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Comment by yrmhm | Hacker News Reader

I keep seeing mention of this, with some projects fairly far along and government sponsored, but no one can answer for me how they get around the limitations of the Inverse Square Law: https://en.wikipedia.org/wiki/Inverse-square_law

Basically, with the distances we're talking about, only a super tiny fraction of the energy beamed from space would make it to an earth-based receiver. I can't reconcile this basic fundamental truth with the fact that these projects actually seem real. Can anyone provide insight here? Are these just fanciful proof-of-concepts that aren't intended for actual large-scale power generation?

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Lasers don't work that way.

See, the inverse-square law is about an emitted source diminishing because it broadcasts spherically - the surface area grows with r^2 because the surface is 2D.

A laser doesn't work that way, nearly. Sure it diminishes, but the spread is astronomically (!) small. So for a distance of say 24000 miles you can 'beat' the law to a great degree.

You use masers to beam the power down. The inverse square law is based on the idea that the power that you send is radiating out in all directions (thus, the power experienced at distance d from the radiator is based on the surface area of the sphere with radius d, thus dominated by a 1/d^2 relationship).

With masers, you aren't radiating out, you're pumping all the power in a straight line and you can capture approximately all of it by building a capture point as wide as the line.

(More technically, since of course you won't create perfectly parallel microwaves, there will eventually be dispersion, but it's not meaningful over the distances that you care about.)

Not trying to argue for the feasibility of space based solar power, but the inverse square law applies in the far field i.e. when the emitter can be approximated as a point source. Depending on the wavelength and the antenna size this is not necessarily the case: https://en.m.wikipedia.org/wiki/Fraunhofer_distance

E.g. for 3 GHz and a 500 m antenna, the far field starts at about 5,000 km

Inverse square law works for light that goes every direction like sun or light bulbs, but many of these projects plan to send energy directionally like lasers or mirror based solutions so the dispersion of light is as minimum as it can get

You're thinking of the inverse square law the wrong way. What it means is that at a distance, d, the power from the source is distributed over an area proportional to d^2. Hence, if you double distance, your power is distributed over an area 4 times as large. However, if your receiver still covers the whole area, there is (in theory) no power lost. Ideally, what you have is parallel rays transmitting the power, which would imply the area doesn't actually increase at all as distance increases

I don't know if this is how it actually works, but here's my hunch. The ISL says that the energy will decrease by 4 (AKA, spread out over twice the arc length) for a distance increase of 2x. Note that it doesn't specify any actual distance, just a ratio. If you concentrated the energy so that the arc length is what you want at distance ratio 1, then the ISL doesn't apply because you will always be staying at ratio 1 as long as the solar system doesn't go any closer or further.

I found this, seems like it might be similar not sure though:

https://www.quora.com/Does-the-inverse-square-law-apply-to-m...

This is what I think could be happening from the link:

> That is not the case with the telecom tower, or a flashlight, or a laser. In those cases, radiation is directed, not equal in every direction. The inverse square law still applies, but distance is calculated from an apparent source well behind the actual energy source.

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