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Assuming the Sun to be a spherical body of radius R at a temperature T K, evaluate the total radiant power incident of Earth at a distance r from the Sun

1. 4πr0² R² σ T⁴ / r²
2. πr0² R² σ T⁴ / r²
3. r0² R² σ T⁴ /(4πr²)
4. R² σ T⁴ / r²

Correct answer: πr0² R² σ T⁴ / r²

Solution

The Sun radiates 4*pi*R^2*sigma*T^4. At distance r the intensity is sigma*T^4*R^2/r^2. Multiplying by Earth's intercepting cross-section pi*r0^2 gives incident power = pi*r0^2*R^2*sigma*T^4/r^2.

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