Answer:
the relative brightness of the three stars as seen from Earth is:
-The star that is 100 light years away has a brightness of 1 times its actual luminosity.
-The star that is 200 light years away has a brightness of 1/4 times its actual luminosity.
-The star that is 300 light years away has a brightness of 1/9 times its actual luminosity.
So, the star that is closest to Earth (100 light years away) appears the brightest, while the star that is farthest away (300 light years away) appears the dimmest.
Step-by-step explanation:
The brightness of a star depends on its luminosity (the total amount of energy it emits per second) and its distance from Earth. The luminosity of a star is a characteristic property of the star itself and is not affected by its distance from Earth. However, the distance of a star from Earth does affect the amount of starlight that reaches us, and this is what determines its apparent brightness as seen from Earth.
The amount of light energy reaching Earth from a star decreases with distance, following the inverse square law. This means that if we double the distance of a star from Earth, the amount of light energy reaching us decreases by a factor of 4. Similarly, if we triple the distance of a star from Earth, the amount of light energy reaching us decreases by a factor of 9.
In this case, the three blue giant stars are identical, which means they have the same luminosity. However, their distances from Earth are different. The star that is 100 light years away from Earth has its light energy spread out over a larger distance than the star that is 200 light years away, which in turn has its light energy spread out over a larger distance than the star that is 300 light years away.
Using the inverse square law, we can calculate the relative brightness of the three stars as seen from Earth:
-The star that is 100 light years away is at a distance that is 1 times closer than the star that is 200 light years away, and 3 times closer than the star that is 300 light years away. Therefore, its brightness as seen from Earth is (1/1)^2 = 1 times its actual luminosity.
-The star that is 200 light years away is at a distance that is 2 times farther than the star that is 100 light years away, and 1.5 times closer than the star that is 300 light years away. Therefore, its brightness as seen from Earth is (1/2)^2 = 1/4 times its actual luminosity.
-The star that is 300 light years away is at a distance that is 3 times farther than the star that is 100 light years away, and 1.5 times farther than the star that is 200 light years away. Therefore, its brightness as seen from Earth is (1/3)^2 = 1/9 times its actual luminosity.
Therefore, the relative brightness of the three stars as seen from Earth is:
-The star that is 100 light years away has a brightness of 1 times its actual luminosity.
-The star that is 200 light years away has a brightness of 1/4 times its actual luminosity.
-The star that is 300 light years away has a brightness of 1/9 times its actual luminosity.
So, the star that is closest to Earth (100 light years away) appears the brightest, while the star that is farthest away (300 light years away) appears the dimmest.