Angular Size of The Sun and Its Physical Size (Diameter)
Box Instrument
Try to obtain a cardboard box, which is at least 3 feet long. Cut a small square
into the center of the front end of the box. Tape some aluminum foil over the square hole
in the front. Punch a tiny hole through the foil with a pin, trying to be as close to the
center of front end of the box as possible.
Next, tape a sheet of white paper on the inside of the other end of the box. Leave
part of the top of the box open so you can see the sheet of paper to measure the image
size. Tape a section of photocopied ruler like this one near (but not at the center) of the
screen to measure the image size in cm.
Figure 1. Ruler that will be taped inside the box, on the screen
Front of box
Figure 2. The main elements of our instrument
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Figure 3. Three large corrugated cardboard “grocery” boxes taped together
Above is an alternative way to make a long box from short boxes if you can’t find
a long one. Three shoe boxes are useful. Indoors, try pointing your box at an unshielded
light bulb or unshaded sunny window to see an image of the light or window.
Figure 4. The use of the instrument you created
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Mirror Method
Rather than a box, one can use a mirror with a piece of card board over it. A small hole
is punch in the card like that from a notebook paper hole punch. As shown in the
photographs below, a really good mirror to use is one in a lady’s face powder compact.
The compact is set on a table reflecting the image horizontally to a distant screen taped
on a shaded wall as shown in the second figure below. The use of a ruler to measure the
diameter of the image is shown. With the mirror, one can make the image much more
distant than convenient with a box. A tape measure is useful to measure the large
distance from the mirror “pin-hole” to the screen. If one is forced to use inches to
measure the distance and image size, remember that ½ inch is 0.5 inch, ¼ is 0.25 inch,
1/8 is 0.125 inch etc.
Figures 5 and 6
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Question 1
Is the image right side up or upside down? Check figure 11 and explain why.
Now point your cardboard box at the Sun. You can do this without looking at the
Sun by observing the shadow, which the box casts on the ground. When the shadow is at
its smallest and has the same shape as the ends of the cardboard box then you are very
close to being pointed directly at the Sun. Move the box about slightly until a small
image of the Sun appears on the white paper.
Question 2
Measure the diameter of the image of the Sun and the length of the box as accurately
as possible (in cm). What are your values?
Now study the figures again. Note that the angle made by the Sun as seen from
the pinhole is the same as the angle made by the Sun’s image at the pinhole. Also notice
that the ratio of the diameter of the Sun to the distance to the Sun is the same as the ratio
of the diameter of the image of the Sun to the distance from the pinhole. Thus, if we
could form an image 93,000,000 miles from the pinhole it would have the same diameter
as the Sun.
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Figure 7. Diagram illustrating the principle of using your simple instrument
You can figure out the angular diameter of the Sun using the formula:
angular diameter of the Sun  57.3 o 
diameter of the image
length of box
Question 3
Now calculate the diameter of the Sun in miles (or km) using the formula below. Show
your work.
diameter of image
diameter of Sun diameter of Sun


length of box
93,000,000 miles 150,000,000 km
`
Question 4
What item of data are you using without having measured it yourself in this
calculation of the Sun’s diameter?
If you made a similar observation of the Moon with your instrument you would
find the angular diameter of ½ degrees.
Question 5
How does this angular size compare to the value you found for the Sun? Since the
Moon is closer to us than the Sun is, which is larger the Sun or the Moon? Explain
your reasoning.
Question 6
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Divide the size of the Sun you obtained by the size of the Earth (8,000 miles in
diameter). Evaluate exactly how significant is the Earth compared to the Sun.
Finally, if you are ever so fortunate as to view a solar eclipse, your pin-hole camera is the
safe way to do it.
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