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Measuring The Distance to a Star

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  • 0:01 Ways to Measure Distance
  • 0:33 Surveyors & Triangulation
  • 2:29 Triangulation & Astronomy
  • 7:01 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov
This lesson will tell you how astronomers can measure the distance to a star and how it relates to the way surveyors measure distances to landmarks right here on Earth.

Ways to Measure Distance

Here on Earth, we can use familiar things to measure the distance to something. I know you can think of most of them. There's rulers, yardsticks, tape measures, and laser rangefinders. I even know of people who know the length of their fingers to approximate short distances!

But how in the world do you measure the distance to a faraway star? We don't have any ruler long enough for that. Well, this lesson will solve that mystery for you.

Surveyors and Triangulation

Have you ever driven by a new construction site, or a proposed one, and saw a man or woman wearing a hardhat with some odd-looking instrument on a tripod? They look through this instrument and it seems like they're taking pictures. Those men and women are not photographers; they are surveyors, people who measure distances and angles between points.

Let's simplify one of the methods surveyors can use to find the distance to a landmark with an easy example. An example that also happens to relate to how we measure the distance to a faraway star.

For our example, we'll pretend we want to find out how far away a mountain on the horizon is. To do this, you first take two stakes. Not the kind you eat. Rather, the ones you can drive into the ground. You put the stakes into the ground a known distance apart. The distance between the stakes is known as the baseline of our measurement.

You can then draw an imaginary line, one from each stake, to the distant mountain, to form a triangle between our three points. Then, using the surveying instruments I hinted at before, you can measure the angles the imaginary lines drawn between each stake and the mountain make with the baseline. Using simple trigonometry, you can then figure out the distance from the baseline to the distant mountain to get your answer!

This method, a method of finding the distance to a landmark by first measuring the distance between two points whose location is known and then measuring the angles between the known points and the landmark, is called triangulation. Now, the farther away the object whose distance you're trying to determine is, the longer a baseline you will need to have to measure the object's distance accurately.

Triangulation and Astronomy

This means that in order to find the distance to a star, you'll need to have a very long baseline! How long? In our example, the diameter of the Earth's orbit, which is two AU. An AU is an astronomical unit, the average distance from the Earth to the sun. Such a distance is equal to 1.5 * 10^8 kilometers, which is 93 * 10^6 miles. But, for simplicity's sake, we'll stick to just saying AU instead of the miles or kilometers involved.

Anyways, what you can do is metaphorically plant one stake by taking a photograph of a star you are interested in. Then, in six months time, as the Earth completes half of its rotation around the sun, you plant another stake by taking another photograph of the same star. The distance between the two positions of the Earth six months apart along its orbit is equal to the diameter of Earth's orbit, our baseline, which is two AU. The lines of sight from the two positions of the Earth and to the star we are observing help to form a triangle, just like from the example we talked about before.

However, when you look at your photos, you'll notice that the star you were looking at isn't in the same exact place as it was six months prior. This effect is called parallax, the apparent shift in position of an object as a result of a change in the location of the observer.

This means that the star hasn't moved; it just looks like it has moved because the Earth moved. You can easily demonstrate this concept for yourself. Go ahead and hold out a pencil vertically in front of you. Note some sort of object in the background, like a tree. Now, while holding the pencil still, close one eye and then switch eyes. Can you see how the tree looks like it's shifting to the left and to the right of the stationary pencil? The tree isn't actually moving, but it appears to be because your line of sight is. That's parallax. The farther away you hold this pencil, the smaller the parallax becomes.

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