We can reason about whether things are necessary or sufficient.
To be sufficient as a theory of (n-body) gravity, a theory of gravity must also describe superfluidic gravity in order to describe gravitational dynamics within e.g. Bose-Einstein condensate superfluids.
Newtonian mechanics are insufficient to describe gravity in superfluids like Bose-Einstein condensates: Newtonian numerical methods do not predict superfluidic gravity effects with low error. Newtonian numerical methods probably cannot predict superfluidic gravity effects with low error. New
The three-body problem as commonly depicted is an abstract math problem wherein other physical fields are not modeled: electrostatic forces are not modeled in the three-body gravity problem as a classical mechanics problem (a Newtonian numerical methods problem).
Were there to be, say, solar wind pushing a three-body system in the vacuum of very cold space containing superfluidic Helium at very low pressure, we would then recognize the need to model solar wind and thus fluids in order to predict the relative positions of n masses with gravity in real physical space after time t.
Is that changing the goal posts? When do ideal 3 point attractor systems exist in isolation outside of abstact mathematics using expensive HPC time?
We observe steady flows in attractor systems which all eventually decay to states with less relativistic motion per Newtonian inertia and the second law of thermodynamics.
But entropy always increases,, so could there be actual 3-body (or n-body) perpetual motion machines in space? Well, there's e.g. solar pressure and superfluidity in space and we model that with fluids: with curl and viscosity, and vortices.
And it is unknown which fluidic solutions the posted numerical n-body solutions must correspond to (if a theory of gravity is suffcient, and any of such solutions are ever experimentally confirmed)
If Newtonian mechanics is not sufficient to model gravity in superfluid systems like Bose-Einstein condensates and Helium in the cold of space, then Newtonian mechanics cannot predict all n-body gravity solutions.
Other intersections between fluids and gravity? Planes, rockets, gliders; for these we must model fluids in order to predict "lift" and "thrust" counter to gravity (which is a weak force).
We often model fluids with Bernoulli's and Navier-Stokes.
Which axioms of relative motion model fluids and gravity in order to actually predict an experimental outcome given initial parameters?
Gravity is observed to be downward at 9.8ms/2 at sea level at many points on Earth.
The relation between gravitational force and distance is an inverse square relation.
Gravity decreases with the square of the distance from the greatest local mass centroid; . The relative gravitational force between objects at twice the distance is 1/(2*2)=1/4 the strength.
Electromagnetic signal power also decreases with the square of the distance. We're familiar with cross sections of EM field lines from e.g. experiments with metal shavings on (electro)magnetic field lines: while the force potential between two points is just one real complex scalar, there's an apparently deterministic unchanging field between two magnetic poles given metal shavings and magnets. But in real experiments, shortwave radio waves in and out and we say it's due to atomospheric disturbance and atmospheres are also fluidic.
Models of relativistic effects of gravity demonstrate the degree to which mass warps space. We like to start with quantized space (a regular 3d grid) and then add objects with mass and velocity; with tabula rasa as a closed system in isolation.
Typically we fail to model other fields due to specialization and lack of time for unified model search (because our solutions are internally consistent with the axioms chosen for simulation). But as with all of physics, real problems occur in real space and "there is yet no known way to subtract the effects of other fields that aren't modeled".
What the chosen predictive axioms fail to model with sufficient predictive error is what we should be concerned with over enumerating additional solutions given a known insufficient model of gravity and other fields. There are various theories of Quantum Gravity (QG), Quantum Field Theory (QFT), and alternative theories of non-quantum gravity. A sufficient theory of quantum gravity must describe n-body gravity within Bose-Einstein Condensates and also quantum levitation.
Newtonian mechanics (classical mechanics) does not explain quantum levitation or quantum locking; which is observably demonstrated in this video of Quantum Levitation of a (nitrogen-chilled) disc on a track formed into a mobius strip: https://www.youtube.com/watch?v=Vxror-fnOL4 and this video https://www.youtube.com/watch?v=f2Z8HyojgLQ. Note that the disc does not level around its mass centroid like maglev trains; the disc retains its locked position independent of gravity until the disc approaches thermal equilibrium with the track as it absorbs thermal entropy.
Newtonian numerical methods do not predict quantum levitation n-body solutions.
A sufficient theory of superfluid quantum gravity must predict for example quantum levitation n-body problems, Bose-Einstein Condensate n-body problems, what we call the Bernoulli effect, and might need to be compatible with GR: General Relativity.
Is downward gravity relevant to modeling the relative motions of objects in free-fall without wind resistance (in a zero-g plane, for example)? What about in microgravity? How does the gravitational mass centroid of the n-body system initially rooted at a zero-gravity Lagrangian point change the centroid of the Lagrangian point? Such dynamics are not modeled with closed-system numerical methods.
To be sufficient as a theory of (n-body) gravity, a theory of gravity must also describe superfluidic gravity in order to describe gravitational dynamics within e.g. Bose-Einstein condensate superfluids.
Newtonian mechanics are insufficient to describe gravity in superfluids like Bose-Einstein condensates: Newtonian numerical methods do not predict superfluidic gravity effects with low error. Newtonian numerical methods probably cannot predict superfluidic gravity effects with low error. New
The three-body problem as commonly depicted is an abstract math problem wherein other physical fields are not modeled: electrostatic forces are not modeled in the three-body gravity problem as a classical mechanics problem (a Newtonian numerical methods problem). Were there to be, say, solar wind pushing a three-body system in the vacuum of very cold space containing superfluidic Helium at very low pressure, we would then recognize the need to model solar wind and thus fluids in order to predict the relative positions of n masses with gravity in real physical space after time t.
Is that changing the goal posts? When do ideal 3 point attractor systems exist in isolation outside of abstact mathematics using expensive HPC time?
We observe steady flows in attractor systems which all eventually decay to states with less relativistic motion per Newtonian inertia and the second law of thermodynamics.
But entropy always increases,, so could there be actual 3-body (or n-body) perpetual motion machines in space? Well, there's e.g. solar pressure and superfluidity in space and we model that with fluids: with curl and viscosity, and vortices.
And it is unknown which fluidic solutions the posted numerical n-body solutions must correspond to (if a theory of gravity is suffcient, and any of such solutions are ever experimentally confirmed)
One application of n-body gravity problems: "Gravitational Machines" (2023) https://news.ycombinator.com/item?id=36266570
If Newtonian mechanics is not sufficient to model gravity in superfluid systems like Bose-Einstein condensates and Helium in the cold of space, then Newtonian mechanics cannot predict all n-body gravity solutions.