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Re: Brahe -> Kepler -> Newton 'factoids' (fwd)



....problem is that Newton's work in gravitation relied on advanced knowledge
of geometric arcana not routinely stdied today. His mathematics was different
and Feynman (although he studied it) used different mathematics to recapitulate
this part of Newton's work. For a nice treatment of this, see

Goodstein & Goodstein (1996). Feynman's Lost Lecture: The motion of
planets around the sun. Norton:NY.
(nifty pix & a CD of the original lecture audio tape are included.)

The quote in the book is
[Feynman] goes on to say that he could not follow Newton's arguments
any further, and that he "cooked up" the rest of the demonstration
of the law of ellipses himself. p94

The "law of ellipses" is K1 (Kepler's 1st Law) and can be shown to be a
logical outcome of N1 + N2 + R^(-2) Grav Force. K3 (equal areas etc)
is trivial by comparison with either calc or geometry (see Ellis Knowles
paper in TPT a few years back for a derivation using ellipses).

Goodstein recaps both Newton's and Feynman's K1 derivations. Neither is
simple, though simple geometry is used. K3 on the other hand, is a great
intro derivation knowing any intro calculus and assuming ang mom (L)
conservation for ellipses and circles.

Dan M

Dan MacIsaac, Assistant Professor of Physics and Astronomy, Northern AZ Univ
danmac@nau.edu http://www.phy.nau.edu/~danmac

Ed Eckel wrote:

Zell writes:
As for knowing the historical development of Newton's mechanics, I'm far
from an expert, so I just did some reading in Feyman's lectures. Feynman
stated that Newton used Kepler's 2nd and 3rd laws to deduce (Feynman's
word) the law of gravitation. If Feynman's reading of history is
correct, K's laws, rather than being only an interesting stop in the
development of Newton's law of gravitation, were crucial to its
development. That being the case, would it not be useful for students to
be shown how Kepler's analyses of Brahe's observations were used by
Newton to deduce a physical model. Moreover, as the logic behind the
demonstration would loosely follow Newton's logic in deducing the law of
gravitation, would we not preserve the integrity of the experience for
the students?

I am interested in seeing a development of this 'history' into a unit
for a current classroom of, say, 10th graders in a first course with no
more than an Algebra 2 background. Understanding Brahe's observations
might be used to motivate kinematics, computer modeling of the data
might make a nice introduction to developing alternate representations
(what we see in the sky, what lists of numbers tell us, what graphs of
dependent/independent variables tell us, what closed forms tell us, what
color coded representations of data tell us, etc) and follow this with
interpreting and generalizing the resulting "Kepler's Laws" to the
"Newton's Laws".

Can one find Brahe's data online? And can someone point me toward a
useful history of Kepler/Newton in this regard?


An early attempt to develop a unit such as you have suggested is found
in the _Project Physics Course_, Holt, Rinehart, and Winston, 1970,
mostly in Unit 2 ("Motion in the Heavens"). I attended a Summer
Institute in Harvard Project Physics at the U. of Northern Colorado in
1973. I recall constructing the orbit of Mars by Kepler's method,
although I don't think Tyco Brahe's original data was used. The work of
Kepler was tied in with that of Newton in Chapter 8 of Unit 2 ("Unity of
Earth and Sky --the Work of Newton"). At the moment, I have access only
to the _Handbook_ containing experiments and observations, but not the
_Text_. (There was also a _Reader_ for each unit containing relevant
articles-- many of a historical nature). The _Handbook_ contains an
"Orbit" computer program, but being of early date, it was written in
FORTRAN. The mathematical level does not go beyond algebra, but there is
much graphical analysis. However, I found this unit to be the most
intellectually demanding of the course. I am not sure that these Project
Physics publications are still in print, but they should not be
difficult to locate. The _Project Physics Course_ seems to have
disappeared from the face of the Earth, judging from my attempts to
find it on the Internet. I think much of Unit 2 would be amenable to
more up-to-date computer techniques. Fairly recently, someone in the
PHYSHARE discussion group mentioned that Mars orbit materials were still
available from http://www.vwrsp.com, but I don't know if these are the
same as those used in _Project Physics_.

Hugh Logan