Using the circles and chords method described earlier, I measured the radius of the shadow to be 17.0 cm, making the diameter of the shadow 34.0 cm. I also measured the diameter of the Moon (from the image) to be 13.8 cm. Thus, we can draw a ratio between the diameter of the shadow and the diameter of the Moon (as measured in the image):

In other words, the diameter of the shadow is 2.5 times the diameter of the Moon. If we know the diameter of the shadow, then we can determine the diameter of the Moon. Can we assume that the diameter of the shadow is the same as the diameter of the Earth?

In order to answer this question, try shining a flashlight (or a bright light) toward a soft ball. (Place the flashlight several feet away from the ball, and view the shadow several inches away from the ball. Note that the distance between the Moon and the Earth is very small relative to the distance between the Sun and the Earth.) Compare the size of the ball with the size of the shadow.

As described earlier (using the knowledge of a total solar eclipse), we can approximate the diamter of the shadow as one Moon diameter less than the diameter of Earth. Since we know that the diameter of the shadow is 2.5 times the diameter of the Moon, then we can say that the diamter of the Earth is 3.5 times the diameter of the Moon. Or,

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