Updated 2019-09-18
Planetary energy balance:
AKA blackbody radiation.
There are two conditions required for blackbody radiation:
The body must be in thermal equilibrium - has a well-defined temperature T
The body is dense/opaque such that photos can’t simply pass through it but instead bounce around many times on the way to exiting.
The total flux of blackbody radiation is given by: \(F=\sigma T^4\quad[\text{Js}^{-1}\text{m}^{-2}]\) Where $\sigma$ is the Stefan-Boltzmann constant which is 5.56×10^{-8} Js^{-1}m^{-2}K^{-4}.
For humans, our body is at 310 K, objects radiate about 500Wm^{-2} where 1W is 1Js^{-1}. If the average human surface area is 2m^{2} then we radiate about 1000W.
The surface of the Sun is around 5780K. Which radiates about 6.3×10^{6} Wm^{-2}.
Now we looked at the total flux, it’s actually an integral of the intensity for all wavelengths: \(F=\sigma T^4 = \pi\int_0^\infty I_\lambda \mathrm d\lambda\) Where $I_\lambda$ is the intensity per unit wavelength.
Temperature is the only parameter needed to describe the blackbody radiation.