## Planetary Emission Temperature

The Earth receives almost all of its energy from the Sun. At the present time in its evolution the Sun emits energy at a rate of Q = 3.87 x 1026 W. The flux of solar energy at the Earth, called the solar constant, depends on the distance of the Earth from the Sun, r, and is given by the inverse square law, So = Q/4nr2. Of course, because of variations in the Earth's orbit (see Sections 5.1.1 and 12.3.5) the solar constant is not really constant; the terrestrial value

TABLE 2.1. Properties of some of the planets. So is the solar constant at a distance r from the Sun, ap is the planetary albedo, Te is the emission temperature computed from Eq. 2-4, Tm is the measured emission temperature, and Ts is the global mean surface temperature. The rotation period, T, is given in Earth days.

r S0 ap

109m Wm-2

Venus 108 2632 0.77

Earth 150 1367 0.30

Mars 228 589 0.24

Jupiter 780 51 0.51

Tm Ts T

K K K Earth days

227 230 760 243

255 250 288 1.00

211 220 230 1.03

### 103 130 134 0.41

S0 = 1367Wm , set out in Table 2.1, along with that for other planets, is an average corresponding to the average distance of Earth from the Sun, r = 150 x 109 m.

The way radiation interacts with an atmosphere depends on the wavelength as well as the intensity of the radiative flux. The relation between the energy flux and wavelength, which is the spectrum, is plotted in Fig. 2.2. The Sun emits radiation that is primarily in the visible part of the spectrum, corresponding to the colors of the rainbow—red, orange, yellow, green, blue, indigo and violet—with the energy flux decreasing toward longer (infrared, IR) and shorter (ultraviolet, UV) wavelengths.

Why does the spectrum have this pattern? Such behavior is characteristic of the radiation emitted by incandescent material, as can be observed for example in a coal fire. The hottest parts of the fire are almost white and emit the most intense radiation, with a wavelength that is shorter than that coming from the warm parts of the fire, which glow red. The coldest parts of the fire do not seem to be radiating at all, but are, in fact, radiating in the infrared. Experiment FIGURE 2.2. The energy emitted from the Sun plotted against wavelength based on a black body curve with T = Tsun. Most of the energy is in the visible spectrum, and 95% of the total energy lies between 0.25 and 2.5^m(10-6m).

and theory show that the wavelength at which the intensity of radiation is maximum, and the flux of emitted radiation, depend only on the temperature of the source. The theoretical spectrum, one of the jewels of physics, was worked out by Planck,1 and is known as the Planck or

In 1900 Max Planck (1858—1947) combined the formulae of Wien and Rayleigh, describing the distribution of energy as a function of wavelength of the radiation in a cavity at temperature T, to arrive at what is now known as Planck's radiation curve. He went on to a complete theoretical deduction, introduced quanta of energy, and set the scene for the development of quantum mechanics. 24,000 K

12,000 K

24,000 K

12,000 K 