An easy calculation is to start with the solar constant, the power (energy per unit time) produced by solar radiation at a distance of one astronomical unit. This is 1.361 kilowatts per square meter. The surface area of the Earth is , where is the radius of the Earth, while the cross section of the Earth to solar radiation is . Thus the Earth as a whole receives 1/4 of that solar constant.
Therefore the magnitude of the incident radiation flux is equal to:
where is Solar constant.
Due to the fact that the Earth reflects part of the radiation, taking into account the average Earth’s albedo over the entire spectrum, the energy flux absorbed by the planet will be equal to:
where is geometric albedo of the Earth.
In equilibrium, the flux of absorbed energy is equal to the radiated flux (expressed from the Stefan-Boltzmann law), therefore we obtain the equality
where is Stefan–Boltzmann constant and is effective temperature.So, we have
Assuming Earth re emits all the radiations it receives from the sun we have . So,
Comments