Find the distance to a Sun-like star (L=3.8×1026 watts) whose apparent brightness at Earth is 1.0 x10-10 watt/m2.

Question

Find the distance to a Sun-like star (L=3.8×1026 watts) whose apparent brightness at Earth is 1.0 x10-10 watt/m2.

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Thạch Thảo 5 years 2021-08-12T21:41:07+00:00 1 Answers 57 views 0

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  1. Jezebel
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    2021-08-12T21:42:08+00:00
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    Answer:

    5.49 x 10^17 m  is the distance between the sun-like star to the earth

    Explanation:

    Radiation intensity on Earth = 1.0 x 10^-10 W/m^2

    Power of radiation of the star = 3.8 x 10^26 W

    Recall that the intensity of radiation is given as

    I = \frac{P}{A}

    where

    I = intensity of radiation

    P = power of radiation

    A is the area through which the radiation spreads out in all three dimensional direction.

    A = \frac{P}{I} = \frac{3.8*10^{26} }{1.0*10^{-10} } = 3.8 x 10^36 m^2

    This area is spread out in the form of a sphere of area

    A = 4\pi r^{2} = 4 x 3.142 x r^{2}

    3.8 x 10^36 = 12.568r^{2}

    r^{2} =  (3.8 x 10^36)/12.568 = 3.02 x 10^35

    r = \sqrt{3.02*10^{35} } = 5.49 x 10^17 m   this is the distance of the star to the Earth

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