>> 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?
> After giving them the factoids of Kepler's laws I simply *tell* them
>that the first and third laws were derived by Newton using the law of
>motion, the law of universal gravitation, and the calculus, all of which
>were his own inventions (oversimplifying a bit). Derivation of these
>results (not of the laws themselves - those are "received factoids")
>usually has to be postponed until the students' mathematical
>armamentarium has been considerablt enhanced. I like to introduce
>Kepler's laws very early in a science student's education.
>