Those rare collisions that take place will tend to have random results. Most commonly colliding bodies in a fairly elastic collision will depart each other at a considerable rate. Picture one of those lottery machines with the bouncing balls but no walls. Even if speed equalization were to take place you would need to show that takes place at a faster rate than dispersion. It isn't even close.
If you had a lottery ball entering a swarm of other lottery balls that were not moving, what are the odds that the ball could bounce off the other balls and exit the swarm? I suppose it could if it hit something near the outer edge, but if it made it into the inner part of the swarm, it would not "disperse"...it would become a part of that swarm.
It is far more likely that a collision will take place in which the incoming ball will not only bounce out of the "swarm" but will knock another ball (or balls) out of the swarm. Example, breaking the rack in billiards. By far, most of the trajectories for incoming objects will result in the breaking up of the swarm. Remember, these objects are not (yet) held together by gravity. Even if they are, it is pretty minimal. For even the largest, most massive, objects (a 50m diameter rock) a velocity difference of less than 0.647 m/sec (out of 11,200) is enough to prevent capture. That's 0.00058%.
Pi>>The (shotgun pellet) analogy is not only fair, it is ideal for Brown's "swarm." Do you have any reason to think the pellets would be drawn together by gravity if the shotgun were fired from the ISS during a space walk? How about if we sent a shotgun into space between Earth and Mars and fired it there .... do you think the pellets would be drawn together by gravity?>>
I would concede that in space, shotgun pellets could not be pulled together by their mutual gravity. The question is whether the analogy holds true when you scale it up.
First, a clarification. I've watched some high speed videos of shotguns. The shot leaves the barrel still surrounded by the wadding. This means separation of the shot does not begin until after the "swarm" of bb's has exited the muzzle.
Scaling up is a simple matter .... we can pick a distance, say 60 yards at 600 fps. For the shotgun, that means reaching the target would take 0.03 seconds. A difference of 0.00058% in velocity would mean a difference of a about 0.0124 inches (front to back). With the swarm starting out at a length of around one inch, that means it would still be within about 1.02 inches in distance (front to back) at 60 yards. I had also calculated an the angle of trajectory must be within about 0.001o. At 60 yards and assuming an initial barrel diameter of one inch, the pattern should spread no more than 0.04 inches in width at 60 yards. Most of the patterns I saw were 30 inches at 30 yards and up to 150 inches at 60 yards. In other words.... if the bb "swarm" from a shotgun were 50m rocks (which are exceedingly rare, according to you) they would need to be within 0.04 inches laterally and 0.02 inches longitudinally at 60 yards to have any chance of "capture." All of the videos I found were much more spread out than that.
Scaling up does not help.
Pi>>In the case of a shotgun, the pellets start out closely packed and are launched down a smooth bore tube at almost identical velocities. These are ideal conditions to keep a "swarm" together.<<
This would be true of any objects which are at 1 AU. If they are less than 1 AU, then eventually they would be accelerated enough (by solar forces) until they were at 1 AU and at the same speed.
All objects launched from Earth start at 1AU with an orbit that intersects their point of launch (with adjustment for perturbations). Solar forces will act on all objects as a function of their distance from the Sun, surface area, and mass. There is no equalizing aspect of solar forces that will cause them to settle in "at 1AU and at the same speed." Nor is there any equalizing aspect of those forces that will circularize their orbits at the asteroid belt.
Pi>>We've discussed the equalization of speeds that would be necessary. For even the largest rocks to be gravitationally bound requires speed within a fraction of a meter per second and trajectory within thousandths of a degree. Otherwise they just sail right past each other on divergent trajectories. Collisions will be increasingly rare over time as the launched material spreads out. >>
Those objects on the yellow line trajectory would be slowed until they were travelling the same speed and direction and at some point, as the swarm grew by random collisions of new objects, the gravity would take over to hold them together.
So your rebuttal consists of a drawing with arbitrary lines drawn on it to illustrate potential zones of capture.
OK... I will agree that there are trajectories that will miss entirely. There are trajectories in which an object will pass thru a "swarm." And there are trajectories that will result in some kind of capture. Those facts are not in dispute.
The point is that the ones that result in a capture are far fewer than those that will pass by or thru. In fact, in terms of collisions, there are far more trajectories that will knock an existing part of the swarm out than there are that will result in capture.
.... all I have time for right now..... I think I have one more "back" post of Indy's I really want to answer.....