SIZES AND DISTANCES
IN THE SUN-EARTH-MOON SYSTEM:
An Introductory Astronomy Lab

Introduction

In this excercise you will be following the methods of the Ancients (Greek Astronomers of Alexandria) to determine the sizes of the Earth, Moon and Sun and also the distances between them. Most of these measurements were quite difficult for the ancient astronomers to carry out and although you will be following their methods you will be using better observations than were available to them. In fact, you will see that the simple model which the Ancients had of the Sun-Earth-Moon system allows quite accurate determination of distances when good observations are used.

What you will be carrying out is a form of "Distance Ladder", a term which will be encountered again when learning about determination of distances to galaxies. What it means is that a very direct, local measurement of distance is extended, in a series of indirect steps (rungs), to distance estimates of objects which are much further away. In this case our distance ladder will carry us from a small terrestial distance of 780 km to the very much larger distance of 150,000,000 km, the distance to the Sun. Naturally, we cannot measure the distance to the Sun with a yardstick, we need a more indirect means of estimating this large distance and this requires that we have a good model for the Sun-Earth-Moon system. Any good scientific model lets us make new inferences about the natural world, in this case the sizes of the Earth, Moon and Sun and also the distances between them.

Remember, that although today we accept for granted the fact that the Moon obits the Earth which is itself round and orbiting the Sun, these were all revolutionary ideas in the history of science. Consider yourself as unbiased by what you have learned and imagine how hard it would be to come up with these ideas by simply looking at what you see in the sky!