Find the distance to a Sun-like star (L=3.8x1026 watts) whose apparent brightness at Earth is 1.0 x10-10 watt/m2.

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

=

where

= intensity of radiation

P = power of radiation

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

A = = = 3.8 x 10^36 m^2

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

A = = 4 x 3.142 x

3.8 x 10^36 = 12.568

=  (3.8 x 10^36)/12.568 = 3.02 x 10^35

r = = 5.49 x 10^17 m   this is the distance of the star to the Earth

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