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How to convert arcseconds to parsecs

Updated October 04, 2018

Your location when observing a star and the Earth's position in its orbit can affect your view of the star's surroundings and its location in the sky. The change in perspective is known as parallax and is measured as an angle between your location now, the star, and your location three months earlier or later. The value of the angle is expressed in units known as arcseconds, also known as arc seconds or seconds of arc. You need this value in order to figure out the distance to the star, which is expressed in parsecs, derived from "parallax of one arcsecond."

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  1. Convert to arcseconds if necessary. Some stars are so far away that their arcsecond values may be written as milliarcseconds. As with other metric conversions, all you have to do is divide by 1,000. For example, 3 milliarcseconds equals 0.003 arcseconds.

  2. Divide 1 by the number of arcseconds to get the number of parsecs. Don't be surprised if you find yourself working with numbers smaller than zero; Proxima Centauri, the nearest star to our solar system, has a parallax of 0.77 arcseconds. This would give you less than 1.3 parsecs. The values only get smaller as you look at stars that are farther away.

  3. Use the parsec value in Step 2 to find either the apparent or absolute magnitude of stars if you already know one of the magnitudes. Remember the apparent magnitude minus the absolute magnitude equals -5 + 5log(d), where (d) is the distance in parsecs and the log is a basic log base 10 -- use the LOG key on your calculator.

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About the Author

Suzanne S. Wiley is an editor and writer in Southern California. She has been editing since 1989 and began writing in 2009. Wiley received her master's degree from the University of Texas and her work appears on various websites.

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