Assuming merely attitude control, sure only radiative cooling is available, but its very easy to design for arbitrary cooling rates assuming any given operating temperature:

Budget the solar panel area as a function of the maximum computational load.

The rest of the satellite must be within the shade of the solar panel, so it basically only sees cold space, so we need a convex body shape, to insure that every surface of the satellite (ignoring the solar panels) is radiatively cooling over its full hemisphere.

So pretend the sun is "below", the solar panels are facing down, then select an extra point above the solar panel base to form a pyramid. The area of the slanted top sides of the pyramid are the cooling surfaces, no matter how close or far above the solar panels we place this apex point, the sides will never see the sun because they are shielded by the solar panel base. Given a target operating temperature, each unit surface area (emissivity 1) will radiate at a specific rate, and we can choose the total cooling rate by making the pyramid arbitrarily long and sharp, thus increasing the cooling area. We can set the satellite temperature to be arbitrarily low.

Forget the armchair "autodidact" computer nerds for a minute

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adrian_b 8 hours ago | parent | next [-]

Making the pyramid arbitrarily long and sharp will arbitrarily diminish the heat conductance through the pyramid, so the farther from the pyramid base, the colder it will be and the less it will radiate.

So no, you cannot increase too much the height of the pyramid, there will be some optimum value at which the pyramid will certainly not be sharp. The optimum height will depend on how much of the pyramid is solid and which is the heat conductance of the material. Circulating liquid through the pyramid will also have limited benefits, as the power required for that will generate additional heat that must be dissipated.

A practical radiation panel will be covered with cones or some other such shapes in order to increase its radiating surface, but the ratio in which the surface can be increased in comparison with a flat panel is limited.

	▲	DoctorOetker 4 hours ago \| parent [-]
		we are not discussing a schoolbook exercise, we are not calculating passive heat conduction of a pyramid heated to a base, since it's not a schoolbook exercise we can decide on the condition, we could put in heat pipes etc. its CPU/GPU clusters, so we don't have 0 control on where to locate what heat generators, but even if we had 0 control over it, the shape and height of the pyramid does not preclude heat pipes (not solid bars of metal, but having a hot side where latent heat of a gas condensing to a liquid on the cold side and then evaporating on the hot side). heat pipes have enormous thermal conductivities

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yetihehe 9 hours ago | parent | prev [-]

> The rest of the satellite must be within the shade of the solar panel,

Problem is with solar panels themselves. When you get 1.3kW of energy per square meter and use 325w of that for electricity (25% efficiency) that means you have to get rid of almost 1kW of energy for each meter of your panel. You can do it radiatively with back surface of panels, but your panels might reach equilibrium at over 120°C, which means they stop actually producing energy. If you want to do it purely radiatively, you would need to increase temperature of some surface pointing away from sun to much more than 120°C and pump heat from your panels with some heatpump.

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adrian_b 8 hours ago | parent | next [-]

When the cost of the solar panels does not matter you can reach an efficiency close to 50% (with multi-junction solar cells) and the panels will also be able to work at higher temperatures.

Nevertheless, the problem described by you remains, the panels must dissipate an amount of heat at least equal with the amount of useful power that is generated. Therefore they cannot have other heat radiators on their backside, except those for their own heat.

	▲	DoctorOetker 4 hours ago \| parent [-]
		the point is that even with 100% INefficient solar panels the pyramidal sides can be made to have an arbitrarily large area, and due to convexity of the pyramid each infinitesimal surface element of the radiating sides can emit the full hemisphere, so given any target temperature, we can design the pyramid sharp enough (same base, different height, so that heat absorbed is constant and heat emitted must equal it in steady state, then by basic thermal radiation math, the asymptotic temperature it will settle at can be made arbitrarily close to temperature of the universe, by making the pyramid sharper.)

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DoctorOetker 4 hours ago | parent | prev [-]

no matter how inefficient the solar panels, even with 1% efficiency, you could make the pyramid sharp enough to dissipate the heat stabilizing at any arbitrary low temperature (well, must still be above the temperature of CMB)