Error 2
estimating cooling or energy loss due to emitted planetary radiation
Energy is intercepted and absorbed on the side that faces the sun. The earth rotates through this radiation field and it gets complicated if we try to account for everywhere the energy goes in the real system. What is discussed here is radiation from a black body, a simplifying assumption to help work through the effect of major variables as they affect a planet's average surface temperature. Regardless of which assumption we use, the law of conservation of energy still applies. Energy in must equal energy out or we've moved into science denial, again.
As a side note, we calculate average earth temperature, so the rotation of the earth isn't important in an ideal case. The side that is not facing the sun is colder and the side facing the sun at the equator is hottest but we average all this variation into one number. The earth rotates and all the planet is exposed to the sun, which spreads energy input over a larger surface area but the total input is the same. Again, we calculate average surface temperature, so differences at the poles or equator or due to rotation are cancelled out.
Very hot objects like the sun emit radiation at very high frequencies or low wavelength. The earth, being much cooler, emits long wavelength radiation however the total energy absorbed is equal to the total energy radiated minus whatever is used in chemical reactions, wear due to friction from expansion and contraction and so forth. In this application, we assume an ideal condition where the energy input is equal to the energy output.
Just to make this relevant to RIU, can you identify the region of photo-synthetically available radiation in the graph below?
The input energy is equal to:
- E = total energy intercepted (technically, energy flux = energy per unit time, in watts)
- KS = solar insolation ("solar constant") = 1,361 watts per square meter
- RE = radius of Earth = 6,371 km = 6,371,000 meters
- Albedo = Radiation that is not absorbed due to reflection = 0.31 or 0.30 by Heckler's estimate.
This and other stuff was lifted from:
http://scied.ucar.edu/planetary-energy-balance-temperature-calculate
The amount of radiation emitted by an object depends on the temperature of the object. The equation for this relationship is called the Stefan-Boltzmann law. Notice that the amount of energy emitted is proportional to the 4th power of the temperature. Energy emissions go up A LOT as temperature rises! Please note that this is settled science and has been settled for about 200 years. Even Heckler didn't rewrite this.
Stefan-Boltzmann law
j* = energy flux = energy per unit time per unit area (joules per second per square meter or watts per square meter)
σ = Stefan-Boltzmann constant = 5.670373 x 10-8 watts / m2 K4 (m = meters, K = kelvins)
T = temperature (in the Kelvin scale)
The SB law tells us how much radiation is emitted per unit area with units in Watts/square meter. In order to balance the energy equation, we need to input the surface area of the planet.
This is where Heckler makes his rather surprisingly ignorant mistake. He assumes only half the black body radiates heat. A black body is an ideal construct that is infinitesimally thin, reflects no light and emits radiation at frequencies that are relative to its temperature.
A spherical black body would radiate over its entire surface, the total radiated energy is proportional to the surface area, 4piR^2
Heckler quite rightly assumes only half the earth or a Hemisphere is illuminated by the sun at any time. The area of the surface of a hemisphere is half that of a globe or 2piR^2. This halves the surface area for radiation and forces surface temperature up compared to a sphere.
What he misses is that an idealized hemispherical black body has two sides. Using
@heckler73 's strange concept of a hemisphere-shaped black body to represent a planet, the correct term to use for surface area is 2*(2piR^2) or 4piR^2. What a relief! Planetary physicists for generations have not been proven wrong.
So, we have:
Putting it all together in energy balance equation, we get:
Rearranging algebraically and substituting terms into the equation we get:
Again, 200 years of work by planetary physicists are saved from Heckler the magnificent. Using an idealized system, the surface of planet earth sans air, and represented as a black body emitter is -19.5 C, not 88.5 C as Heckler would have us believe. This is not a trivial matter with respect to global warming theory.