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)

▲

petsfed an hour ago | parent | next [-]

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?

▲

raincole 5 hours ago | parent | prev | next [-]

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?

▲

mr_mitm 4 hours ago | parent | next [-]

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.

▲

crisf an hour ago | parent | prev | next [-]

Each orbit is a spinning top. You pull on a top from the side, it's spin axis precesses.

▲

hammock 5 hours ago | parent | prev | next [-]

It’s an arbitrary plane, chosen at each moment just so you can flatten it

▲

raverbashing 5 hours ago | parent | prev [-]

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)

	▲	twnettytwo 5 hours ago \| parent [-]
		One of the necessary conditions here is that the three objects return to their exact initial position, and so does the centre of mass. Initial conditions with non-zero momentum must trivially be ruled out. But this doesn't stop them from having velocities perpendicular to the initial plane that cancel out perfectly, so this doesn't refute the assertion that the planes keep changing.

▲

nautilus12 2 hours ago | parent | prev [-]

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