Why do astronomers measure “size” in

degrees?

[Introduction to Angular Measure]

The circle below shows the view through a telescope. Which object is the biggest?

What if I told you that A is a distant star larger than our Sun, B is the Moon, and C is a weather balloon? Now which would you say is the biggest?

Clearly, the size of the image that we see in the telescope depends on more than just the size of the object we are looking at. How big an object is, and how far away it is, both affect the size of it’s image. This isn’t only true for telescopes – it’s true for anything we look at. To see an example, close or cover one eye and look at someone across the room from you. Now move your thumb in front of your eye until it totally blocks your view of the person’s head. When your thumb is close to your eye, it takes up more room (“area”, to be precise) than the the person’s head.

No one would believe that their thumb is bigger than a person’s head, but that’s because we are familiar with thumbs and heads and know how big they are to start with. Astronomers have a trickier job. Often they do not know the size nor the distance to the objects that they observe. All they see is the size and position of the dots of light viewed through their telescope. Since they can’t tell which dots come from closer objects and which dots come from more distant objects, it’s impossible to say how big the things they are looking at are. Instead, astronomers measure how much “room” on the sky each object occupies – or, more precisely, it’s angular size.

Measuring the Angular Size of Your Thumb

[Materials required: a meter stick, a protractor, pencil, and paper]

This mini-activity should help you better understand how the size of an object, its distance, and its angular size are related. We can then extend these ideas to astronomical measurements.

When you hold your thumb out at arm’s length and look at it with one eye open, it takes up a certain proportion of your field of view. You can determine the exact angular size of your thumb held at

arms length by measuring the distance from your eye to your thumb and the width of your thumb. Use these measurements to draw a long, skinny triangle:

If you are familiar with trigonometry, use the lengths of this isosceles triangle to determine the angle. If you are not familiar with trigonometry, draw the diagram full size (or to scale) and measure the angle with a protractor.

The angle you found is the angular size of your thumb at arm’s length. This is the way an astronomer would describe the size of your thumb. However, since the astronomer doesn’t usually know the distances and sizes of the objects she views, she wouldn’t be able to figure out the angle the same way. Instead, she would measure the angle by measuring what fraction of the telescope’s “field of view” the object takes up. Read on¼

Field of View & Estimating Angular Size

[Materials Required: a paper towel tube (or something similar), a meter stick & a protractor]

The “field of view” is the angular size of everything you can see without moving your eyes (or your telescope). To measure your own field of view for your eyes, stare straight ahead at a spot on the wall and hold your arms straight out sideways. Slowly bring your arms forward (still looking straight ahead) until you can just barely begin to see your hands at the edge of you vision. The angle made by your arms at this point is the measure of your field of view. It should be about 160° to 170°.

Now look through the paper towel tube. How does this affect your field of view?

To determine the field of view of your cardboard tube “telescope”, make measurements and calculations similar to those you did to measure the angular size of your thumb. While a partner holds a meter stick flat against the wall, stand a few meters from the wall and look at the meter stick through your telescope. Holding the telescope steady, determine the length of the meter stick that you can see from edge to edge of your field of view. Have your partner write this down. Don’t move yet! Your partner now needs to measure how far your eye is from the wall (to make the measurement easier, this should be about the same as the distance from your toes to the wall). Use these measurements to draw a triangle and determine the angular size of your field of view.

Now that you know the angular size of the field of view of your cardboard tube telescope, you can estimate the angular size of objects you view through it. If something you look at takes up about a fourth of distance across your field of view, its angular size must be about a fourth of the angular size of your field of view. For example, if your telescope has a field of view of 3°, and an object you are looking at appears to be about 1/5 as wide as the total field of view, then the angular size of the object is: (3°) x (1/5) = 3/5°.

This is similar to how astronomers measure the angular size of objects they observe through their telescopes. Now we can go back to the diagram at the beginning of this section. The field of view shown in the diagram is 2.0°. Use this information, along with your understanding of angular size, to answer the following questions:

What is the angular size of the Moon?

What is the angular distance between the center of the Moon and star A?

The distance to the Moon is 384,000 km. Use this distance, and its angular size, to determine the diameter of the Moon.

Now Take It To The Stars:

Now that you have had some practice estimating angular size, use your cardboard tube “telescope” to estimate the angular distance between stars in the night sky and to estimate the angular size of the Moon. As a class, you may want to choose a few prominent stars in constellations everyone is familiar with. This way you can then compare your measurements as a class the next day and maybe even have a contest to see who can make the most accurate estimates.

It’s interesting to note that the angular size of objects is universal for all observers on Earth – everyone measures the same angle, regardless of the size of the telescope’s field of view. This is very important since it allows astronomers all over the world, using a wide variety of telescopes, to share there observations and measurements.