QUESTION #439

# If a planet was at a distance of 3.6 parsecs, how many light years away is this planet?

A parsec is a measure of distance. Something that is one parsec away is 3.26 light years away. So, the simple answer to your question is a simple multiplication problem. 3.6 multiplied by 3.26 is 11.74. So, 3.6 parsecs is 11.74 light years. Simple.

But, I am sure you are wondering how in the world we go 3.26 light years per parsec! The word 'parsec' comes from two words: parallax and second. A parsec is the reciprocal of the parallax of a distant object. I am sure that makes perfect sense!

Well, this is how parallax, seconds and reciprocals fit together. First we will look at parallax. (No pun intended!) If you hold your thumb in front of your face and look at a distant object you will see your thumb in the foreground of the distant object. Now, close one eye and note where your thumb is relative to the distant object. Open the closed eye and close the open eye. You can tell that your thumb is in a different position relative to the distant object. It is the change of the relative position of your thumb against the background of the distant object that is parallax.

Three things affect the changes due to parallax. The distance the background is from your thumb is one. As you might imagine, or even try, the farther away the background is the less your thumb will appear to move as you change eyes. The distance your thumb is from your eyes. Try this too! And third, the distance your eyes are from each other. No! Do not try this! Well, actually, you could if you had a periscope turned sideways.

Now, imagine this with the earth and distant stars. Take as the background the stars that are as far away as they can be and still be seen. In place of your thumb place a nearer star. And, instead of the distance between your eyes take the diameter of earth's orbit around the sun. If you take a picture of a near star in January and note its position relative to stars behind it and then take a picture of the same star in June you will note that the near stare appeared to move. If you make an angle with the earth at the center and the two positions of the star you would have a parallax angle. If that angle were exactly one degree than the distance of the near star must be, guess what? Exactly 3.26 light years away.

So, how is that a parsec? Well, draw a circle and draw two radii exactly one degree apart. That part of the circle's circumference between the two radii you drew is exactly one second of the arc of that circle. So a parallax angle of one degree makes an arc in the sky of one second. That is a parsec.

By the way, one second of arc is not to be confused as a measure of time! We call a second of time a second because when the second hand of a clock moves for a period of time we call one second the angle through which the second hand moved is, you guessed it, one degree!

When distant stars are measured using this parallax method you might get numbers like 0.34 degrees of parallax, or 1.56 degrees of parallax. If you divide these numbers into one you get 2.94 parsecs and 0.64 parsecs. Notice that just as you observed with your thumb the closer the nearby star (0.64Parsecs) the larger the apparent change in parallax.

It's kind of nice how all of this fits together isn't it? The smaller the number of parsecs the closer the star is and the more it appears to shift.

By the way, none of the planets around our sun are anywhere nearly this far away!
Answered by: Tom Young, B.A., Science Teacher, Whitehouse High School