Midterm Solutions

We can either use the result from d or note from c

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Unformatted text preview: Almost the same! Page 7 of 16 Physics 160 Fall 2013 Midterm Exam (d) [15 pts] Derive a general equation relating the equilibrium surface temperature Tp of a planet of radius Rp to the surface temperature T* of a star of radius R* separated by a distance d. Assume that both objects radiate as uniform blackbodies at these temperatures, and that the planet reflects a fraction A of the incident radiation back into space (this value is known as the albedo). Thermal equilibrium implies that the energy per second absorbed by the planet is equal to the energy per second emitted. The powers in and out are: Power in = σT*4 x (R*/d)2 x πRp2 x (1 ­A) Power out = 4πRp2σTp4 Power out = Power in =&gt; 4πRp2σTp4 = σT*4 x (R*/d)2 x πRp2 x (1 ­A) =&gt; Tp = 0.71 T*(R*/d)1/2 (1 ­A)1/4 Note that this is independent of the planet’s radius!...
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