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Re: Earth's shadow



At 10:34 -0700 10/3/02, John Mallinckrodt wrote:

To put this thread in context, note that Hewitt's discussion of the
Earth and Moon shadows is intended to explain Aristarchus' estimation
of the ratio of the size of the Earth to that of the Moon. Knowing
that the Earth's shadow tapers by (approximately) one Moon diameter
on the way to the Moon and that the remaining shadow is still 2.5
times the diameter of the Moon, it is trivial (if also clever) to
deduce that the Earth's diameter is about 3.5 times that of the Moon.

I think Hewitt may be fairly criticized for tossing off the remark
that the Earth's shadow tapers by the same amount as the Moon's both
because it isn't obvious and because it isn't even (quite) true.
Nevertheless, showing that the Earth's shadow tapers at *nearly* the
same rate as the Moon's is a pretty simple exercise in geometry. The
result is that the Earth's shadow tapers about 99.4% of the amount
that the Moon's shadow does.

In the old days (that is the time of Aristarchus and his pals), the
question was always "How big. . .?" "How far . . .?" "How many . .
.?" "What is it made of?" and the like. And those old guys found some
pretty clever ways to at least try to answer those questions, not
always with success. Now we pretty much know the answers to all those
questions, so the students, when they look in their book and see the
numbers that the ancients were mostly ignorant of all printed out
neatly in a table, just as if it were a copy of a telegram from God,
need to be asking the question "How do we know all this neat stuff?"
But, unfortunately, they have heard the numbers so often over the
years that they take our understanding of the universe now as
"received wisdom"--it really does come in the form of a telegram from
God (well, this is the modern era--maybe a FAX from God).

It is our job as physics and astronomy teachers to do our best to
infuse our students with a sense of awe at what we have accomplished.
Not just in recent technology, which wasn't even imagined by the
ancients, but in answering those questions that the ancients asked,
but could not, for the most part, answer with any degree of
confidence. When someone like Hewitt tosses off one of these clever
(even if trivial by current standards--these ideas are seldom trivial
to the first person to think them up) concepts without also pointing
out just what was done and why it may have been important in the
history of humankind, he does the students no service.

I note that Eratosthenes' measurement of the circumference of the
earth was first on the list of the "10 most beautiful experiments"
recently published. And rightly so. But it isn't obvious to students
who read daily about satellites orbiting the earth, people flying hot
air balloons around the earth, and other fairly routine things like
that, that achievements like that of Eratosthenes should be
celebrated as major steps in our understanding of the cosmos.

It is important that our students, if they get nothing more from our
courses, learn to not be afraid to ask "How do you know that?" when
confronted with some piece of scientific arcana. And when told how,
they need to appreciate what and how it was done enough to at least
be able to say "Wow!"

They need to know that God doesn't have a FAX machine.

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

Let's face it. People use a Mac because they want to, Windows because they
have to..
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This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.