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Chapter 1: Problem 31

The star Altair is \(5.15\) pc from Earth. (a) What is the distance to Altair in kilometers? Use powers-of-ten notation. (b) How long does it take for light emanating from Altair to reach Earth? Give your answer in years. (Hint: You do not need to know the value of the speed of light.)

Short Answer

Expert verified
The distance to Altair is \(1.58939 \times 10^{14}\) km and it takes light approximately 16.79 years to travel from Altair to Earth.

Step by step solution

01

Conversion of Parsecs to Kilometers

Altair is given to be 5.15 parsecs away. To convert this to kilometers, multiply by the conversion factor for parsecs to kilometers which is \(3.086 \times 10^{13}\) km/pc. \[5.15 \, \text{pc} \times 3.086 \times 10^{13} \, \text{km/pc} = 1.58939 \times 10^{14} \, \text{km}\] Note that the 'pc' cancels out leaving the answer in kilometers.
02

Conversion of Parsecs to Light-years

To find out how long it takes for light to reach from Altair to Earth, convert the given distance from parsecs to light-years. The conversion factor for parsecs to light-years is approximately \(3.26\) light-years/parsec. \[5.15 \, \text{pc} \times 3.26 \, \text{light-years/pc} = 16.789 \, \text{light-years}\] Remember that a light-year is the distance light travels in a year so the 'light-year' can be interpreted as 'year'.

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