The background temp at Earth's orbit is due to the incidence of solar flux, which I took account of.

I'm assuming the radiators are shaded from that flux by the rest of the satellite, for efficiency reasons, so we don't need to account for solar flux directly heating up the radiators themselves and reducing their efficiency.

In the shade, the radiators emission is relative to the background temp of empty space, which is only 2.7 K[0]. I did neglect to account for that temperature, that's true, but it should be negligible in its effects (for our rough estimate purposes).

[0] https://sciencenotes.org/how-cold-is-space-what-is-its-tempe...