Given: A $1\mathrm{.}25$ m diameter spherical space probe in outer space is subjected to a solar heat flux of $850\frac{W}{m^2}$ on all surfaces. The probe has solar absorptivity of $0\mathrm{.}40$ and has an emissivity of $0\mathrm{.}9.$ The probe generates $175$ W of power.

For steady$-$state conditions, what is the surface temperature of the probe?

ssume: $1.$ The surrounding temperature in space is $0$ K $.$