Back of the napkin calculations for Powersat by Ben Bova

I’ve just finished reading Powersat, a 2005 book by Ben Bova about an electricity generating solar array in geosynchronous orbit that transmits power to earth via microwaves.

I had a gnawing feeling that from a science and technology point of view, the book was quite a bit off the mark - particularly around how this satellite could be constructed. I thought it would be fun to do some back of the napkin calculations on its cost.

Given its size (4km x 4km = 16 sq. km), and supposing the mass of solar panels is 10kg / sq. m (based on terrestrial panels), and disregarding all the other structures, it means that 160K tons would need to be delivered into LEO. Assuming a launch vehicle with 64 ton capacity (e.g. SpaceX’s Falcon Heavy going to LEO), that requires 2500 launches just to deliver the solar panels, not counting any other equipment, people etc. That’s nearly 7 years of launches at 1 per day! But where is the capacity for that? It’s not mentioned in the book. Perhaps I’m overestimating the mass of solar panels if space based solar panels can be much lighter than terrestrial ones, but there’s still a whole lot of other stuff required: magnetrons, other electrical equipment and wiring, some sort of scaffolding to hold it all together, and so on.

It also means that the cost per launch would have to be way less than $20M to build a satellite at a cost of less than $50B (the book suggests it costs “several times more than a nuclear power plant”; a nuclear plant is estimated to be $9B in 2017). In 2017, SpaceX suggests $62M to deliver just 5.5 tons to LEO. Sure, you’d get a good bulk discount for thousands of launches, but again - that requires enormous infrastructure. I’m not sure what would be involved in boosting this whole structure to geosynchronous orbit after it’s built - presumably that’s not trivial either.

OK, what about the amount of power generated by this array? The book suggests 10GW captured on Earth’s surface. Given extraterrestrial solar radiation is 1367 watts per square meter when Earth and Sun are at 1AU, and given solar panel efficiency of 44% (which is very high and very expensive as of 2017), I get 1367 x 0.44 x 16M = 9.6GW - and that’s before the losses in conversion to microwaves and back! So that doesn’t stack up either.

The company details mentioned in the book are seemingly off too. How can a company that has a $30-50B asset in orbit, (not to mention a spaceplane, a launch base and heaps of other facilities) be valued at $15B - and that’s given in the context of revising the valuation upwards? How can a company like that have less than a thousand employees when SpaceX has more than 4000?

So while this was an engaging enough read, its level of research and attention to detail is nowhere near, say, Andy Weir’s The Martian or Greg Egan’s books.