in question is microwaves. I don't know how sheep like that. I suppose that the sheep experiences much less power density than that, because the rectenna grabs almost all the energy.

Anyway the power density was such that if the beam lost directionality, no appreciable harm would be done.

After those calculations, I begin to suppose that I have underestimated the power they planned. Very likely they would have wanted to displace not 100 power stations but 1,000 or even 10,000. With 99 percent efficient rectennas the sheep could still safely graze.

The idea was that the O'Neill colonies would supplement their own production by buying things from the earth with whatever money the supply of electricity would fetch.

The colonies were supposed to be in earth orbit at the moon's L-5 point. This is a stable orbit at lunar distance, 60 degrees behind the moon. It seems to me that a (Polish?) telescope search claimed to have detected some meteoritic type junk there.

If the radiation were 20 cm, and the rectenna were 10 km in diameter and the moon is 400,000 km away, the beam would need an angle of 1/(40,000) = 2.5 x 10^(-5) radians. The antenna that created the beam would then need a diameter of a few times 20 x 40,000 cm = 800 meters. It would be more symmetric if the antenna in space and the rectenna on the ground were the same size, so perhaps we should make the wave length one or two meters. This gives not so tight a spacing of the wires of the rectenna.

The feasibility of the scheme depends on the cost of transporting large quantities of material for the construction of the system to the L-5 point. It requires enormously lower launch costs than NASA has achieved or plans to achieve within its planning horizon.

The plan also involved getting much of the material from the moon and launching it from the moon with electromagnetic mass drivers. Since the moon has no atmosphere and has less gravity than the earth, the idea has some advantages.

It also assumes the more exotic idea that the U.S. and other nations - or possibly a world government - would spend vast sums so that a few hundred thousand or a few million people could live idyllic, green lives in the O'Neill cylinders.