Re: Galileo and science teaching

"On Tue, 14 Aug 2007 08:19:02 +0100, in article
<Y6OdnWrCl6v3ylzbnZ2dnUVZ8silnZ2d@xxxxxx>, Mike Dworetsky stated..."

"TomS" <TomS_member@xxxxxxxxxxx> wrote in message
news:196924297.00012a5d.007.0001@xxxxxxxxxxxxxxxxxx
"On Sat, 11 Aug 2007 23:27:38 +0200, in article
<1i2pcj4.zdsblt1z10rnnN@xxxxxxxxxxxxxxxxx>, J. J. Lodder stated..."

TomS <TomS_member@xxxxxxxxxxx> wrote:

"On Sat, 11 Aug 2007 13:27:33 +0200, in article
<1i2odei.n1jqn9klcmnN@xxxxxxxxxxxxxxxxx>, J. J. Lodder stated..."

<bimms@xxxxxxxx> wrote:


No prizes for picking out the analogy.

You are trying to make a false analogy between Copernican astronomy
and evolution.

Only one teensy little problem. You see, Copernican astronomy made
precise mathematical predictions about planetary motion, that could
be
directly observed with mathematical precision.

None that Ptolemian astronomy couldn't make.
The superioriy of Copernicus was based only
on a thousand years of extra observation time.
[...snip...]

And Copernican astronomy made one prediction which was *not*
confirmed by observation. Not until centuries later, long after the
motion of the earth was universally accepted.

If the earth is in motion, relative to the "fixed stars", then one
should be able to observe that relative motion, known as "stellar
parallax". Stellar parallax, as it turns out, is far too small to have
been observable without telescopes, good telescopes, and it was
first observed only in 1838.

Copernicus couldn't, and didn't, predict
how large the parallax should be.
He, and others, like Tycho and Kepler, understood
that parallax was limited to what they called
'sub-lunary' phenomena.
They used simple techniques (with threads)
to establish that comets and supernovea are not sub-lunary.
Since no one doubted that the fixed stars were not sub-lunary
the absence of stellar parallax wasn't an argument against Copernicus.

I am puzzled by this.

I don't understand how, for example, Kepler could have calculated
the positions of Mars without taking into account the parallax
coming from the annual motion of the earth. Or why there would
be any annual parallax to account for, for the Moon or anything
else closer than the Moon.


I teach about how he did this in my solar system class. Kepler was able to
show how, using Copernican theory, you could determine the true sidereal
period of a planet from its observed synodic period. Thus to fix the orbit
of Mars you would pair observations taken from Earth exactly one sidereal
martian period apart. Earth would be in different positions because the
periods are different, but Earth's position could be determined from the
longitude of the Sun. Hence you could draw a triangle with the two Earth
positions and Mars at the vertices. Do this enough times for different
locations of Mars and you could literally draw a diagram of its orbit.

Kepler didn't need a parallax observation from Earth, but it did mean he had
to give all distances in terms of the astronomical unit, the mean Earth-Sun
distance.
[...snip...]

Thank you for that. It's a very elegant method, easy to understand, although,
of course, there had to be a lot of calculation involved. Without an insight
like this, the problem seems intractable. (I don't know why I've never seen
this method described before. I think it deserves mention in any history of
the era.)


--
---Tom S.
"... to call in a special or miraculous act of creation reduces every
conceivable world to accident."
Jacob Bronowski, in "American Scholar" v.43 (1974) page 400

.

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