Gravitational capture occurs when one object enters a stable orbit around another (typically referring to natural orbits rather than orbit insertion of a spacecraft with an orbital maneuvers).

So saying it “is not possible” is verifiably wrong. The perceived rarity of gravitational capture is most likely just due to how empty space is, not the unlikelihood of stability.

On that note, I think you might want to do some math yourself. You seem to be laboring under the impression that there are limited or maybe only a single exact state of stability for systems like this. “You have to perfectly set the velocities and magnetic moments” I’m not sure about magnets but I am sure about gravitation, and you don’t need to be very precise at all.

If you know how to code I’d suggest you try simulating two bodies with random masses traveling at random velocities. You’ll see that many times they do swing apart and a few times they will directly collide but there is a wide range of stable orbits. Sure, if you wanted to get perfectly circular orbits, you’d need to be more precise, but circular orbits are not necessary at all. Most orbits are at least a little eccentric, and eccentric orbits are still stable orbits. Importantly, they can be created without precision.

Next, while binary systems are assumed to form during star formation as you assert, the quote I listed from Wikipedia says it is possible for binary systems to form via gravitational capture.

Anyway, since that wasn’t enough evidence for you I decided to find an example of a combination system. Fortunately I didn’t have to look very far.

Alpha Centauri (our nearest stellar neighbor and triple star system) is a specific example of stable combination. Rigil and Toliman are main sequence stars that likely formed the way you listed since they are very close together and roughly the same size with slightly more massive than the other.

However, Proxima Centauri is a red dwarf that orbits the two circumbinarily. It is .2 light years from the other two which means it is roughly 5% of the distance to us from the barycenter of Toliman and Rigil.

However, despite the distance, it is “gravitationally bound” to them and its orbit has a 30deg inclination relative to them. This out of plane motion, the large distance, and the eccentricity of its orbit, imply that Proxima Centauri did not form from in the ways you listed. It may have formed in the same nebula as the other two, but it also very possibly could have travelled before getting gravitationally captured. In either case, it was gravitationally captured by some means and has formed a stable system despite having an out of plane velocity.

Proxima Centauri even has circumstellar planets, and its small mass and large distance from the binary pair mean it very easily could be stolen from the system if another main sequence star passed closely by. So it’s a great example of this “bonding” I’ve described.

Now magnets. Your magnet analogy is not similar to these scenarios because electromagnetism is highly directional. I don’t think you’d be able to combine systems of spinning magnets in any stable configuration other than a straight (spinning) line of them. However—as shown by the Alpha Centauri system—it is very possible to form stable multistellar systems from the combination of two stable systems.

Lastly you are correct that there are many many differences between atoms and gravitational systems. I mean shit, we don’t even know how atoms really work. String theory and particle physics don’t play nice and there are many more theories for unifying relativity and quantum physics that would impact what the “true” internal structure of an atom is like.

However, as mentioned in my last comment, that is not the point! My point was simply that there are some similarities and that you could do certain things with them that would have chemistry analogues. Does that make sense? I’m not saying “these are the same” I’m saying “it might be possible to use these in some similar ways to atoms.” And I’ve now found proof it is possible because of this debate, but the point of my original comment was curiosity/discovery not debate.