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(B) The total power radiated by the sun is given by the Stefan-Boltzmann law: $P = \sigma A_{sun} T^4 = \sigma (4\pi R^2) T^4$.At a distance $r$ from

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$\pi r_0^2 R^2 \sigma T^4 / r^2$

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(B) The total power radiated by the sun is given by the Stefan-Boltzmann law: $P = \sigma A_{sun} T^4 = \sigma (4\pi R^2) T^4$.At a distance $r$ from the sun,this power is spread over a spherical surface area of $4\pi r^2$.The intensity $I$ of radiation at distance $r$ is $I = P / (4\pi r^2) = (\sigma 4\pi R^2 T^4) / (4\pi r^2) = \sigma R^2 T^4 / r^2$.The Earth intercepts this radiation with its cross-sectional area,which is $\pi r_0^2$.Therefore,the total radiant power incident on Earth is $P_{Earth} = I 	imes \pi r_0^2 = (\sigma R^2 T^4 / r^2) 	imes \pi r_0^2 = \pi r_0^2 R^2 \sigma T^4 / r^2$.

Assuming the sun to be a spherical body of radius $R$ at a temperature of $T \ K$,evaluate the total radiant power incident on Earth at a distance $r$ from the sun (where the radius of the Earth is $r_0$).

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