In article , Brian Tung wrote:
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.

Yes, there is an intuitive reason: the orbits are ellipses with the
Sun at one of the foci because gravity follows an inverse-square law.
If gravity had varied in some other way, then the orbits would (usually)
not have been ellipses.

One example: if gravity would have been directly proportional to
distance (i.e. if gravity had *increased* with distance - we could
call this hypothetical case "rubber band gravity") the orbits would
have been ellipses too, but the Sun would have been at the *center*
of the ellipse, not at one of the foci of the ellipse. This case can
be simulated with a little ball attached to a stick with a very
elastic rubber band.

Another hypothetical case: if gravity would have varied as the inverse
*fifth* power of the distance, all orbits would have been spirals.
I.e. all planets would have either spiralled into the Sun or spiralled
out into space. Needless to say, a solar system would under such
circumstances become very short-lived.


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/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt


--
----------------------------------------------------------------
Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://stjarnhimlen.se/