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10 December, 20:39

The intensity of light from a star varies inversely as the square of the distance. If you lived on a planet ten times farther away from the sun than the Earth, how would the light intensity of the sun compare with that on Earth?

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  1. 10 December, 21:08
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    the intensity of the sun on the other planet is a hundredth of that of the intensity of the sun on earth.

    That is,

    Intensity of sun on the other planet, Iₒ = (intensity of the sun on earth, Iₑ) / 100

    Explanation:

    Let the intensity of light be represented by I

    Let the distance of the star be d

    I ∝ (1/d²)

    I = k/d²

    For the earth,

    Iₑ = k/dₑ²

    k = Iₑdₑ²

    For the other planet, let intensity be Iₒ and distance be dₒ

    Iₒ = k/dₒ²

    But dₒ = 10dₑ

    Iₒ = k / (10dₑ) ²

    Iₒ = k/100dₑ²

    But k = Iₑdₑ²

    Iₒ = Iₑdₑ²/100dₑ² = Iₑ/100

    Iₒ = Iₑ/100

    Meaning the intensity of the sun on the other planet is a hundredth of that of the intensity on earth.
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