In a solar system far, far away the sun's intensity is 400 W/m2 for an inner planet located a distance R away. What is the sun's intensity for an outer planet (in W/m2) located at a distance of 4 R from the Sun

 I₂ = 25 W / m²

Explanation:

Intensity is defined as the relationship between power and area

       I = P / A

the power emitted by the sun is constant

      P = I A

for the two points of interest

      I₁ A₁ = I₂ A₂

energy is distributed on the surface of a sphere

      A = 4π R²

      I₁ R₁² = I₂ R₂²

      I₂ =

let's calculate

      I₂ =    

      I₂ = 25 W / m²

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