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Chapter 18: Problem 30

In the direction of a particular star cluster, interstellar extinction allows only \(15 \%\) of a star's light to pass through each kiloparsec \((1000 \mathrm{pc})\) of the interstellar medium. If the star cluster is \(3.0\) kiloparsecs away, what percentage of its photons survive the trip to the Earth?

Short Answer

Expert verified
Only 0.3375% of the light reaches us from a star located 3 kiloparsecs away due to the interstellar medium.

Step by step solution

01

Determine the initial percentage of light.

Start with 100% of the star's light. This is the initial light which the star emits before it travels any distance. So, for the first kiloparsec, the starting amount of light is considered as 100%.
02

Calculate the percentage of light after one kiloparsec.

Only 15% of a star's light can travel through a kiloparsec of the interstellar medium. Therefore, apply the percentage of light that survives after every kiloparsec, which is 15%. So, through the first kiloparsec, the light is reduced by \(15\%\) of \(100\% = 15\%\).
03

Apply the percentage reduction for the second kiloparsec.

Through the next kiloparsec, the light is further reduced by \(15\%\) of the remaining percentage, which is calculated as \(15\% \) of the previous reduction \(15\% = 2.25\%\).
04

Apply the percentage reduction for the third kiloparsec.

Through the final kiloparsec, the light is again reduced to \(15\%\) of the last remaining percentage. This is calculated as \(15\%\) of the remaining \(2.25\% = 0.3375\%\). This is the light that reaches us from the star.

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