This is exactly right, and an important fact is that there is a limited bandwidth for heat radiation. So essentially they need to create a giant lightbulb...
> Additionally, deep space is cold, which is accurate in that the "effective" ambient temperature is around -270°C, corresponding to the temperature of the cosmic microwave background.
There's a lot of bad information in their document too. This -270C temperature is ambient space, i.e. deep space. You may experience this when you're in the shadow of Earth or on the dark side of the moon but you're going to switch that negative sign to a positive when you're facing the sun... Which is clearly something they want to do considering that they are talking about solar power. Which means they have to deal with HEATING as well! I don't see any information about this in the document.
> he mass of radiation shielding scales linearly with the container surface area, whereas the compute per container scales with the volume
This is also a weird statement designed to be deceptive. Your radiation shielding is a shell enclosing some volume.
> Therefore the mass of shielding needed per compute unit decreases linearly with container size.
They clearly do not understand the mass volume relationship here. Density (ρ) is mass (m) divided by volume (V).
m = ρV.
Let's simplify and assume we're using a sphere since this is the most efficient, giving V = 4/3r^3. Your shield is going to be approximately constant density since you need to shield from all directions (can optimize by using other things in your system).
m ∝ ρr^3
I'm not sure what here is decreasing nor what is a linear relationship. To adjust this to a shell you just need to consider the thickness so you can do Δr = r_outer - r_inner and that doesn't take away the cubic relationship.
FWIW, i think their description for the radiation shielding is fine. Your analysis is off. If we assume the spherical case, the mass of the shielding is proportional to surface area, not the volume[0]. You might be confusing general radiation shielding and thermal shielding. Thermal shielding is easier because you can point things towards the sun, earth, and moon.
I am more concerned about heat dissipation, which should scale with surface area, but heat generation scales with compute volume.
[0]:
shell thickness, t
compute radius, r
shell volume is (r+t)^3 - r^3 = 3 r^2 t + 3 r t^2 + t^3 = O(r^2)
shielding/compute is O(r^2)/O(r^3) = O(1/r), ie their linear decrease
m = ρV.
Let's simplify and assume we're using a sphere since this is the most efficient, giving V = 4/3r^3. Your shield is going to be approximately constant density since you need to shield from all directions (can optimize by using other things in your system).
m ∝ ρr^3
I'm not sure what here is decreasing nor what is a linear relationship. To adjust this to a shell you just need to consider the thickness so you can do Δr = r_outer - r_inner and that doesn't take away the cubic relationship.
https://en.wikipedia.org/wiki/Thermal_radiation#Characterist...
https://en.wikipedia.org/wiki/Black-body_radiation
https://www.nasa.gov/smallsat-institute/sst-soa/thermal-cont...
https://ocw.mit.edu/courses/16-851-satellite-engineering-fal...