Question

This is from Principles of Planetary Climate, Problem 1.13

The thick CO2 atmosphere of Venus is nearly opaque in the infrared, so observations of Venus in the infrared spectrum provide no direct information about the temperature of the ground. However, the atmosphere is nearly transparent to microwave radiation, so the microwave emission of the planet can be used to infer its surface temperature. Indeed, this is how it was inferred in the 1960s that the surface of the planet was hotter than a pizza oven, rather than the steamy jungle world earlier science fiction authors had envisioned.

a) Assuming the ground to radiate like a blackbody in the microwave, compute the net power (in W) radiated by Venus in the wavelength band from 1 millimeter to 100 millimeters, if the surface temperature is uniform at 737 K. What would the radiated power be if the surface temperature were 300 K instead? Hint: You can use the result from Problem 3.12. Why is this valid?

b) At its closest approach, Venus is about 41 million km distant from Earth. Using the 1/r2 law, what microwave energy flux (in W/m2) would be seen from Earth orbit by a microwave antenna directed toward Venus? How much microwave power would be collected by an antenna with area 100 m2?

****Problem 3.12 Show that if both ν1 and ν2 are in the frequency range where hν/kT<<1, then the total flux per steradian emitted between ν1 and ν2 is 2/3(kT/c^2) (ν2^3 −ν1^3)****

Answer 1