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f10_oct26 - Thermal Equilibrium(from 10/12 Ast 307 Oct 26...

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Ast 307 - Oct. 26 , 2010 ch. 16: Our Star, The Sun Thermal Equilibrium (from 10/12) Consider a solid body orbiting the Sun. It is heated by absorbing some of the sunlight that falls on it. What happens to the sunlight that it doesn’t absorb? If it behaves like a blackbody (obeys the laws of bb radiation), it radiates energy at a rate given by: P out = Surface Area x ! T 4 = 4 ! R 2 ! T 4 (for a sphere) The temperature will come to equilibrium if the radiated energy output (energy per second = power) equals the absorbed energy per second. Calculating the equilibrium temperature The absorbed energy is the flux of sunlight multiplied by the projected area of the rock that faces the Sun. P in = A face x F sunlight = ! R 2 F sunlight The strength (flux) of the sunlight falling on it is determined by the inverse-square law of light: F sunlight = L sun / (4 ! d 2 ) where d is the distance from the Sun (in what units?) and L sun is a known quantity. To find T eq : Do the math For a sphere, A face /A surface = ! , because the incident light is virtually parallel & sees a projected area of " R 2 . P out = A surface " T eq 4 = P in = A face F sunlight T eq 4 = F sunlight " A face A surface # T eq = F sunlight " A face A surface 4 = F sunlight 4 " $ % & ' ( ) 0.25
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