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from matplotlib import pyplot as plt



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%matplotlib inline

A satellite is in orbit 400 km above the surface, with a nadir pixel with a radius of 50 km. Use the approach of the geometry/radiance lecture to integrate the solid angle subtended by the satellite telescope. (Assume that the surface is flat and pixel is circular). Here's the figure with the geometry:



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img = plt.imread('images/sat_problem.png')
fig,axis=plt.subplots(1,1,figsize=(6,6))
the_img=axis.imshow(img)
the_img.set_cmap('gray')

Q1) What is the field of view of the satellite telescope, in steradians? (Use python to do the calculation below)



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Q2: Suppose the satellite is observing the ground (which is emitting as a blackbody at a temperature of 300 K) with the field of view calculated in Q1. What is the flux ($W\, m^{-2}$) reaching the satellite from that pixel, assuming no atmospheric absorption/emission, in the wavelength range $10\ \mu m < \lambda < 12\ \mu m$? (fill in the python commands in the cell below -- I used planckwavelen in the planck.py module for my answer. Don't forget that planckwavelen calculates irradiance and you are going to need radiance.)



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