I had a couple thoughts on how you might get around Bertrand's Theorem, but I don't know if they would actually work. 1. Give up on central forces. Maybe inste

I had a couple thoughts on how you might get around Bertrand's Theorem, but I don't know if they would actually work. 1. Give up on central forces. Maybe instead of the particle being attracted to the position of another particle, it's to where that particle will be in 10 seconds if it maintains its current velocity, or to a point halfway between the two particles. No idea if something like that could result in a stable orbit, or what conditions would be required for that to happen. 2. Give up on rotational symmetry (which I believe Betrand's theorem implicitly requires, not positive). Have some defined "north" direction, and forces behave differently depending on how a particle is moving relative to it. 3. Maybe asymptotically stable orbits are enough for life, if they are very asymptotically stable.