Assuming the sun to be a spherical body of radius R at a temperature of T K, evaluate the total radiant power incident on the earth, at a distance r from the sun, where r₀ is the radius of the earth and σ is Stefan's constant.

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(3) (π r₀²R²σ T⁴)/(r²). Idea: find the intensity reaching the earth's orbit, then multiply by the area the earth actually blocks. Power leaving the sun, by Stefan's law over its whole surface: P=σ(4π R²)T⁴. At distance r this is spread over a sphere of area 4π r², so the intensity is I=(σ 4π R²T⁴)/(4π r²)=(σ R²T⁴)/(r²). The earth intercepts this parallel beam over its shadow disc, of area π r₀². P_incident=I×π r₀²=(π r₀²R²σ T⁴)/(r²).

Assuming the sun to be a spherical body of radius R at a temperature of T K, evaluate the total radiant power incident on the earth, at a distance r from the sun, where r₀ is the radius of the earth and σ is Stefan's constant.

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