Hipparchus: Relative Size of Earth and Moon

Copyright © 2001 by FJE Enterprises

At the left of the screen is an image of the partially eclipsed moon. By adjusting the slider at the top of the screen you can outline the earth's shadow, and thereby estimate the ratio of the earth's size to that of the moon.

While you can determine an approximate size for the earth in terms of the moon's size this way, it is not easy to determine the ratio of sizes accurately. Can you think of any other way to achieve this objective?