Homework 8. Angular Size of the Sun

Name: ________________________ Due 10/24 ID Number: ________________________

If we could gaze comfortably at the Sun, we would see it as a glowing circle. Imagine a narrow triangle extending from your eye to the opposite sides of the Sun, as shown just below. The angle between the long sides of this triangle, labeled with the Greek letter `' in this diagram, is the angular size of the Sun.

With very simple equipment you can observe the Sun and measure its angular size. The measurement technique is illustrated at left. You will need two index cards, a sharp pencil, a length of thread, some tape, a ruler, and a sunny day.

First, using the pencil, punch a small hole in one of the index cards. The hole should be about 1 mm or 2 mm in diameter; try to make it as smooth and round as you can.

Next, cut a piece of thread a bit longer than your arm. Take one end of the thread and tape it along the edge of one card. Take the other end and tape it along the edge of the other card. Measure the length of the thread left between the cards, and call that length `L'. The thread enables you to hold the two cards a fixed distance apart.

To make your observation, hold the two cards parallel to each other and facing the Sun. Let the sunlight shine through the hole and fall on the other card, which acts as a screen. Now move the cards apart, keeping the spot of sunlight centered on the other card. The spot will spread out and get fainter as you move the cards apart, but you should still be able to see it even when the thread is stretched between the cards. Enlarge the hole if the spot is very faint or hard to see, but don't make it any bigger than necessary.

Now with the thread stretched between the cards, measure the diameter of the spot of sunlight. Call that diameter `d'.

Having measured L and d, you can now find the angular size of the Sun. The triangle with height L and base d is similar to the triangle between your eye and the Sun, and similar triangles have the same angles. To compute the angle in degrees, use the small-angle formula:

Record your work below. First write down the values of L and d, being sure to include the units! Then calculate , using the equation just given.

Of course, no measurement perfectly accurate. How accurate do you think your measurement is? What could you do to make it more accurate?

Joshua E. Barnes (barnes@ifa.hawaii.edu)
Last modified: October 21, 2006
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