Comment by nautilus12
9 hours ago
Is this assumed to be 2D? I was going to ask if there are any observed examples of 3 body equilibrium observed in nature.
9 hours ago
Is this assumed to be 2D? I was going to ask if there are any observed examples of 3 body equilibrium observed in nature.
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.
Yes. Because 3 points are coplanar, so every "3D problem" with 3 objects can be turned into a 2D problem on the correspondent plane
(of course in real life your plane would keep changing, and probably some other complicated math I can't think right now)
Put another way, while their positions are one set of 3 points, their momenta are another set of 3 points, and there is no requirement that 6 points will always lay on the same plane.
I wonder what phantom forces would appear when the reference frame changes in some complicated fashion. We get centrifugal "force" when we reconstruct F=dP/dt in a rotating reference frame, what would the 3-body "force" look like?
Why would the plane keep changing? If there are only these three objects, won't the vectors of their gravitational pull to each other all be on this plane too?
If you define the initial conditions such that their relative velocity is zero or parallel to the plane, yes. But that's not the case in general.
Each orbit is a spinning top. You pull on a top from the side, it's spin axis precesses.
It’s an arbitrary plane, chosen at each moment just so you can flatten it
Not from an external point of view, as you might have a momentum component perpendicular to that plane
(but yes I think you might be right if we're centered on the CG)
6 replies →
Oh makes perfect sense, do you have thoughts about real life examples? I did some research using AI and it said there were examples of restricted 3 body problems like the trojan asteroids, but no examples in real life similar to what is in this web app