Comment by btilly
5 hours ago
https://numericaltank.sjtu.edu.cn/three-body/three-body.htm shows that there are three dimensional solutions.
We have no observed examples in nature of three body equilibrium. But then again, all places we have looked are either influenced by the chaotic orbits around them of the Solar System, our surrounding galaxy, or nearby galaxies in a cluster.
There aren't a lot of orbiting three bodies without external gravitational influences disturbing them.
> There aren't a lot of orbiting three bodies without external gravitational influences disturbing them.
This is of course a relative statement. Every object affects every other object, subject to the limitations of lightspeed propagation of gravity waves through expanding space.
But as you point out, we still haven't noticed any examples that are stable short-term.
That depends on what you mean by stable short-term.
The Sun, Jupiter, and any small asteroid at L4 of L5 is, by itself, linearly stable. Meaning that any small perturbation will only grow linearly.
But, of course, this system interacts with Saturn. The arrangement of those three objects is still remarkably stable. But the interaction with Saturn makes for a chaotic system again.