# Energy Balance and Planetary Temperatures

## ACS Climate Science Toolkit

Sun and nine planets
Credit: Calvin J. Hamilton

The temperature at the surface of Venus is high enough to melt lead. The temperature on Mars is so low that almost all its relatively small amount of water is frozen. Our Earth, orbiting between these two inhospitable neighbors, enjoys a climate that has evolved a vast variety of complex life. An appropriate temperature is one requirement for life as we know it. The factors responsible for the great differences and our good fortune are the topic of this module.

All objects, including stars and planets, radiate energy to their surroundings. The wavelengths of the emitted radiation depend on the temperature of the object. Although you cannot see the radiation from a warm radiator, you can feel the warming infrared emission absorbed by your skin. If you raise the temperature of an object high enough, some of the emitted wavelengths are in the visible region of the spectrum and you see the object glowing, first red-hot and then, as its temperature increases, white-hot like the filament of an incandescent light bulb.

The emission energies as a function of wavelength from such objects can be approximated by the Planck equation for emission from a black body. A black body is an object that absorbs all wavelengths of light that fall on it. Emission from a black body is closely approximated by the emission from a tiny hole in a hollow object held at a constant temperature and was measured in the 19th century. This module of the ACS Climate Science Toolkit is based on the black-body emission properties of the sun and planets of our solar system.

Black body emission curves graph
Credit: Jerry Bell

The Planck equation is complex and most easily interpreted graphically as in this figure. Note that the emission scales differ by a factor of a million for the hot object that represents the sun and cool object that represents the Earth. The emission from a black body goes to a maximum at a wavelength that decreases as the temperature increases. The wavelength scale in the figure is logarithmic—emission from the sun includes the visible region of the spectrum and emission from the Earth is in the invisible infrared.

The total energy flux emitted by a black body is given by the Stefan-Boltzmann equation: E = σT4, where σ is the Stefan-Boltzmann constant, 5.67 × 10–8 W·m–2·K–4 (watts per square meter per Kelvin to the fourth power). In climate science, watts, units of power, 1 W = 1 J·s–1, rather than energy units are usually used. We will, however, continue to refer to this emission as energy. The numerical value of this energy flux is equivalent to the area under the emission curve for the black body, which is shown in the figure.

Credit: United States Geological Survey

In our planetary solar system, the sun is the source of radiant energy that falls on each planet and warms its surface and atmosphere, if any. The warmed planet radiates energy back into the universe. To a reasonable approximation, both the sun and the planets emit as black bodies. In order for a planet to remain at a constant average temperature, the total energy radiated from its surface (and atmosphere, if any) must equal the total energy absorbed from the sun. In this module you can explore:

The interior of the Earth is very hot. Some of this energy is left over in the core from planetary accretion when the Earth formed, but the great majority is from radioactive decay of long-lived isotopes like 40K and 238U. The crust acts as a good insulator that makes the average flux of energy from the interior a little less than 0.1 W·m–2. Some of this energy escapes in concentrated amounts at tectonic boundaries that are a source of geothermal power and also essential to sustain life around deep seafloor vents. The total amount is only about 1/10,000 the total heat flux driven by solar radiation, and has a negligible effect on the surface temperature of the planet.

However, the interior energy of the Earth can indirectly affect the surface temperature by causing explosive volcanic eruptions that eject large quantities of sulfate-forming matter into the stratosphere. During the 1 to 3 years required to wash this debris out of the stratosphere, the sulfate particles nucleate clouds that act much like a sunshade to reduce the amount of sunlight reaching the surface and therefore produce a transient cooling effect.