Equilibrium Equation of Thermal Radiation of Earth and Solution

The Earth is isolate on its orbit motion around the Sun. The thermal radiation on Earth determines climate warmer or colder. By Kirchhoff’s law, the thermal radian on Earth must be in an equilibrium state. Which equivalents to an optimum problem. This paper establishes an equilibrium equation of thermal radiation of Earth, transmits it to an optimum problem, and proves that the equilibrium of thermal radiation of Earth is an indifferent equilibrium, neither stable, nor un-stable, based on the Stefan-Boltzmann law and the emissivity formula. The result means that the climate neither getting warmer and warmer, nor getting colder and colder.