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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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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Parsecs
In astrophysics, parsecs are a unit of measurement used to express distances between celestial objects outside our solar system. The term 'parsec' combines 'parallax' and 'arcsecond', referring to the technique of parallax, which measures the apparent shift of an object against a distant background due to a change in the observer's point of view. A parsec is equivalent to about 3.086 x 10^{13} kilometers. This makes it a convenient measure for astronomers who deal with vast distances where miles or kilometers would result in cumbersome figures. The star Altair, for instance, is 5.15 parsecs away, a distance that would otherwise seem unfathomable in everyday terms.
Light-year
The light-year is another astronomical distance unit, defined by how far light travels in one year in the vacuum of space. Light travels at a speed of about 299,792 kilometers per second. Over the course of a single year, this amounts to roughly 9.461 trillion kilometers. Interestingly, the light-year measures distance, not time, as the name might suggest. In practical use, knowing the distance to a celestial object in light-years helps astronomers understand how far back in time they are observing it, due to the finite speed of light. For example, if Altair is 16.789 light-years away, we are seeing light that left the star nearly 17 years ago.
Distance Conversion
Converting between astronomical units like parsecs and light-years is essential in astrophysical calculations and understanding. For instance, one parsec can be converted to approximately 3.26 light-years. This conversion facilitates comparing distances across different units that might serve different purposes in varying contexts. In the given example, Altair's distance is known in parsecs. Converting this distance to light-years gives us insight into how long the light takes to travel from Altair to Earth. Meanwhile, converting parsecs to kilometers employs a factor of 3.086 x 10^{13}, providing a perspective on the sheer scale of cosmic distances in more conventional human terms. Through such conversions, astronomers can effectively communicate distances using the most suitable units for their purpose.

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Most popular questions from this chapter

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