And also, there are no "attractor trajectories" either. That is, in a Hamiltonian system, there is no energy (or entropy) loss mechanism, so no trajectory can attract all nearby ones. However, in the solar system there are slight non-Hamiltonian effects (beyond merely Newton laws) such as tidal friction losses. It is only as a result of these, that certain "attractor" configurations, such as trojans, and also such as 2:1 resonances, tidal locking of Earth's moon (does not rotate) have happened. To return to the original problem -- which we now see is more interesting that I thought -- PUZZLE: find every configuration of N point masses, which (1) form a stationary configuration in rotating reference frame, and which (2) is stable. FACT 1: The N bodies must all lie in a single plane perpendicular to the rotation axis since otherwise could decrease energy by "flattening" configuration into said plane. FACT 2: My repaired proof, if no further problems spotted, shows N<=6. FACT 3: Requirement (1) is a set of polynomial equations which can be solved by Grobner basis, elimination, etc methods, but it might get pretty damn difficult especially if you are naive about it. Apparently Lagrange settled the "2 and a half bodies" problem (2 bodies, plus one more of negligible mass) but I do not think even the 3-body case has been done?