Measuring the Size of the Sun

Physics of the Mundane

Adam Johnston

This activity uses some simple optics to project an image of the Sun, and some simple geometry to determine the size of the Sun.  All one needs is a sunny day and a few simple materials, including:

"       the Sun (cloudy days won=t work)

"       measuring equipment, such as ruler, measuring tape, meter sticks, string, etc.

"       board with a pinhole

"       piece of paper or screen for projection

You should pierce a small hole (smaller is generally better B about 1-2mm is probably good) in a piece of cardboard, if there isn’t a hole already.  Hold the cardboard so that sunlight shines through the hole, and can be projected onto a piece of paper or screen.  The projection should be a rough image of the Sun.  It may be necessary to adjust the size of the hole to allow enough light to shine through it, and it may also be necessary to use some kind of shading so that the paper or screen isn’t bathed in sunlight and thus washing out the desired image.

[Optionally, you could first try this indoors, using a clear light bulb instead of the Sun.  This will give you an idea of what you’re doing before you go outside.]

By knowing that the average distance to the Sun is 150,000,000 km, one can make some measurements and do some geometry to determine the Sun=s size.  It can be shown (with a little geometry) that the following ratio is in effect:

in which the distance to the image refers to that between the screen and the pinhole.  Once data is collected, the only unknown in this equation is the diameter of the Sun, which can be solved for with some algebra. 

The measurements should be done several different times for several different image sizes.  You should consider which measurements you think are the most accurate, and how you want to decide what to report as your “final answer” for the diameter of the Sun.  (Be sure to show your work for this and all answers that you report in your notebook.)

Additional questions:

·         Notice that your meter stick can cast a shadow on a sunny day.  Describe how the length of this shadow depends on the length of your meter stick and the position of the Sun in the sky. 

·         How would this shadow be different if you were farther south?  What does this tell you about the Earth?  (Note that around 235 BC, Eratosthenes measured the size of the Earth to be around 12,700 km in diameter using a method very similar to comparing the shadows of two meter sticks.)