Astronomy 105

Inverse Square Law

13. Inverse Square Law (Page 67) (Additional Problem, Set 2, Problems 10-3, 13-1)
    

    The inverse square law shows how the brightness of an object decreases as you move away from it. This is common sense: car taillights, for example, seem to get dimmer as the car moves away from you. But this can be quantified using a simple formula:

    

    The symbol indicates proportionality. This can be turned into an equation in the following way:

     

    In practice this equation is used mostly to find the relative brightness of two objects (the ratio ).
    

    Example. How much brighter is a candle when you are one meter away from it than when you are four meters away from it? Here solve for the relative brightness:

    

    The same equation is used to determine the relative illumination of planets by sunlight. For example, Pluto is 39.5 times farther from the Sun than the Earth. The ratio of sunlight on Pluto to sunlight on Earth can be found using Equation :

    

    Thus the Earth receives 1560 times more sunlight per unit area than does Pluto.

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