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Dear Mitch,

How can we figure out how far away from the sun we are on earth?


C, R, J – The Triplets T.

Boston, MA


Dear C, R, J -- The Trips T,

The way that the experts in measuring huge distances in the sky like that (people called "astronomers") figure out how far away the sun and the different stars are from the earth is by using a method called "trigonometric parallax". . .

BUT WAIT—I promise, the name for the method sounds much scarier and harder to understand than it really is.

In fact, the whole idea is not very hard to understand once you know what the fancy words mean. So, let's just take it one step at a time, and I think you'll see what I mean.

First, do this: Stretch your arm out as far as it will go (just one arm). Then, while you keep it stretched out there, stick out your thumb (pointing it upwards.).

Next, close your left eye and notice where your thumb appears compared to something on the other side of the room. (In other words, for example, if there is a great big picture hanging on the opposite wall, which spot on the picture is your thumb covering?). Remember that spot.

Next, keeping your same arm stretched out in the same position, and keep your thumb up in the same position, and now open your left eye and close your right eye (really close it, and notice where your thumb appears compared to the things on the opposite wall. For example, if there really is a big picture there, I bet your thumb is covering a different spot on that picture, or maybe it is even completely off the picture).

But the important thing is this: You should notice that your thumb appears to move from one place to another in the air when you close a different eye. BUT, if you were careful, your thumb didn't really move. This appearance of its move (even though you tried to hold it still) is called "the parallax effect". It occurs because your eyes are separated by a small difference, probably a couple of inches or even less, but that difference in starting point for your view causes your whole line of sight to change depending upon which eye is open. If you could somehow draw a line in the air, starting from each eye, and continuing it all the way through your thumb (ouch!!), you would notice that the lines cross at a point on your thumb or inside your thumb (double-ouch!!).

And guess what? The angle between these two lines which you somehow drew is called the "parallax angle". (Remember than an angle is just two lines --or line segments -- that meet at one point and then continue out).

Well, if you know the distance between your two eyes, and you can measure that "parallax angle" of the crossing lines of each eye's sight, say with a giant angle-measurer, which is a very simple tool called a "protractor," you can figure out the distance from your face to your thumb. How? By using an area of math that is based on the relationship between angles and lengths (or 'distances') from triangles. It's a part of math is called "trigonometry".

Still, you are probably wondering, BUT HOW?

THIS WAY: Very often in math (and in other subjects) when there are three possible pieces of information, if you know two of them, and you know how all three pieces of information are RELATED, then you can figure out the third piece of information.

FOR EXAMPLE, if you know that a relative of yours lives sixty miles away (that's one piece of information), and you know that you are traveling to that person's house in a car that is going thirty-miles-per-hour (that's a second piece of information), you can figure out that it will take you two hours to get to that relative's house. (The amount of time, the two hours, is the THIRD piece of information which you did not have but were able to figure out from the other two bits of information, which you did know). So there you knew the distance, you knew the speed you were traveling, but you did NOT know how long it would take, and you were able to figure it out!

Or, if you did NOT know how far away that relative's house was, but you knew ONE FACT, you were going thirty-miles-per-hour, and you kept your eyes on your watch the whole time and saw that it took exactly two hours to get there, which is a SECOND FACT, you could then figure out the other THIRD FACT (or piece of information), which is that your relative lives sixty miles away from where you started your drive. Why? Because 30-miles-per-hour for two hours will add up to sixty miles traveled.

Okay, that's the idea you need to know for the first part of measuring the sun's distance from earth, and you need it to understand the second part.


In a very similar way to what we just did with your eyes and your thumb, we can measure the distance to the sun by having two people work together from different parts of the world. Let's say you are in Boston (Which I know you are!), and let's say you have a science partner who is standing on the opposite side of the earth (you can look at a globe to figure out where that might be!).

Now, think of you and your faraway science friend like a very spread apart pair of eyes, with each one of you being one eye, and think of the sun as your thumb, and some faraway star is the object (picture?) across the room, the "parallax angle" can be measured just as it could when you used your thumb in your own house. That's one piece of information. And since we can measure the distance between you and your partner across the world (with maps, or something called radar, for example), we now have the second of the three pieces of information. Then, from those two we can figure out the distance to the sun using a formula that is simpler than you would probably guess! But I think we should save that for another day.

And that is one of the ways astronomers figure out the distance between the sun and the earth. By the way, since both the sun and the earth move, the distance changes throughout the year, so it actually becomes important to be able to figure out distances such as these and how much they change and why they do what they do. It leads to all kinds of other information, much of which we can actually use for understanding more and more about the incredible world around us. But start with something you have in the house, like your thumb.

Hope this helps,