Grrr. I hate correcting myself twice!!!
Posted by Natalie L. Smith on Mar 20, 2002 at 15:37
(65.194.128.59)Re: That old devil called gravity (Natalie L. Smith)
Ok. Even for ellipses, the speed, regardless of direction of the velocity vector, will still be dependant on the radius. (What can I say. It was late. sigh) However, this still doesn't mean the objects will be on the same path, seeing as an infinite number of different elliptical orbits could still satisfy the same position/velocity combination. So, their individual paths would still be independant. Every so often there comes a comet that has a brief position at the same radius of orbit as planet Earth. At that time it also has earth's speed. But, that doesn't mean we are moving any closer to the comet.
It is true that if two objects orbiting the same third object were at DIFFERENT radius', the object farther out would have an acceleration vector that would appear to be in the direction towards the closer-in body, vaguely mimicking mutual gravitational pull. However, that would mean that the inner body would have an acceleration vector that would be in the direction AWAY from the outer body, appearing as if it were some sort of repulsive force.
IMHO, I think you are spending a lot of time barking up an empty tree, but I certainly could be wrong. When you are famous, of course, I'll say I always knew you were onto something.