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The concept of a sun gun is of a parabolic reflector, placed it orbit around a planet, which focuses sunlight as a deadly beam on a specific point of the surface.
What I want to know is this: what if, to deter such attacks, sun guns were built on the surface; reflecting sunlight back into space? Admittedly, the filtering effect of the atmosphere might affect the beam’s intensity, but then presumably it would do the same to a space-based sun gun in orbit.
Would such a weapon work?
No, scale issues
Sending the light down to the planet is easy.. all you'd need to focus this weapon is clear skies, accurate servo positioning, a life camera connection and a telescope. Using a cursor on a map, the device can be positioned before actually turning the mirrors directing the light.
Going the other way (up) ...
Hitting a satellite with a laser weapon can be done, but I doubt if reflected sunlight could be used for that. A satellite can be destroyed by melting it, but the focusing region would be far smaller than a target spot on the planet. It would require very accurate focusing of a huge parabolic mirror.
A defense on the planet reflecting the attack light back to the satellite is impossible imho. The light spot on the planet will be too large to reflect with a single defensive weapon.
It would not so much be a sun 'gun' (i.e. not a single 'thing', not fast), but it would be able to destroy pretty much anything in orbit... unless that object was built 'sun-gun-bulletproof' :)
The suns radiation is filtered by the atmosphere - about half of the energy actually arrives on ground level. This filtering is not uniform, though - some wavelengths are completely filtered out, some come through pretty unhindered. For the reverse journey we have to account for this. Both the orbit of an object and the suns angle of incidence at any given time are computable within incredibly tight margins.
The angle of a mirror to reflect the sunlight towards this object is thus also easily computable in advance. This makes the servos mechanically very unproblematic, we can build as many flat plate mirrors (for simplicitys sake; we could also go parabolic, but why complicate things for no real gain?) scattered over earths surface as we are willing to build. About 50% of our reflected light will actually make it through to space, now it's just a question of scale. Reflectivity comes into play, but we can only build ~96% reflective, so the difference between targeting a 'perfect' reflecting body vs a black body is just that we need 20x more mirrors for the same effect.
If the target knows what's coming though, the going gets tough. Anything we heat up, itself starts to radiate, with a factor of T⁴; meaning for every doubling (2x) of temperature the object radiates (2x 2x 2x 2x) 16 times the energy it did at lower temperature. We need to overmatch that radiated energy to keep heating. An object around the melting point of tungsten (3700K) radiates 10627180W/m², i.e 10.5MW/m² - any other means of cooling vanish behind that.
So we need to get 11MW/m² up into LEO to make an object with a tungsten heat shield suffer. We need about 10m² of earthbound mirror to get 1kW/m² back into LEO, so 11 000m² of mirror array will do the trick. Let's go for overkill and have one square kilometer (1000 000m²) of individually aimed mirror plates, and we are golden.
This is not in the realm of a few IKEA mirrors and an Arduino, but we have both proven to have the aiming capabilities (telescopes solve the same problem), the capabilities in manufacturing precise mirrors (especially if we allow them to be flat, and go for an array instead of a perfect bowl) and the computational chops (again, telescopes) do solve this. The invest would be far, far beyond what a rocket with warhead would cost but its definitely feasible.
A dyson swarm would work. https://en.wikipedia.org/wiki/Dyson_sphere#Dyson_swarm That way each of the sections could be drones,and could have a reflector or two to each. then you can rearrange them for precise targeting. Instead of building the swarm around the sun, build it around the earth in low orbit.
Sun Guns need a lot of surface area to be able to attack a relatively small target. The problem with making sun guns for destroying other sun guns is that it would take an incredibly long time to do any significant damage to a sun gun using another one. Assuming your solar weapon is built in a nice cloud free desert, it would take over 1000 square meters of mirrors to be able to eventually heat up a single square meter of orbital sun gun hot enough to melt the silver backing and potentially damage part of the attacker's sun gun... and that is assuming they stick with basic silver and glass mirrors, if sun gun on sun gun warfare is to be expected, then the silver reflector could be sandwiched between borosilicate glass plates which would make counter beams even far less efficient than that. Basically it would take each weapon days of shooting each other to do any meaningful damage.
That said, mirrors shatter pretty easily. If there is one thing giant mirrors don't like, it's getting hit by little fast moving rocks; so, the best way to destroy a weapon made out of lots of mirrors is to hit it with lots rocks.
A far more effective counter weapon would be some sort of gravel missile. Basically you launch a missile in the general direction of the mirror array and protect it with a thermal shield similar to that used for atmospheric re-entry. As it turns out, it does not matter how many mirrors you use, there is a limit to how hot you can make a target using sun light for um reasons... so, if you focus on really good heat shields you can make your missile exceedingly hard to destroy with a sun gun. Then once you get close enough, you release a giant cloud of gravel or sand in the sun gun's general direction.
