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>> Moreover, with simplifying assumptions and some basic physics,
>>students can be shown how the 3rd law can be used to derive Newton's
>>law of gravitation.
>Well... Circular orbits around immovable force centers, I think you
>mean. In my opinion it would be deleterious to the students'
>intellectual development to hoodwink them into thinking that the law >of
gravitation can be derived, since of course it can't.
You read me correctly...I was assuming uniform circular planetary motion
and a familiarity on students' parts with 'centripetal acceleration =
speed squared over r.' Finally, perhaps I should have used 'deduced'
instead of 'derived'.
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?
That may be what Feynman says, but he is a physicist like us, and if
one uses physics textbooks as primary historical sources then perhaps
that story is correct (I don't recall reading that particular account).
I tell the following story for which, alas, I can give no primary
reference citation, but it has always appealed to me. Newton gives, in
his *Principia* (which I have read neither in its original Latin nor
in translation), a set of Rules for Reasoning in Natural Philosophy.
Among these rules is what has come to be called the Law of parsimony.
Again, from very faulty memory, this law goes something like "Nature
does not that by many [mechanisms] which may be done by few." Newton
applied this to the kinematics of the fall of a stone on Earth (not
the proverbial apple) and to one in the sky, the Moon, which he
conjected were impelled by the same force, Earth's gravity. Now the
orbit of the Moon was not very well characterized at the time Newton
did his calculation. The size of the orbit was inaccurate by
something like 10%. He calculated the acceleration of the Moon and
of the stone at Earth's surface and seized almost immediately on the
idea that the two were to each other inversely as the squares of their
distances from the center of the Earth This is an easy calculation to
carry out (numerically) for students, and that's what I do.
Application of Newton's second law and of the constancy of acceleration
due to gravity to this result leads to the Law of Universal Gravitation
which I capitalize because I think it is Newton's greatest triumph.
He didn't publish the result until much later, after more accurate
lunar distances had been measured, and after Edmund Halley badgered him
into doing so. By that time he had derived versions of Kepler's first
and third laws which were appropriate to the solar system.
Now I recount this version not to gainsay Feynman, but to more or less
agree with your point. I also tell my students that I am no historian,
and that when I tell them history my knowledge is not deep. What I have
related to them could well have happened as I said it did; in any event
the physics is right. I prefer it to your (Feynman's?) story because I
find it more believable. One really sees the inverse square law much
nearer the surface of the phenomena in the example of the "fall of
stones on the Earth and in the sky" than one does in the other case.
Historical integrity is questionable here, and I welcome instruction
from the group - accompanied by appropriate citation from *Principia*,
of course!
Leigh