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It's well known that we can focus sunlight with a parabolic dish to collect heat. But if we look at the thermal images of the sky we can see that the clear blue sky is quite cool. So by turning the parabolic dish to a clear blue part of the sky, can we exploit its coldness to cool down the object at the focus?

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    $\begingroup$ You can stand in the shade of the dish, and it will be cooler than standing in the sun. $\endgroup$ – The Photon Jun 16 at 17:00
  • $\begingroup$ @ThePhoton And definitely more cooler than standing in the focus when the dish points towards the sun. The question is that whether focused heat transfer works both ways, so if you point the dish towards a cold area a of the sky, would the object lose heat faster than putting it just in a shade? $\endgroup$ – Calmarius Jun 17 at 8:51
  • $\begingroup$ Rather than focusing the "cold" you might reduce the "warm". Right as with dark and light. $\endgroup$ – Alchimista Jun 17 at 13:43
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Not exactly a parabolic dish method, but it is possible to cool things this way. The Persians used to make ice for sherbet even in the hot summer by filling shallow pans with water and leaving them out on clear nights. The water would freeze even though the ambient air temperature was never below freezing. See Nocturnal ice making in Early India and Iran.

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Coldness is not radiated in beams like infrared radiation. It is the absence of heat, and you cannot concentrate it with a parabolic reflector.

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    $\begingroup$ No, but the reflector should allow the object to radiate heat away in more directions, shouldn't it? (Radiation from the object towards the reflector will be reflected towards the sky, the same as if the reflector were also sky) $\endgroup$ – user253751 Jun 16 at 23:56
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Without our atmosphere, the sky would be equivalent to a black body at 3K. A mirror (insulated on the back) would shield you from radiation coming from the ground, effectively making you surrounded by the black body.

With the atmosphere it is more complicated. This paper (see Figure 2) describes using mirror cones to restrict the angular range of the apparatus to around the zenith direction.

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