Expert: Paul Wagner - 8/10/2009

Question
I am looking for a simple explanation of calculating the distance of a star using stellar parallax. Most of the web sites I have found, even Wikipedia, seem to be college level explanations. I need to explain it to a middle school student. Can you either give me a simple explanation or a link to a site that may help. Thank you.

Answer
Hi Dan

The challenge is that using parallax also involves using Trigonometry.  The system is simple, but you do need Trig to get an actual answer.  And I don't know how to teach Trig to middle school students!

Here is one way I have explained this.  Hold your thumb up at arm's length in front of your face, and close one eye.  Now sight along your thumb to an object on the horizon.  Line up your thumb with the object on the horizon...and then close that eye and open the other one.  As you switch from one eye to the other, you can see your thumb apparently change position against the back ground object.  

So far so good? That's the basis for parallax.

The reason this works is that your eyes are separated by a known distance...about 2 1/2 inches or so) and your thumb isn't as far away as the horizon.  

Now draw a diagram of the horizon, your two eyes, and your thumb.  What you will see is that one eye lines up your thumb with one point on the horizon, and the other eye lines up your thumb with another point on the horizon.  It will look like a long skinny X.  If you move the center of the X (your thumb--or the nearby star) farther way, it won't change much against the horizon---because the differences become so small.  The X eventually becomes a long V....with center of the X meeting at the horizon.  That object has no parallax.

Here is the hard part.  Trigonometry teaches us that if we know one side of a triangle, and two of the angles, we can find the length of the other two sides.  We know the distance between our eyes, and the two angles between those eyes and our thumb by measuring them against the horizon.  So Trigonometry will tell us that our thumb is about 2-3 feet away from our eyes.  

How can we use that to measure the stars?  If we think of the Earth's orbit as our face...then the Earth in Summer is on one side of our face, and in winter it is on the other side of our face.  So now we can observe some of the closer stars against the distant objects in the Universe.  And what we discover is that some of the closer ones seem to change position a little bit between summer and winter. In  other words, they are close enough so that it looks like they move against the horizon--just like our thumb.  

Back to Trigonometry.  We know the distance between the Earth's position in summer and winter--about 186,000,000 miles.  So now we use the same equation to figure out how far some of those stars are.  It only works for stars that are close...ones that are very far away just do not appear to change...so we can't measure things that small.  

Does that help?

Good luck.  People who teach middle school are all saints.  

Paul Wagner