canopus56 wrote:

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.

It sounds like you're saying that, for example, the sun is pulled to one
focus of an ellipse by the gravity of each planet. That's not right.

Mars's distance from the sun varies by 40 million kilometers, almost 30
solar diameters.

- Ernie http://home.comcast.net/~erniew