# Size of the Sun

Project for Elementary Astronomy

In this project you will make a simple measurement of the Sun using a homemade pinhole projection device, then use this measurement and the known distance to the Sun to calculate the Sun's diameter. The key to getting good results is making careful observations.

WARNING: At no point in this project do you need to look directly at the Sun. Directly looking at the Sun can cause serious and permanent damage to your eyes.

To conduct this observing project, follow this procedure:
• Construct a solar pinhole projector like the one shown in the figure above. You will need some heavy cardboard or cardstock, some aluminum foil, and a sheet of white paper on a clipboard to use as a projection screen. The larger the piece holding the pinholed aluminum foil the better; it will cast a darker shadow on your drawing surface, making it easier to sketch the Sun. The hole in the cardboard, which is covered by the aluminum foil, should be only an inch or two across.
• You may try several different pinhole sizes. Small holes, made with a single pin-prick, work for short projections (a meter or so), while larger pinholes work for larger projections (images have been projected over 20 meters!). In general, smaller pinholes are better. Start small; you can always make a small pinhole bigger!
• Make your observations on a clear day when the Sun is reasonably high in the sky. Rigidly support the pinhole device on a ladder, chair back, camera tripod or post (for example). The observations will work best if the screens are all perpendicular to the direction to the Sun (especially the drawing screen).
• Use the pinhole to cast an image of the Sun on your screen. Make sure that the projected image is many times larger than the pinhole itself; if it isn't, move the screen farther back. Outline the image with a pencil, then measure its diameter and its distance from the pinhole. Repeat this procedure at different distances (and with different pinhole sizes if you wish) to collect at least 5 measurements.
• One way to make accurate measurements is to pre-draw precise circles of different sizes on your drawing screen, then adjust the distance to the pinhole so the Sun's image exactly fills each circle. This reduces your field measurements to only the distance between the screens.
• If you have trouble seeing the projected image of the Sun at a great enough distance, try setting up your viewing screen so it is mostly shaded from the sky. It is actually best to make your measurements indoors, with the sun shining in a south-facing window.
• If possible, take a photo of your observational setup showing both the pinhole device and the projection screen. Include this photo in your report.
To complete the project, include the following in your analysis:
• The estimate of the solar diameter is based on the idea of similar triangles; in this case the two triangles are the one formed by the solar image with the pinhole, and the one formed by the Sun and the pinhole. The analysis of these similar triangles says that the ratios of the diameters to distances are equal:
• Look up the known distance to the Sun, and use the above formula to calculate the diameter of the Sun for each of your measurements. Be careful to use the same units in all cases. I recommend you work in meters. Round off your answers (for the sun's diameter) to the nearest million meters or so.
• Average your results and compare them to the official value of the diameter of the Sun. Calculate the percentage difference between your result and the official value. Cite your source(s) for the distance and for the official value of the diameter.
• Your report should also explain how the distance to the Sun (which you used in your calculation) is measured. Unfortunately, this measurement is much more difficult so you won't be able to make the measurement yourself. Be sure to cite the whatever sources you use for this information.
• Please attach your pinhole device (perhaps cut down to a reasonable size) and your projection screen (with sun images drawn) to your report. If you enlarged your pinhole in the course of your observations, be sure to indicate which pinhole sizes were used for which observations.
• Be sure to follow the general instructions applicable to all projects.