P = the power of waste heat the radiator can get rid of (watts)
σ = 5.670373×10-8 = Stefan-Boltzmann constant (W m-2K-4)
ε = emissivity of radiator (theoretical maximum is 1.0 for a perfect black body, real world radiator will be less. Should be at least 0.8 or above to be worth-while)
A = area of radiator (m2)
T = temperature of radiator, this assumes temperature of space is zero degrees (degrees K)
x^4 = raise x to the fourth power, i.e, x * x * x * x
Probably bigger if you don’t want the coolant to be boiling hot.
…Do you know how expensive that would be?
I’ll give you a hint: orders of magnitude more expensive than geothermal loops for Earth-based datacenters. And even those are apparently too expensive for them to construct.
Musk is completely delusional, and he’s surrounded by yes men telling him want he wants to hear.
I did the math for it, and you’d need a radiator at least a kilometer wide for a ‘typical’ datacenter setup, according to the equation here: https://projectrho.com/public_html/rocket/heatrad.php
Probably bigger if you don’t want the coolant to be boiling hot.
…Do you know how expensive that would be?
I’ll give you a hint: orders of magnitude more expensive than geothermal loops for Earth-based datacenters. And even those are apparently too expensive for them to construct.
Musk is completely delusional, and he’s surrounded by yes men telling him want he wants to hear.