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 ï¿½parsecï¿½ 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 earthï¿½s 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 circleï¿½s 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
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.
Itï¿½s kind of nice how all of this fits together isnï¿½t 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!
Tom Young, B.A., Science Teacher, Whitehouse High School
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