Right, but we're all busy teasing "John Doe" at the moment, because that nym desperately deserves it for all those sanctimonious posts about "silly trolls" and so on.
I wonder if anyone's mom ever named anyone "John Doe". (Or for that matter, "Fred Bloggs" or "Larry Lunchbucket" (rough USAian for "Fred Bloggs").)
You don't need a lot of visual "gain" in this situation. All you need is a reflector below the object which reflects "dark sky". It won't matter very much which part of the dark sky you aim towards.
It's not like a solar furnace, where you want to ensure that all of the ray reflections are pretty much parallel (so you can aim them towards the sun, which isn't all that wide a target).
A parabola would work. The reflector doesn't even need to use curved surfaces to work well... a regular-solid shape with a reasonable number of plane surfaces would be almost as efficient. It would be important to have the reflector (whatever its shape) be tall enough that its lip would be above the focus, so that the object in question couldn't "see" the ground.
It would work best at high altitudes (thinnest atmosphere and least haze above it), in still air.
Even without a reflector of this sort, ground-located objects can drop below freezing (frost) through this effect. The reflector system would speed this up.
The principle of 'superinsulation' is multiple radiation shields; if you have five layers of space blanket (aluminized mylar), the fourth-power law means that (assuming thermal conductivity of supports can be minimized) a hemisphere of dark sky at 4K absorbs heat from the target. The target then can tolerate a small radiation of heat from its layer-5 sunshield, which can then tolerte 1W of heat from its layer-4 sunshield, etc. If the layer-1 is at 'normal ambient' (circa 300K at earth-orbit distance from the sun), the radiative thermal resistance of five layers in series is... enormous, because those resistances are in series.
Some glasses are strong, but very poor heat conductors at low temperature.
Most of the modern sensitive radio telescopes are Cassegrain for eaxctly this reason far better to have the receiver facing up at the sky than down at the noisy ground. Early scopes didn't really have much option.
In the visible and near IR on a good clear night with low humidity the characteristic temperature of the sky radiation is roughly 80K. In the UK summer we sometimes see electric blue noctilucent clouds forming high enough in the stratosphere to catch sunlight long after dark.
It is a routine trick in cryogenics to put a radiation shield in between a cryostat and outside to greatly decrease the thermal losses.
It still works in air but you do have to isolate the surface from the bulk material of the ground. You see it happen every night with the dew forming on car roofs first as an example of faster radiative cooling.
The object reaches an equilibrium when the net flux of radiation from it is balanced by the thermal transfer of heat from the air and ground. The more sky at ~80K it sees and less ground at 300K the cooler it can get.
It isn't a huge effect but it gets you an extra few degrees net cooling.
In a vacuum, a floating object will only get (or lose) heat by radiation. So the temperature it reaches depends on the radiation it receives from the complete sphere around it. Power in radiation increases as the fourth power of absolute temperature of the radiating surface (at least if it is perfectly "black"!).
So even if a perfect reflector acts as if it were deep space at a few degrees absolute (dubious!), it is going to be massively overwhelmed at the focal point by radiation from the surroundings other than that surface.
The idea is to shield it from radiation from local warm stuff. Pretty much simple optics. Solder up a cone from copperclad FR4; it's an excellent reflector at thermal wavelengths.
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Things are cooled by radiation into the night sky. A proper reflector can enhance radiation cooling.
Google freeze at night in the desert
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John Larkin Highland Technology, Inc
Science teaches us to doubt.
Claude Bernard
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