But why an elliptical orbit

Chris L Peterson wrote:
On Wed, 12 Oct 2005 12:13:25 GMT, (Paul Schlyter) wrote:
OK, time to answer your question: the orbit is a conic section (the
ellipse being the most common case) because gravity is inversely
proportional to the square of the distance to the gravitating body...
snip Perhaps that is a satisfying answer to somebody already
familiar with the mathematics behind orbital dynamics, but . . . I
doubt most people find it intuitive that an inverse square
gravity law naturally leads to elliptical orbits. . . .

I always thought it is was because gravitational attraction between two
bodies was the result of two force vectors, not one.

The second smaller body has an orbital speed (angular momentum)
combined with its mass. The causes the second smaller body to pull the
larger body slightly off-center. Conversely, the larger body generates
sufficient gravitational force to still hold the smaller orbiting body
in place. As a consequence, a smaller body and larger body always orbit
a common dynamical center, offset from the true gravitational center of
gravity of the larger body.

Although a true circular orbit is theoretically possible assuming an
idealized set of initial conditions, in practice any body perturbing a
two-body orbital system will distort the idealized two-body circular
orbit. Considering the age of solar system and the density of objects
in it, the likelihood of finding any solar system object that has not
be perturbed from a true circular orbit into an elliptical orbit seems
remote.

- Canopus56