tt40 wrote:
In everything I've read about planets and elliptical orbits, I can't
ever recall any author (Feynman, Newton, 'Ask an Astronomer' etc.),
explaining exactly 'why' the orbit is elliptical. Oh sure there's been
lots of mathematics to explain the orbit and how it works, but most of
the explanations don't provide a definitive statement as to why it IS
elliptical.

I'm afraid there *is* no intuitive reason why it's an ellipse. You have
to remember that a mathematical derivation is generally a rather terse
and compact description of "why" something is true. As Chris says, it's
difficult to translate that into English without losing precision. You
can do it, but then the English is much longer than the math.

Even so, the derivation of a simple fact like Newton's law of universal
gravitation leading to an elliptical orbit is fairly involved. If there
really were a simple and intuitive explanation why it's an ellipse, the
mathematics would be pretty short and straightforward. The fact that it
isn't reveals something deep about mathematics and celestial mechanics.
I think it's one of the most beautiful aspects of theoretical astronomy,
and a major reason why Newton's Principia Mathematica is considered the
crowning achievement of science.

--
Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
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