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Re: Earth's shadow




Ken Fox is probably right about what Hewitt is trying to say. But I
don't get the point. And besides, it is not literally true. If the
earth were the same size as the sun, then the earth's shadow would not
taper at all. If the earth were the same size as the moon, then the
earth's shadow would be just like the moon's shadow and would taper by
one moon diameter over the earth-moon distance. In reality, the size of
the earth is between the size of the sun and the moon, so the earth's
shadow doesn't have zero taper, but it doesn't taper as fast as the
moon's either. Therefore it does not shrink by as much as a lunar
diameter over the earth-moon distance.

Actually since both the earth and the moon are small compared to the sun and
the distances from the sun are about the same, the amount of taper should be
approximately the same. The fact that the Earth's shadow tapers by one moon
diameter is not clearly applied. One has to then look at the relative sizes
of the earth and moon to see how big the shadow is at the moon. I presume
that is what one of the diagrams does. I suspect that these ideas are
totally lost on students, as are most ideas that are communicated
didactically.

If you want to do some really interesting things with light and shadow there
is a wonderful McDermott tutorial on the subject. It improves understanding
of geometric optics by quite a bit.

John M. Clement
Houston, TX

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.