Comment by wat10000
Things on earth also have access to that coldness for about half of each day. How many data centers use radiative cooling into the night sky to supplement their regular cooling? The fact that the answer is “zero” should tell you all you need to know about how useful this is.
The atmosphere is in the way even at night, and re-radiates the energy. The effective background temperature is the temperature of the air, not to mention it would only work at night. I think there would need to be like 50-ish acres of radiators for a 50MW datacenter to radiate from 60 to 30C. This would be a lot smaller in space due to bigger temp delta. Either way opex would be much much less than average Earth DC (PUE almost 1 instead of run-of-the mill 1.5 or as low as 1.1 for hyperscalers). But yeah the upfront cost would be immense.