Measuring the Diameter of the Sun

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Introduction

The Sun is without a doubt the largest object in our solar system, but how do we know exactly how big it is?   Again observation comes to our rescue.

This is a team activity!  Each team should discuss how best to proceed and what they are trying to accomplish.

This activity uses the technique known as a pinhole camera.  A pinhole camera is a safe and easy way to stduy the Sun.  Any shoebox or cardboard tube will work.  Your team's pinhole camera will use the similar traiangle formul D/L = d/l.  You will measure d and l (the diameter of the image of the sun and the distance between the image and the pinhole), you know L, the distance to the sun (150 million km).  You can then solve for D, the diamter of the sun, in kilometers.  See the figure below.

 
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QUESTION!
Can you use the same method to determine the diameter of the moon?  Why or why not?
 

Now lets construct the pinhole camera.

1.  Open up your shoebox.  On one of the end walls, tape the white sheet of paper or the graph paper.  This is the screen where you will see the sun.

2.  On the wall opposite the screen, cut a 1x1 inch hole a little to the right of the center of the wall.  On the left side of the same end, cut another hole about 2 inches by 2 inches (for viewing).

3.  Glue a piece of aluminum foil over the 1 x 1 inch hole in the box.  With the pin, poke a small hole in the center of the foil.

4.  Measure the distance from the hole to the screen in centimeters.  Write this number on the inside of the shoebox.  This is "l".

5.  If you use white paper, tape a copy of the ruler onto the white piece of paper (for measuring).  Put the lid back onto the box.  This is the camera.  It is ready to use.

6.  If you use a cardboard tube, simply tape the aluminum foil over one end and carefully poke a pin hole in the center.  Tape the graph paper (it will be more translucent if you lightly grease it first) to the other end.  Record the length of the tube as "l".  This is the camera, ready to use.
 

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Useing your camera

NOTE:  Never look directly at the sun!!!

1.  Use the camera to get an image of the sun.

2.  Measure the diameter of the image that you see when you look into the pinhole camera.

3.  If you use a tube camera, aim the end with pinhole toward the sun.  Measure the image of the sun that you see on the back of your paper.  Recorde the diamter of the image as "d".
 

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At last the diameter

Sine we know the distance to the Sun (L), we can now determine the sun's actual diameter (D).  The key is the similar triangle formula:
D/L = d/l

We have measured l and d.  Since L is known, we can determine D.  All you need to do is to solve for the unknown and substitue.  The distance to the sun is L = 150,000,000 kilometers.  Your answer will be in kilometers.  Now determine your error from (D- Ro)/Ro, where Ro is the actual diameter of the Sun:  Ro = 700,000 kilometers.

A table similar to the following may prove useful.

Distance image to pinhole 1(mm) = _______________
 
 
Try
Distance d(mm)
Sun's Diameter (km)
Error (D-Ro)/Ro
1
2
3
Average
 
Questions:

1.  Does it matter what units you use to measure the diamter of the sun's image or the distance from the pinhole to the image?  Explain.

2.  This methods assumes you know the distance to the sun.  could it be sued to the distance to the sun?  What do you need to know and what would the formula look like?