V1003.HW2.new.2014 - Earth and Environmental Sciences

V1003 Science & Society
Due Monday Sept. 24, 2014 in class
Homework #2
1) What is a blackbody? What is a blackbody spectrum? Why are these concepts useful to planetary
2) Calculate the emission temperatures for these nearby (sort of) stars using their wavelength of
maximum emission.
Epsilon Indi:
Tau Ceti:
Epsilon Eridani:
0.374 µm
0.426 µm
0.630 µm
0.513 µm
0.833 µm
b. Which one has the closest temperature to our Sun (refer to the lecture notes for the Sun’s
3) Now that you know its temperature, you can calculate the emission power, I, from Tau Ceti, the
closest G-class star similar to our Sun (some 11 light-years away!). Use the Stefan-Boltzmann
equation to calculate the energy flux, I (in W/m-2 , See lecture notes for help if you need it!):
I = T4.
(  = 5.67 x 10-8 Watts m-2 K-4 )
4) This star has a radius that is about 20% smaller than the Sun (5.5 x 108 meters). Use the lecture
notes if needed to calculate the emission power (in Watts) from the surface of Tau Ceti.
5) Imagine there is an Earth-like planet exactly the same Earth-Sun distance from Tau Ceti (1.5 x
1011 meters) with the same planetary radius (basically, the Earth). What is the incoming solar
radiation reaching the top of its atmosphere (in W/m2).
6) Is this number more or less than the incoming radiation to the top of Earth’s atmosphere (1365
W m-2) ? Why?
7) If this planet had some oxygen in its atmosphere do you think it would have an ozone layer?
Why or why not?
8) What are the chemical equations for natural ozone production and destruction ?
9) Would you expect to find an ozone hole at either of the poles? Why or why not?