Notes
The rate at which energy is emitted at all wavelengths by such a body per square meter is called its radiant flux. The radiant flux increases with temperature (think of hot coals: dull red if not too hot, much brighter/whiter if you blow on them). The precise dependence of radiant flux on temperatue is given by the Stefan-Boltzmann law (1855): radiant flux is \(\sigma T^4\), where the constant \(\sigma\) is about
The amount of energy emitted by body per unit time is its radiant flux multiplied by its surface area. Energy per unit time has the units of power, measured in watts. The radiant energy per unit time emitted by a spherical body of radius \(R\) is therefore
The solar flux (incoming energy) at the radius of the Earth’s orbit is \(S = 1.37\) kilowatts per square meter. We now ask: how much of that incoming energy is absorbed by the Earth? We know that certain fraction is reflected back into space, while the rest is absorbed. Let \(\alpha\) be the fraction of the energy whih is reflected. This is called the albedo. The albedo of the Earth as a whole epends on cloud cover, the extent of the polar ice caps, etc., but is presently about \(0.3\).