The calculation in Appendix E is wrong. The Earth emits longwave radiation, which are at roughly the same wavelength as the emissions of the radiator itself. Per Kirchhoff’s law, the spectral emissivity equals the spectral absorptivity. Therefore, the correct heat flux due to Earth itself radiating is epsilon x F x sigma x T_earth^4, not alpha x F x sigma x T_earth^4. The contribution from reflected solar radiation due to Earth’s albedo is correct, however.
The heat flux from infrared radiation from Earth is then 53W/m2 instead of the ~5W/m2 your model spits out. It reduces the net rejected power by about 8% in the 20C case, from 633 W/m2 to 585 W/m2. Not enough to change the overall argument, but having the correct physics is always good.
The calculation in Appendix E is wrong. The Earth emits longwave radiation, which are at roughly the same wavelength as the emissions of the radiator itself. Per Kirchhoff’s law, the spectral emissivity equals the spectral absorptivity. Therefore, the correct heat flux due to Earth itself radiating is epsilon x F x sigma x T_earth^4, not alpha x F x sigma x T_earth^4. The contribution from reflected solar radiation due to Earth’s albedo is correct, however. The heat flux from infrared radiation from Earth is then 53W/m2 instead of the ~5W/m2 your model spits out. It reduces the net rejected power by about 8% in the 20C case, from 633 W/m2 to 585 W/m2. Not enough to change the overall argument, but having the correct physics is always good.
Thanks, that’s right. I’ll just link this comment here from the EA Forum: https://forum.effectivealtruism.org/posts/CEaMp2dXKxkh3HhDt/will-we-really-put-data-centers-in-space?commentId=rM9n8CnYFdhgK95c5