You can actually measure the size of the sun by hand! Here's how. Get an index card, a piece of white cardboard or file folder, a yardstick, a pencil, a pin, and a sunny day. With the pin, make a hole in the center of the index card. Mount the file folder (screen) at the zero end of the yardstick. Make a brackett for the index card so that it stands up on the yardstick but is able to slide (see Figure 2). Point the pin hole in the direction of the sun so that an image of the sun is projected through the pinhole onto the screen (see Figure 1). Mark with the pencil around the edge of the sun's image. Record the distance of the index card from the file folder screen (d). Then measure the diameter of the sun's image, also in centimeters (x). The index card is made to slide because the image of the sun will be bigger the farther away from the screen the pin hole is placed. But as the image gets bigger it gets fainter. Adjust the position of the pin hole that is comfortable for you to make the measurements.
As viewed from the pinhole, the angular sizes of the sun's image on the screen and the sun in the sky are the same (see Figure 1). So the ratio of the sun's actual diameter to its distance from the earth is the same as the ratio of the sun's image to the distance between the screen and pinhole:
Let S be the sun's diameter, D the earth-sun distance, x the image diameter, and d the distance from the pinhole to the screen; then
1. Solve equation (1) for S, the sun's diameter.
2. Using this equation, the measured x and d, and D determine the sun's diameter in kilometers. Compare this value with the one in your text.