Well, there seems to be a lower limit, yes. Something like between a third and an eighth of the diameter of an outer planet moon.<br /><br />What I have mostly been looking for in this project is signs of low-energy processes; gravitational capture, like Titan and Triton, or a slow-motion collision, like Miranda or Mimas. Some writers have remarked that they can't see how Mimas held together under the impact. My hypothesis is that the impactor was larger and much slower than that writer was thinking.<br /><br />Lagrange points L4 and L5 orbit the primary at almost the same distance as the secondary. As a result, when they get loose, they will approach the secondary right at escape velocity, plus whatever energy they absorbed when they escaped the Lagrange stability zone (which is not much. Remember, it's the <font color="yellow"><i><b>four</b></i><font color="white"> body problem).<br /><br />Capture into orbit is difficult for Lagrangians, but it is far, far, far less difficult than if the body came from some other place where it will have additional energy with respect to the secondary. I was really happy when Mike Brown found the lost moon of Triton. The energy Triton lost was imparted to Xena, which flung it way out there. But every silver lining has a cloud; when I simulated it, I couldn't get the orbital inclination. So now I have to hypothesize another unknown object to account for that (Nemesis). Fortunately there's other evidence for the newly hypothesised object (Buffy and the slain dinosaurs). At least Xena is no longer unknown.<br /><br />Notice that the pictures of the moons of the outer planets all show their most photogenic side. This one-sided view doesn't help much. Where can I find pictures of the other side of these objects?<br /><br />Thanks to Tony Dunn of GravitySimulator, I have been made aware of another 1:1 resonance, the "horseshoe" orbit. Such an orbit might result in only one object instead of two. But I think the evidence is pretty stro</font></font>