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Basics of Astronomy28 chapters | 325 lessons

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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.

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.

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.

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.

Since the stars we look at are so far away in space, their parallaxes are therefore very small angles. So small, they are expressed in arc seconds. More technically, a stellar parallax (p) is a term for the deviation of a star measured across one AU.

And while surveyors measure the angles at the baseline to help find the distance to an object, astronomers measure the parallax they observe instead to find the distance to a star. In any case, both a surveyor's and an astronomer's measurements reveal the same thing: a particular triangle and therefore the distance to the object, landmark, or star in question.

Because the distance to a star is way farther than the one to a mountain on the horizon, astronomers use a special unit of distance, the **parsec (pc)**, in their calculations. A parsec is the distance to a hypothetical star that has a parallax of one arc second. One parsec is equivalent to 3.26 light years (ly), or 2.06 * 10^5 AU.

Knowing all of this, we can use a very simple equation to figure out the distance to a star once we measure its parallax. All you have to do to find the distance to a star in parsecs (pc) is divide 1 by its stellar parallax (p).

For example, if a star has a parallax (p) of 0.4 arc seconds, then 1 divided by 0.4 is equal to 2.5 parsecs (pc). One parsec is equal to 3.26 light years. This means our star is 8.15 light years away.

**Triangulation** is 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. This concept is used by surveyors and astronomers to find the distance to an object by creating fixed points, a triangle, and measuring angles.

Astronomers have to account for **parallax**, the apparent shift in position of an object as a result of a change in the location of the observer. More technically, a stellar parallax (p) is a term for the deviation of a star measured across one astronomical unit. 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.

Because the stars we look at are so far away, their parallaxes are very small angles and are expressed in arc seconds. Furthermore, since the distance to a star is really long, astronomers use a special unit of distance, the **parsec (pc)**, in their calculations. A parsec is the distance to a hypothetical star that has a parallax of one arc second. One parsec is equivalent to 3.26 light years (ly), or 2.06 * 10^5 AU. Once you have found a star's parallax (in arc seconds), you can find the distance to a star (in parsecs) by dividing 1 by the stellar parallax.

Watching this lesson should enable you to:

- Summarize the process of triangulation and how astronomers use it to measure the distance to stars
- Define AU, parallax, and parsec

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Basics of Astronomy28 chapters | 325 lessons

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