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[Phys-L] diagram swindle +- Kepler's equal-area law



Hi --

An interesting questions recently landed on my desk. Something had been
vaguely bugging me ever since I was a sorcerer's apprentice, but I was
never able to explicitly articulate the problem until now.

It's not every day you get to pick a fight with both Richard Feynman and
Isaac Newton, but today it's my turn. I claim that the diagram used to
explain the equal-area law, which Feynman borrowed from Newton, is a
swindle. The proof is valid for polygons, but it has nothing to do with
actual planets unless you assume that the average force is well approximated
by the instantaneous force. The diagram is a swindle because it assumes
that is true for polygons, which is not only unproven, but provably untrue.

If you want to argue that the error goes away in the limit, fine, but
you have to actually make the argument. You can't just pretend the
error is zero in the non-limiting case.

A detailed writeup including lots of pretty pictures can be found at
http://www.av8n.com/physics/kepler-equal-areas.htm

There is link to the spreadsheet used to compute the figures. Some
folks on this list may be interested in the spreadsheet than anything
else. The method of computing the equal-area diagrams is not entirely
obvious, but it is easy enough if you know the trick.