[typ]

Assuming that we place an iron ball (ideal sphere-shaped and thermal conductivity) on the SSO (solar synchronous orbit), how hot can the object be?

Given the solar constant 1361 W/m^2, you can calculate the temperature range based on the emissivity and absorptivity. With the right shape and “color”, the equilibrium temperature can be cooler than most people thought.

I suppose that a space data center powered 100% by solar is no different than this iron ball in principle.

[eldenring]

The ideal shape would be a shaded, flat panel perpendicular to the sun right?

[typ]

That should be better than a sphere. Though I imagine there could be some fancier 3D geometry designs.

Even for a simple sphere, if we give it different surface roughnesses on the sun-facing side and the "night" side, it can have dramatically different emissivity.

[adastra22]

About 120 degC.