Midterm Solutions

# Assume that both objects radiate as uniform

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Unformatted text preview: ius 5.2 AU) from the Sun in W/m2? Flux = Luminosity/Area = L/4πd2 = 3.84x1026 W / 4π x (5.2 x 1.50x1011 m)2 = 50.2 W/m2 (b) [10 pts] What fraction of the Sun’s luminosity is absorbed by Jupiter, assuming it reflects 20% of incident sunlight? Jupiter has a radius about 0.1 times that of the Sun. Power = Flux x Area = 0.8 x 50.2 W/m2 x πRJ2 = 40.2 W/m2 x π(6.96x107 m)2 = = 6.11x1017 W Power absorbed/Luminosity = 6.11x1017 W/3.84x1026 W = 1.59x10 ­9 (c) [10 pts] Jupiter has a stable effective temperature of about 125 K. What fraction of the radiant energy coming from Jupiter’s is thermally emitted versus reflected from the Sun? Thermal emission = 4πRJ2σTJ4 Reflected emission = L/4πd2 x 0.2 x πRJ2 Ratio = 4πRJ2σTJ4 x 4πd2 / 0.2LπRJ2 = 80π d2 σTJ4 / L = 80π (5.2 x 1.50x1011 m)2 (5.67x10 ­8 W/m2 ­K4) (125 K)4 / (3.84x1026 W) = 0.97...
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