Sizing Up an Eclipse

Here's a real photo of a recent eclipse, described in detail in the amateur astronomy magazine Sky and Telescope. Notice the curved edge of the shadow, much shallower and not centered the way a normal moon phase is, as in these drawings by Galileo. Incidentally, what is the shape of a normal lunar phase? (Hint below) Aristotle pointed out that the curved shadow line in an eclipse implied that the earth was a sphere, because only that figure always casts a circular shadow.

We can see how (relatively) big the circular shadow is by drawing a circle to fit the shadow edge and comparing it to a circle that fits the moon. If you have a Browser that supports Java, you can do that right now.

• Draw the outline of the shadow by clicking on a point on the edge of the shadow on the moon, then drag until the circle fits the shadow edge. (click on the undo button if you want to try again). This is a little tricky to judge: try it too large and too small to see the difference.
• Then draw the outline of the moon by clicking on the edge of the moon and dragging to fit the moon. You can see the ratio of the sizes of the two circles.

Historical footnote for sticklers: if you don't have telescopes and photography, it's really hard to measure the shadow size so directly. (A class recently tried it, though mostly with binoculars.) The ancient Greeks actually did it by timing how long the eclipse lasted, as a fraction of a month, which gives the angular size of the shadow. Details are trickier, since the moon doesn't go through the center of the shadow.

You will have noticed it's not easy to decide on a definite size, just like the Greeks. If you took the hint in the drawing program, you got the "right" answer, about 2.7 for the ratio. Offline extra credit: you now know enough to reverse the Greek method and compute how long a (maximum) lunar eclipse lasts.

So how do we use the dragonmouth (shadow) size? A simple diagram and the concept of similar triangles. If that's not familiar, don't worry. We'll explain everything you need to know.

Next: Computing the distance to the moon

Moon hint:

The line between the light and dark halves of the uneclipsed moon is a circle (the lunar sphere sliced in half; that circle is traditionally called the terminator by astronomers), but we see that circle at a slant, and see only the half facing us. Do you know what mathematical curve an oblique circle is?)

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