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%matplotlib inline

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import site,os

Q1: A satellite is in orbit 400 km above the surface, with a nadir pixel with a diameter 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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from matplotlib import pyplot as plt
import numpy as np
img = plt.imread('images/sat_problem.png')

We need to find the limits of integration for $\theta$. Simple trig gives $\theta_{max} = tan^{-1} (25/400)$

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print "angle is %5.2f degrees" % (theta_max*180./np.pi)

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#use the slide 8 formula
angle=2*np.pi*(-1)*(np.cos(theta_max) - 1)
print "angle is about %7.3f sr" % angle

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#check vs. area/R^2
print "and here is the check %7.3g, not bad" % ((np.pi*25**2.)/400**2.,)

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 problem 1. What is the flux ($W\, m^{-2}$) reaching the satellite from that pixel, assuming no atmospheric absorption/emission, in the wavelength range $10\ \mu m < \lambda < 12\ \mu m$? (Choose nearest value)

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import site
from planck import planckwavelen
flux=planckwavelen(11.e-6,300.)  #output is W/m^2/m binwidth
radiance=flux/np.pi  #turn flux into radiance
delta_lambda=2.e-6 #bin is 2 microns wide
print "answer is about %5.3e W/m^2" % flux

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