John Schutkeker wrote:
"tt40" wrote in news:1129087625.368615.299390
@g47g2000cwa.googlegroups.com:


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.


What I've always wondered is whether it is possible to separate the
elliptical orbits into two components, the way elliptically polarized light
can be separated into counter-rotating beams of circularly polarized light.

What, for instance, remains of a low eccentricity orbit if the circular
orbit is subtracted?

To first order, what remains is an elliptical epicycle, centered on the
circular position. The radial excursion must be a*e, for the perihelion
distance is a(1-e) and the aphelion distance is a(1+e). The downtrack
excursion is twice this, because (again to first order) the true anomaly
f = M + 2e sin M (where M is the mean anomaly).

-- Bill Owen